Hyperbolic arc-(co)secant

Time bar (total: 7.2s)

analyze3.0ms (0%)

Memory
5.5MiB live, 5.5MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
0%0%50%0%0%50%0%3
33.3%12.5%25%0%0%62.5%0%4
60%18.7%12.5%0%0%68.7%0%5
77.8%21.9%6.2%0%0%71.8%0%6
88.2%23.4%3.1%0%0%73.4%0%7
93.9%24.2%1.6%0%0%74.2%0%8
96.9%24.6%0.8%0%0%74.6%0%9
98.4%24.8%0.4%0%0%74.8%0%10
99.2%24.9%0.2%0%0%74.9%0%11
99.6%24.9%0.1%0%0%74.9%0%12
Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.1s (14.6%)

Memory
15.9MiB live, 633.9MiB allocated
Samples
772.0ms8 256×0valid
2.0ms25×0invalid
Precisions
Click to see histograms. Total time spent on operations: 491.0ms
ival-div: 149.0ms (30.3% of total)
ival-log: 129.0ms (26.3% of total)
ival-sqrt: 79.0ms (16.1% of total)
ival-mult: 46.0ms (9.4% of total)
ival-sub: 40.0ms (8.1% of total)
ival-add: 34.0ms (6.9% of total)
ival-true: 6.0ms (1.2% of total)
exact: 4.0ms (0.8% of total)
ival-assert: 3.0ms (0.6% of total)
Bogosity

preprocess918.0ms (12.7%)

Memory
-123.1MiB live, 749.8MiB allocated
Algorithm
2×egg-herbie
Rules
28 400×accelerator-lowering-fma.f32
28 400×accelerator-lowering-fma.f64
3 690×*-lowering-*.f32
3 690×*-lowering-*.f64
2 256×+-lowering-+.f64
Iterations

Useful iterations: 14 (0.0ms)

IterNodesCost
01844
14240
27640
315640
426440
541440
663734
797234
8138934
9191934
10433834
11581834
12684834
13726034
14762834
15778434
0913
11713
22413
33213
44713
56713
611013
730313
858313
9116213
10210513
11384213
12482513
13518213
14551711
15577611
16585711
17606811
18698811
0804411
Stop Event
1×iter limit
1×node limit
1×node limit
Calls
Call 1
Inputs
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
Outputs
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))
Call 2
Inputs
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
(log (+ (/ 1 (neg x)) (/ (sqrt (- 1 (* (neg x) (neg x)))) (neg x))))
(neg (log (+ (/ 1 (neg x)) (/ (sqrt (- 1 (* (neg x) (neg x)))) (neg x)))))
Outputs
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
(log (/ (+ 1 (sqrt (- 1 (* x x)))) x))
(log (+ (/ 1 (neg x)) (/ (sqrt (- 1 (* (neg x) (neg x)))) (neg x))))
(log (/ (- -1 (sqrt (- 1 (* x x)))) x))
(neg (log (+ (/ 1 (neg x)) (/ (sqrt (- 1 (* (neg x) (neg x)))) (neg x)))))
(neg (log (/ (- -1 (sqrt (- 1 (* x x)))) x)))

explain138.0ms (1.9%)

Memory
-0.7MiB live, 237.4MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
00-0-#s(literal 1 binary64)
00-0-(/.f64 #s(literal 1 binary64) x)
00-0-(*.f64 x x)
00-0-(-.f64 #s(literal 1 binary64) (*.f64 x x))
00-0-(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
00-0-(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)
00-0-x
00-0-(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
Confusion
Predicted +Predicted -
+00
-0256
Precision
0/0
Recall
0/0
Confusion?
Predicted +Predicted MaybePredicted -
+000
-00256
Precision?
0/0
Recall?
0/0
Freqs
test
numberfreq
0256
Total Confusion?
Predicted +Predicted MaybePredicted -
+000
-001
Precision?
0/0
Recall?
0/0
Samples
58.0ms512×0valid
Compiler

Compiled 136 to 40 computations (70.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 28.0ms
ival-div: 7.0ms (25.4% of total)
ival-log: 6.0ms (21.7% of total)
ival-mult: 5.0ms (18.1% of total)
ival-sqrt: 4.0ms (14.5% of total)
ival-sub: 3.0ms (10.9% of total)
ival-add: 2.0ms (7.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory
1.1MiB live, 1.1MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify563.0ms (7.8%)

Memory
-29.4MiB live, 531.7MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)
✓cost-diff0
(/.f64 #s(literal 1 binary64) x)
✓cost-diff0
(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
✓cost-diff704
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
Rules
28 400×accelerator-lowering-fma.f32
28 400×accelerator-lowering-fma.f64
3 690×*-lowering-*.f32
3 690×*-lowering-*.f64
2 256×+-lowering-+.f64
Iterations

Useful iterations: 14 (0.0ms)

IterNodesCost
0952
11752
22452
33252
44752
56752
611052
730352
858352
9116252
10210552
11384252
12482552
13518252
14551748
15577648
16585748
17606848
18698848
0804448
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
(/ 1 x)
1
x
(/ (sqrt (- 1 (* x x))) x)
(sqrt (- 1 (* x x)))
(- 1 (* x x))
(* x x)
Outputs
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
(/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(/ (sqrt (- 1 (* x x))) x)
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)
(sqrt (- 1 (* x x)))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(- 1 (* x x))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* x x)
(*.f64 x x)

localize41.0ms (0.6%)

Memory
7.4MiB live, 46.0MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
✓accuracy100.0%
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
✓accuracy100.0%
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓accuracy100.0%
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)
Samples
20.0ms256×0valid
Compiler

Compiled 54 to 11 computations (79.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 13.0ms
ival-div: 4.0ms (30.9% of total)
ival-log: 3.0ms (23.2% of total)
ival-mult: 2.0ms (15.5% of total)
ival-sqrt: 2.0ms (15.5% of total)
ival-add: 1.0ms (7.7% of total)
ival-sub: 1.0ms (7.7% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory
10.0MiB live, 10.0MiB allocated
Counts
5 → 60
Calls
Call 1
Inputs
#<alt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))>
#<alt (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))>
#<alt (/ 1 x)>
#<alt (/ (sqrt (- 1 (* x x))) x)>
#<alt (sqrt (- 1 (* x x)))>
Outputs
#<alt (/ 2 x)>
#<alt (/ (+ 2 (* -1/2 (pow x 2))) x)>
#<alt (/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)>
#<alt (/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)>
#<alt (sqrt -1)>
#<alt (+ (sqrt -1) (/ 1 x))>
#<alt (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x)))>
#<alt (- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))>
#<alt (* -1 (sqrt -1))>
#<alt (+ (* -1 (sqrt -1)) (/ 1 x))>
#<alt (+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x)))>
#<alt (+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x)))>
#<alt (+ (log 2) (* -1 (log x)))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4))))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4))))>
#<alt (log (sqrt -1))>
#<alt (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1))))>
#<alt (- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3))))>
#<alt (- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))>
#<alt (log (* -1 (sqrt -1)))>
#<alt (- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))>
#<alt (+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)))>
#<alt (+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)))>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* -1/2 (pow x 2))) x)>
#<alt (/ (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)>
#<alt (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)>
#<alt (sqrt -1)>
#<alt (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))>
#<alt (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))>
#<alt (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))>
#<alt (* -1 (sqrt -1))>
#<alt (- (* -1 (sqrt -1)) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))>
#<alt (- (+ (* -1 (sqrt -1)) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))) (/ 1/2 (* (pow x 2) (sqrt -1))))>
#<alt (- (+ (* -1 (sqrt -1)) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))>
#<alt (* x (sqrt -1))>
#<alt (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))>
#<alt (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))>
#<alt (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))>
#<alt (* -1 (* x (sqrt -1)))>
#<alt (* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))>
#<alt (* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))>
#<alt (* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))>
Calls

15 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
1.0ms
x
@0
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
1.0ms
x
@-inf
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
1.0ms
x
@inf
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
0.0ms
x
@0
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))

rewrite303.0ms (4.2%)

Memory
6.5MiB live, 326.0MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
4 520×accelerator-lowering-fma.f32
4 520×accelerator-lowering-fma.f64
3 106×*-lowering-*.f32
3 106×*-lowering-*.f64
2 972×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0942
16242
261738
3757738
0833538
Stop Event
1×iter limit
1×node limit
Counts
5 → 321
Calls
Call 1
Inputs
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
(/ 1 x)
(/ (sqrt (- 1 (* x x))) x)
(sqrt (- 1 (* x x)))
Outputs
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
(+.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) (/.f64 #s(literal 1 binary64) x))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 x (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x) (*.f64 x x)))))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 x)))
(-.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) (/.f64 #s(literal -1 binary64) x))
(-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 x (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x) (*.f64 x x))))
(-.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 x x)) (/.f64 (-.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64)) x)) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (-.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64)) x)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
(fma.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) (/.f64 #s(literal 1 binary64) x))
(fma.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 x (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x) (*.f64 x x)))))
(fma.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x) (*.f64 x x)))))
(fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x)) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x) (*.f64 x x)))))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(fma.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 x)) (/.f64 #s(literal 1 binary64) x))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
(fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 x (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x) (*.f64 x x)))))
(fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) x) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (/.f64 #s(literal 1 binary64) x))
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(pow.f64 (exp.f64 (log1p.f64 (neg.f64 (*.f64 x x)))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(*.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) #s(literal -1 binary64))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (fma.f64 (neg.f64 x) (*.f64 x (*.f64 x x)) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 (neg.f64 x) (*.f64 x (*.f64 x x)) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (fma.f64 (neg.f64 x) (*.f64 x (*.f64 x x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64)))

simplify494.0ms (6.8%)

Memory
-13.6MiB live, 585.8MiB allocated
Algorithm
1×egg-herbie
Rules
17 138×accelerator-lowering-fma.f32
17 138×accelerator-lowering-fma.f64
3 282×*-lowering-*.f32
3 282×*-lowering-*.f64
2 100×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0155767
1409742
21098722
33202709
47969709
08467680
Stop Event
1×iter limit
1×node limit
Counts
60 → 60
Calls
Call 1
Inputs
(/ 2 x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)
(sqrt -1)
(+ (sqrt -1) (/ 1 x))
(+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x)))
(- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))
(* -1 (sqrt -1))
(+ (* -1 (sqrt -1)) (/ 1 x))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x)))
(+ (log 2) (* -1 (log x)))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4))))
(log (sqrt -1))
(+ (log (sqrt -1)) (/ 1 (* x (sqrt -1))))
(- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3))))
(- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))
(log (* -1 (sqrt -1)))
(- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ (+ 1 (* -1/2 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)
(sqrt -1)
(+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
(- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))
(- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))
(* -1 (sqrt -1))
(- (* -1 (sqrt -1)) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
(- (+ (* -1 (sqrt -1)) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))) (/ 1/2 (* (pow x 2) (sqrt -1))))
(- (+ (* -1 (sqrt -1)) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5))))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
Outputs
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x)
(/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)
(/.f64 (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)
(/.f64 (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/16 binary64) #s(literal -1/8 binary64))) #s(literal -1/2 binary64))) #s(literal 2 binary64)) x)
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 x))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x))
(+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x)))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))))))
(- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))
(+.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 x x))))
(* -1 (sqrt -1))
(neg.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (/ 1 x))
(-.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x)))
(-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64))))) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x)))
(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) (*.f64 x (sqrt.f64 #s(literal -1 binary64))))) (/.f64 #s(literal -1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (log 2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))
(-.f64 (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (log.f64 #s(literal 2 binary64))) (log.f64 x))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4))))
(-.f64 (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -3/32 binary64)) #s(literal -1/4 binary64))) (log.f64 #s(literal 2 binary64))) (log.f64 x))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4))))
(-.f64 (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -5/96 binary64) #s(literal -3/32 binary64))) #s(literal -1/4 binary64))) (log.f64 #s(literal 2 binary64))) (log.f64 x))
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ 1 (* x (sqrt -1))))
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3))))
(+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (log.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x (sqrt.f64 #s(literal -1 binary64))))))
(- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))
(+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (log.f64 (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (/.f64 #s(literal 3/40 binary64) (*.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))))
(log (* -1 (sqrt -1)))
(log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)))
(+.f64 (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x (sqrt.f64 #s(literal -1 binary64))))) (+.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64))))))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -3/40 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))))) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)
(/ (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)
(/.f64 (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)
(/.f64 (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/16 binary64) #s(literal -1/8 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64)))))
(- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 x x)))
(- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))
(+.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 x x))) (/.f64 #s(literal 1/16 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 x #s(literal 6 binary64)))))
(* -1 (sqrt -1))
(neg.f64 (sqrt.f64 #s(literal -1 binary64)))
(- (* -1 (sqrt -1)) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
(-.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64)))
(- (+ (* -1 (sqrt -1)) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))) (/ 1/2 (* (pow x 2) (sqrt -1))))
(-.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)))
(- (+ (* -1 (sqrt -1)) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5))))))
(+.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1/16 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 x #s(literal 6 binary64)))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/16 binary64) #s(literal -1/8 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* x (sqrt -1))
(*.f64 x (sqrt.f64 #s(literal -1 binary64)))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(fma.f64 x (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(fma.f64 x (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x (*.f64 x (*.f64 x x)))))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(fma.f64 x (+.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x (*.f64 x (*.f64 x x))))))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (neg.f64 x))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(fma.f64 x (-.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x (*.f64 x (*.f64 x x))))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
(fma.f64 x (+.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x (*.f64 x (*.f64 x x))))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1/16 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 x #s(literal 6 binary64))))) (/.f64 #s(literal -1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))

eval63.0ms (0.9%)

Memory
27.6MiB live, 64.9MiB allocated
Compiler

Compiled 10 129 to 1 257 computations (87.6% saved)

prune61.0ms (0.8%)

Memory
-23.4MiB live, 93.5MiB allocated
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New3774381
Fresh000
Picked101
Done000
Total3784382
Accuracy
100.0%
Counts
382 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.4%
(log.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x))
▶100.0%
(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))
▶98.9%
(log.f64 (/.f64 #s(literal 2 binary64) x))
▶0.0%
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
Compiler

Compiled 31 to 23 computations (25.8% saved)

simplify372.0ms (5.1%)

Memory
28.7MiB live, 385.6MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 x #s(literal -1/2 binary64))
✓cost-diff0
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
✓cost-diff0
(log.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x))
✓cost-diff320
(/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x)
✓cost-diff0
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓cost-diff0
(+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
✓cost-diff0
(/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x)
✓cost-diff0
(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))
✓cost-diff0
(/.f64 #s(literal 2 binary64) x)
✓cost-diff0
(log.f64 (/.f64 #s(literal 2 binary64) x))
✓cost-diff0
(sqrt.f64 #s(literal -1 binary64))
✓cost-diff0
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
Rules
10 628×accelerator-lowering-fma.f32
10 628×accelerator-lowering-fma.f64
2 680×*-lowering-*.f32
2 680×*-lowering-*.f64
2 456×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02092
13292
23992
34792
46292
58292
612592
732492
860992
9120592
10226192
11334892
12443288
13609088
0825985
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(log (sqrt -1))
(sqrt -1)
-1
(log (/ 2 x))
(/ 2 x)
2
x
(log (/ (+ 1 (sqrt (- 1 (* x x)))) x))
(/ (+ 1 (sqrt (- 1 (* x x)))) x)
(+ 1 (sqrt (- 1 (* x x))))
1
(sqrt (- 1 (* x x)))
(- 1 (* x x))
(* x x)
x
(log (/ (+ (* x (* x -1/2)) 2) x))
(/ (+ (* x (* x -1/2)) 2) x)
(+ (* x (* x -1/2)) 2)
x
(* x -1/2)
-1/2
2
Outputs
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
-1
#s(literal -1 binary64)
(log (/ 2 x))
(log.f64 (/.f64 #s(literal 2 binary64) x))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
2
#s(literal 2 binary64)
x
(log (/ (+ 1 (sqrt (- 1 (* x x)))) x))
(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))
(/ (+ 1 (sqrt (- 1 (* x x)))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x)
(+ 1 (sqrt (- 1 (* x x))))
(+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
1
#s(literal 1 binary64)
(sqrt (- 1 (* x x)))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(- 1 (* x x))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* x x)
(*.f64 x x)
x
(log (/ (+ (* x (* x -1/2)) 2) x))
(log.f64 (fma.f64 x #s(literal -1/2 binary64) (/.f64 #s(literal 2 binary64) x)))
(/ (+ (* x (* x -1/2)) 2) x)
(fma.f64 x #s(literal -1/2 binary64) (/.f64 #s(literal 2 binary64) x))
(+ (* x (* x -1/2)) 2)
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
x
(* x -1/2)
(*.f64 x #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
2
#s(literal 2 binary64)

localize96.0ms (1.3%)

Memory
10.8MiB live, 86.7MiB allocated
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
✓accuracy100.0%
(/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x)
✓accuracy100.0%
(*.f64 x #s(literal -1/2 binary64))
✓accuracy100.0%
(log.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x))
✓accuracy100.0%
(+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
✓accuracy100.0%
(*.f64 x x)
✓accuracy100.0%
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓accuracy100.0%
(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))
✓accuracy100.0%
(/.f64 #s(literal 2 binary64) x)
✓accuracy100.0%
(log.f64 (/.f64 #s(literal 2 binary64) x))
✓accuracy100.0%
(sqrt.f64 #s(literal -1 binary64))
✓accuracy100.0%
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
Samples
74.0ms256×0invalid
Compiler

Compiled 91 to 22 computations (75.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 62.0ms
ival-mult: 39.0ms (63.2% of total)
ival-log: 10.0ms (16.2% of total)
ival-div: 5.0ms (8.1% of total)
ival-sqrt: 4.0ms (6.5% of total)
ival-add: 2.0ms (3.2% of total)
ival-sub: 1.0ms (1.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series188.0ms (2.6%)

Memory
3.1MiB live, 81.9MiB allocated
Counts
13 → 132
Calls
Call 1
Inputs
#<alt (log (sqrt -1))>
#<alt (sqrt -1)>
#<alt (log (/ 2 x))>
#<alt (/ 2 x)>
#<alt (log (/ (+ 1 (sqrt (- 1 (* x x)))) x))>
#<alt (/ (+ 1 (sqrt (- 1 (* x x)))) x)>
#<alt (+ 1 (sqrt (- 1 (* x x))))>
#<alt (sqrt (- 1 (* x x)))>
#<alt (/ (+ (* x (* x -1/2)) 2) x)>
#<alt (log (/ (+ (* x (* x -1/2)) 2) x))>
#<alt (+ (* x (* x -1/2)) 2)>
#<alt (* x -1/2)>
#<alt (* x x)>
Outputs
#<alt (+ (log 2) (* -1 (log x)))>
#<alt (+ (log 2) (* -1 (log x)))>
#<alt (+ (log 2) (* -1 (log x)))>
#<alt (+ (log 2) (* -1 (log x)))>
#<alt (+ (log 2) (log (/ 1 x)))>
#<alt (+ (log 2) (log (/ 1 x)))>
#<alt (+ (log 2) (log (/ 1 x)))>
#<alt (+ (log 2) (log (/ 1 x)))>
#<alt (+ (log -2) (log (/ -1 x)))>
#<alt (+ (log -2) (log (/ -1 x)))>
#<alt (+ (log -2) (log (/ -1 x)))>
#<alt (+ (log -2) (log (/ -1 x)))>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (+ (log 2) (* -1 (log x)))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4))))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4))))>
#<alt (log (sqrt -1))>
#<alt (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1))))>
#<alt (- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3))))>
#<alt (- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))>
#<alt (log (* -1 (sqrt -1)))>
#<alt (- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))>
#<alt (+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)))>
#<alt (+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)))>
#<alt (/ 2 x)>
#<alt (/ (+ 2 (* -1/2 (pow x 2))) x)>
#<alt (/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)>
#<alt (/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)>
#<alt (sqrt -1)>
#<alt (+ (sqrt -1) (/ 1 x))>
#<alt (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x)))>
#<alt (- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))>
#<alt (* -1 (sqrt -1))>
#<alt (+ (* -1 (sqrt -1)) (/ 1 x))>
#<alt (+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x)))>
#<alt (+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x)))>
#<alt 2>
#<alt (+ 2 (* -1/2 (pow x 2)))>
#<alt (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))>
#<alt (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))>
#<alt (* x (sqrt -1))>
#<alt (* x (+ (sqrt -1) (/ 1 x)))>
#<alt (* x (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x))))>
#<alt (* x (- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))>
#<alt (* -1 (* x (sqrt -1)))>
#<alt (* -1 (* x (- (sqrt -1) (/ 1 x))))>
#<alt (* -1 (* x (+ (sqrt -1) (* -1 (/ (- 1 (* 1/2 (/ 1 (* x (sqrt -1))))) x)))))>
#<alt (* -1 (* x (+ (sqrt -1) (* -1 (/ (+ 1 (* -1 (/ (- (* 1/2 (/ 1 (sqrt -1))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x))) x)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))>
#<alt (* x (sqrt -1))>
#<alt (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))>
#<alt (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))>
#<alt (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))>
#<alt (* -1 (* x (sqrt -1)))>
#<alt (* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))>
#<alt (* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))>
#<alt (* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))>
#<alt (/ 2 x)>
#<alt (/ (+ 2 (* -1/2 (pow x 2))) x)>
#<alt (/ (+ 2 (* -1/2 (pow x 2))) x)>
#<alt (/ (+ 2 (* -1/2 (pow x 2))) x)>
#<alt (* -1/2 x)>
#<alt (* x (- (* 2 (/ 1 (pow x 2))) 1/2))>
#<alt (* x (- (* 2 (/ 1 (pow x 2))) 1/2))>
#<alt (* x (- (* 2 (/ 1 (pow x 2))) 1/2))>
#<alt (* -1/2 x)>
#<alt (* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))>
#<alt (+ (log 2) (* -1 (log x)))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -1/32 (pow x 2)) 1/4))))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -1/192 (pow x 2)) 1/32)) 1/4))))>
#<alt (+ (log -1/2) (* -1 (log (/ 1 x))))>
#<alt (- (+ (log -1/2) (* -1 (log (/ 1 x)))) (* 4 (/ 1 (pow x 2))))>
#<alt (+ (log -1/2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 4 (* 8 (/ 1 (pow x 2)))) (pow x 2)))))>
#<alt (- (+ (log -1/2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 8 (* 64/3 (/ 1 (pow x 2)))) (pow x 4))))) (* 4 (/ 1 (pow x 2))))>
#<alt (+ (log 1/2) (* -1 (log (/ -1 x))))>
#<alt (- (+ (log 1/2) (* -1 (log (/ -1 x)))) (* 4 (/ 1 (pow x 2))))>
#<alt (+ (log 1/2) (+ (* -1 (log (/ -1 x))) (* -1 (/ (+ 4 (* 8 (/ 1 (pow x 2)))) (pow x 2)))))>
#<alt (- (+ (log 1/2) (+ (* -1 (log (/ -1 x))) (* -1 (/ (+ 8 (* 64/3 (/ 1 (pow x 2)))) (pow x 4))))) (* 4 (/ 1 (pow x 2))))>
#<alt 2>
#<alt (+ 2 (* -1/2 (pow x 2)))>
#<alt (+ 2 (* -1/2 (pow x 2)))>
#<alt (+ 2 (* -1/2 (pow x 2)))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))>
#<alt (* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))>
#<alt (* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))>
#<alt (* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))>
#<alt (* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
Calls

33 calls:

TimeVariablePointExpression
136.0ms
x
@inf
(log (/ 2 x))
28.0ms
x
@0
(log (/ 2 x))
18.0ms
x
@-inf
(log (/ 2 x))
1.0ms
x
@inf
(/ (+ (* x (* x -1/2)) 2) x)
0.0ms
x
@inf
(log (/ (+ (* x (* x -1/2)) 2) x))

rewrite462.0ms (6.4%)

Memory
-32.8MiB live, 567.6MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
5 416×accelerator-lowering-fma.f32
5 416×accelerator-lowering-fma.f64
3 510×*-lowering-*.f32
3 510×*-lowering-*.f64
2 924×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02079
19779
267879
3678879
0916975
Stop Event
1×iter limit
1×node limit
Counts
13 → 759
Calls
Call 1
Inputs
(log (sqrt -1))
(sqrt -1)
(log (/ 2 x))
(/ 2 x)
(log (/ (+ 1 (sqrt (- 1 (* x x)))) x))
(/ (+ 1 (sqrt (- 1 (* x x)))) x)
(+ 1 (sqrt (- 1 (* x x))))
(sqrt (- 1 (* x x)))
(/ (+ (* x (* x -1/2)) 2) x)
(log (/ (+ (* x (* x -1/2)) 2) x))
(+ (* x (* x -1/2)) 2)
(* x -1/2)
(* x x)
Outputs
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+.f64 (log.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64))) (log.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64))))
(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal -1 binary64)))
(*.f64 (log.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal -1 binary64))))
(sqrt.f64 #s(literal -1 binary64))
(pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))
(pow.f64 #s(literal 1 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)))
(log.f64 (/.f64 #s(literal 2 binary64) x))
(+.f64 (neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 0 binary64))
(+.f64 (log.f64 #s(literal 2 binary64)) (neg.f64 (log.f64 x)))
(+.f64 #s(literal 0 binary64) (neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64)))))
(+.f64 (log.f64 #s(literal -2 binary64)) (neg.f64 (log.f64 (neg.f64 x))))
(+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -2 binary64) x)))
(+.f64 (neg.f64 (log.f64 x)) (log.f64 #s(literal 2 binary64)))
(+.f64 (neg.f64 (log.f64 (neg.f64 x))) (log.f64 #s(literal -2 binary64)))
(+.f64 (log.f64 (pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal -1/2 binary64))) (log.f64 (pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal -1/2 binary64))))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(-.f64 #s(literal 0 binary64) (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(-.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (neg.f64 x)))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (*.f64 x #s(literal -1/2 binary64))))
(-.f64 (neg.f64 (log.f64 x)) (log.f64 #s(literal 1/2 binary64)))
(-.f64 (/.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 (log.f64 x) (log.f64 (*.f64 #s(literal 2 binary64) x)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (fma.f64 (log.f64 x) (log.f64 (*.f64 #s(literal 2 binary64) x)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))))
(-.f64 (/.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) x))) (/.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) x))))
(fma.f64 #s(literal -1 binary64) (log.f64 x) (log.f64 #s(literal 2 binary64)))
(fma.f64 #s(literal -1 binary64) (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 0 binary64))
(fma.f64 (-.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (log.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (log.f64 x) (log.f64 (*.f64 #s(literal 2 binary64) x)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) x)) (neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))) (/.f64 #s(literal 1 binary64) (log.f64 (*.f64 #s(literal 2 binary64) x))) #s(literal 0 binary64))
(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (log.f64 x) (log.f64 (*.f64 #s(literal 2 binary64) x)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))) (-.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (log.f64 x) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) x)) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) x)) (neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64)))))))
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(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1/64 binary64) #s(literal -64 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64)) #s(literal 4 binary64)))) (fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) #s(literal -8 binary64)))
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1/64 binary64) #s(literal -64 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal 2 binary64)))) (fma.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/16 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal 16 binary64))))
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/16 binary64) #s(literal -16 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal 2 binary64)))) (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) #s(literal 4 binary64)))
(pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal -2 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal -2 binary64)))
(*.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(*.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) #s(literal 8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64)) #s(literal 4 binary64))))
(*.f64 (fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) #s(literal 8 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1 binary64)))
(*.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -4 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal 2 binary64))))
(*.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -4 binary64)) (*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal 2 binary64))) #s(literal 1 binary64)))
(*.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) #s(literal 8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64)) #s(literal 4 binary64)))))
(*.f64 (neg.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) #s(literal 8 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal 2 binary64))) (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -4 binary64)))
(*.f64 (-.f64 #s(literal 4 binary64) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/4 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -4 binary64)) (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -4 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(*.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) #s(literal 8 binary64)) (fma.f64 (fma.f64 x x #s(literal 4 binary64)) (*.f64 (fma.f64 x x #s(literal 4 binary64)) (fma.f64 x x #s(literal 4 binary64))) (*.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1/64 binary64)))) (fma.f64 (fma.f64 x x #s(literal 4 binary64)) (-.f64 (fma.f64 x x #s(literal 4 binary64)) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/4 binary64))))) (*.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/16 binary64))))
(*.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) #s(literal 8 binary64)) (*.f64 (fma.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64)) #s(literal 4 binary64)) (-.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/4 binary64)))) (fma.f64 x x #s(literal 4 binary64))))) (-.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/4 binary64)))) (fma.f64 x x #s(literal 4 binary64))))
(*.f64 (/.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -4 binary64)) (fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) #s(literal -8 binary64))) (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) (fma.f64 x (neg.f64 x) #s(literal 4 binary64))))
(-.f64 #s(literal 0 binary64) (*.f64 x #s(literal 1/2 binary64)))
(neg.f64 (*.f64 x #s(literal 1/2 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) x))
(/.f64 x #s(literal -2 binary64))
(/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) x)))
(/.f64 (neg.f64 x) #s(literal 2 binary64))
(*.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 (neg.f64 x) #s(literal 1/2 binary64))
(+.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))
(+.f64 #s(literal 0 binary64) (*.f64 x x))
(+.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))
(+.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))))
(+.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))) (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 x x #s(literal 1 binary64))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 0 binary64) (*.f64 x (neg.f64 x)))
(-.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64))) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (*.f64 x x))) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (-.f64 #s(literal 2 binary64) (*.f64 x x))))
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) #s(literal 1 binary64))
(fma.f64 (fma.f64 (*.f64 x x) (neg.f64 (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))) #s(literal 1 binary64))
(fma.f64 (fma.f64 (*.f64 x x) (*.f64 x (neg.f64 x)) #s(literal 1 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64))
(fma.f64 (neg.f64 (fma.f64 (*.f64 x x) (neg.f64 (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))
(fma.f64 (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))
(fma.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64))
(fma.f64 (*.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) #s(literal 1 binary64))
(neg.f64 (*.f64 x (neg.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 2 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x x))))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (-.f64 #s(literal 2 binary64) (*.f64 x x)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))))) #s(literal 1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) #s(literal 1 binary64)) (-.f64 #s(literal 2 binary64) (*.f64 x x)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (neg.f64 (-.f64 #s(literal 2 binary64) (*.f64 x x))))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (*.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (-.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 #s(literal -1 binary64) (*.f64 x (neg.f64 x)))
(*.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(*.f64 x x)
(*.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 (*.f64 x #s(literal -1/2 binary64)) (neg.f64 (*.f64 #s(literal 2 binary64) x)))
(*.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) #s(literal -2 binary64))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 #s(literal -2 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))
(*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 2 binary64) x))
(*.f64 (*.f64 x (neg.f64 x)) #s(literal -1 binary64))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64))))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (*.f64 x x))))
(*.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))

simplify452.0ms (6.3%)

Memory
24.0MiB live, 614.6MiB allocated
Algorithm
1×egg-herbie
Rules
15 700×accelerator-lowering-fma.f32
15 700×accelerator-lowering-fma.f64
3 714×+-lowering-+.f64
3 714×+-lowering-+.f32
3 370×*-lowering-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02281244
16261187
217171152
349051136
083981084
Stop Event
1×iter limit
1×node limit
Counts
132 → 132
Calls
Call 1
Inputs
(+ (log 2) (* -1 (log x)))
(+ (log 2) (* -1 (log x)))
(+ (log 2) (* -1 (log x)))
(+ (log 2) (* -1 (log x)))
(+ (log 2) (log (/ 1 x)))
(+ (log 2) (log (/ 1 x)))
(+ (log 2) (log (/ 1 x)))
(+ (log 2) (log (/ 1 x)))
(+ (log -2) (log (/ -1 x)))
(+ (log -2) (log (/ -1 x)))
(+ (log -2) (log (/ -1 x)))
(+ (log -2) (log (/ -1 x)))
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(+ (log 2) (* -1 (log x)))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4))))
(log (sqrt -1))
(+ (log (sqrt -1)) (/ 1 (* x (sqrt -1))))
(- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3))))
(- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))
(log (* -1 (sqrt -1)))
(- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)))
(/ 2 x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)
(sqrt -1)
(+ (sqrt -1) (/ 1 x))
(+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x)))
(- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))
(* -1 (sqrt -1))
(+ (* -1 (sqrt -1)) (/ 1 x))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x)))
2
(+ 2 (* -1/2 (pow x 2)))
(+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(* x (sqrt -1))
(* x (+ (sqrt -1) (/ 1 x)))
(* x (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x))))
(* x (- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (sqrt -1)))
(* -1 (* x (- (sqrt -1) (/ 1 x))))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (- 1 (* 1/2 (/ 1 (* x (sqrt -1))))) x)))))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ 1 (* -1 (/ (- (* 1/2 (/ 1 (sqrt -1))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x))) x)))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
(/ 2 x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(* -1/2 x)
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(* -1/2 x)
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(+ (log 2) (* -1 (log x)))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -1/32 (pow x 2)) 1/4))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -1/192 (pow x 2)) 1/32)) 1/4))))
(+ (log -1/2) (* -1 (log (/ 1 x))))
(- (+ (log -1/2) (* -1 (log (/ 1 x)))) (* 4 (/ 1 (pow x 2))))
(+ (log -1/2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 4 (* 8 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log -1/2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 8 (* 64/3 (/ 1 (pow x 2)))) (pow x 4))))) (* 4 (/ 1 (pow x 2))))
(+ (log 1/2) (* -1 (log (/ -1 x))))
(- (+ (log 1/2) (* -1 (log (/ -1 x)))) (* 4 (/ 1 (pow x 2))))
(+ (log 1/2) (+ (* -1 (log (/ -1 x))) (* -1 (/ (+ 4 (* 8 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 1/2) (+ (* -1 (log (/ -1 x))) (* -1 (/ (+ 8 (* 64/3 (/ 1 (pow x 2)))) (pow x 4))))) (* 4 (/ 1 (pow x 2))))
2
(+ 2 (* -1/2 (pow x 2)))
(+ 2 (* -1/2 (pow x 2)))
(+ 2 (* -1/2 (pow x 2)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
Outputs
(+ (log 2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (log (/ 1 x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (log (/ 1 x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (log (/ 1 x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (log (/ 1 x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log -2) (log (/ -1 x)))
(-.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (neg.f64 x)))
(+ (log -2) (log (/ -1 x)))
(-.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (neg.f64 x)))
(+ (log -2) (log (/ -1 x)))
(-.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (neg.f64 x)))
(+ (log -2) (log (/ -1 x)))
(-.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (neg.f64 x)))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(+ (log 2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))
(-.f64 (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (log.f64 #s(literal 2 binary64))) (log.f64 x))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4))))
(-.f64 (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -3/32 binary64)) #s(literal -1/4 binary64))) (log.f64 #s(literal 2 binary64))) (log.f64 x))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4))))
(-.f64 (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -5/96 binary64) #s(literal -3/32 binary64))) #s(literal -1/4 binary64))) (log.f64 #s(literal 2 binary64))) (log.f64 x))
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ 1 (* x (sqrt -1))))
(+.f64 (log.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3))))
(+.f64 (log.f64 (sqrt.f64 #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))))
(- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))
(+.f64 (log.f64 (sqrt.f64 #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 3/40 binary64) (*.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x (sqrt.f64 #s(literal -1 binary64))))))))
(log (* -1 (sqrt -1)))
(log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x (sqrt.f64 #s(literal -1 binary64))))) (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64))))))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (sqrt.f64 #s(literal -1 binary64))))) (-.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 3/40 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))))) x))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x)
(/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)
(/.f64 (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)
(/.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/16 binary64)) #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) x)
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 x))
(+.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x)))
(+.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (sqrt.f64 #s(literal -1 binary64))))))
(- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))
(+.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (sqrt.f64 #s(literal -1 binary64))))) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))))))
(* -1 (sqrt -1))
(neg.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (/ 1 x))
(-.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x)))
(-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64))))) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x)))
(-.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 x #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) #s(literal 1 binary64)) x) (sqrt.f64 #s(literal -1 binary64)))
2
#s(literal 2 binary64)
(+ 2 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/16 binary64)) #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(* x (sqrt -1))
(*.f64 x (sqrt.f64 #s(literal -1 binary64)))
(* x (+ (sqrt -1) (/ 1 x)))
(fma.f64 x (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64))
(* x (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x))))
(+.f64 #s(literal 1 binary64) (fma.f64 x (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64))))))
(* x (- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(+.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64))))))
(* -1 (* x (sqrt -1)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* x (- (sqrt -1) (/ 1 x))))
(-.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (- 1 (* 1/2 (/ 1 (* x (sqrt -1))))) x)))))
(+.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ 1 (* -1 (/ (- (* 1/2 (/ 1 (sqrt -1))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x))) x)))))
(-.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 x #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 #s(literal -1 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/16 binary64)) #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* x (sqrt -1))
(*.f64 x (sqrt.f64 #s(literal -1 binary64)))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(fma.f64 x (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(fma.f64 x (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(fma.f64 x (+.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (sqrt -1)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(fma.f64 x (-.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
(fma.f64 (neg.f64 x) (+.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))))) (/.f64 #s(literal -1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x)
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(*.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(*.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(*.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(*.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(*.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(*.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))
(+ (log 2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))
(-.f64 (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (log.f64 #s(literal 2 binary64))) (log.f64 x))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -1/32 (pow x 2)) 1/4))))
(-.f64 (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/32 binary64)) #s(literal -1/4 binary64)) (log.f64 #s(literal 2 binary64))) (log.f64 x))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -1/192 (pow x 2)) 1/32)) 1/4))))
(-.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/192 binary64)) #s(literal -1/32 binary64)) #s(literal -1/4 binary64))) (log.f64 #s(literal 2 binary64))) (log.f64 x))
(+ (log -1/2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 x))
(- (+ (log -1/2) (* -1 (log (/ 1 x)))) (* 4 (/ 1 (pow x 2))))
(+.f64 (log.f64 #s(literal -1/2 binary64)) (+.f64 (log.f64 x) (/.f64 #s(literal -4 binary64) (*.f64 x x))))
(+ (log -1/2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 4 (* 8 (/ 1 (pow x 2)))) (pow x 2)))))
(+.f64 (log.f64 #s(literal -1/2 binary64)) (-.f64 (log.f64 x) (/.f64 (+.f64 #s(literal 4 binary64) (/.f64 #s(literal 8 binary64) (*.f64 x x))) (*.f64 x x))))
(- (+ (log -1/2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 8 (* 64/3 (/ 1 (pow x 2)))) (pow x 4))))) (* 4 (/ 1 (pow x 2))))
(+.f64 (log.f64 x) (+.f64 (/.f64 (+.f64 #s(literal -8 binary64) (/.f64 #s(literal -64/3 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 (log.f64 #s(literal -1/2 binary64)) (/.f64 #s(literal -4 binary64) (*.f64 x x)))))
(+ (log 1/2) (* -1 (log (/ -1 x))))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 (neg.f64 x)))
(- (+ (log 1/2) (* -1 (log (/ -1 x)))) (* 4 (/ 1 (pow x 2))))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (+.f64 (log.f64 (neg.f64 x)) (/.f64 #s(literal -4 binary64) (*.f64 x x))))
(+ (log 1/2) (+ (* -1 (log (/ -1 x))) (* -1 (/ (+ 4 (* 8 (/ 1 (pow x 2)))) (pow x 2)))))
(+.f64 (/.f64 (-.f64 #s(literal -4 binary64) (/.f64 #s(literal 8 binary64) (*.f64 x x))) (*.f64 x x)) (+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 (neg.f64 x))))
(- (+ (log 1/2) (+ (* -1 (log (/ -1 x))) (* -1 (/ (+ 8 (* 64/3 (/ 1 (pow x 2)))) (pow x 4))))) (* 4 (/ 1 (pow x 2))))
(+.f64 (+.f64 (/.f64 (+.f64 #s(literal -8 binary64) (/.f64 #s(literal -64/3 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 (neg.f64 x)))) (/.f64 #s(literal -4 binary64) (*.f64 x x)))
2
#s(literal 2 binary64)
(+ 2 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(+ 2 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(+ 2 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(* -1/2 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/2 binary64)))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(* -1/2 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/2 binary64)))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

eval127.0ms (1.8%)

Memory
21.8MiB live, 214.9MiB allocated
Compiler

Compiled 20 339 to 2 699 computations (86.7% saved)

prune140.0ms (1.9%)

Memory
-29.8MiB live, 206.2MiB allocated
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New8892891
Fresh000
Picked224
Done000
Total8914895
Accuracy
100.0%
Counts
895 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶0.0%
(*.f64 (log.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))
▶98.9%
(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
✓99.4%
(log.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x))
✓100.0%
(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))
Compiler

Compiled 33 to 25 computations (24.2% saved)

simplify4.0ms (0.1%)

Memory
6.6MiB live, 6.6MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 5 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(log.f64 #s(literal -1 binary64))
✓cost-diff0
(*.f64 (log.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))
✓cost-diff0
(*.f64 x #s(literal 1/2 binary64))
✓cost-diff0
(log.f64 (*.f64 x #s(literal 1/2 binary64)))
✓cost-diff0
(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
Rules
12×*-lowering-*.f32
12×*-lowering-*.f64
8×+-lowering-+.f64
8×+-lowering-+.f32
6×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0822
11322
21522
31722
41922
52322
62822
02822
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(neg (log (* x 1/2)))
(log (* x 1/2))
(* x 1/2)
x
1/2
(* (log -1) 1/2)
(log -1)
-1
1/2
Outputs
(neg (log (* x 1/2)))
(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(log (* x 1/2))
(log.f64 (*.f64 x #s(literal 1/2 binary64)))
(* x 1/2)
(*.f64 x #s(literal 1/2 binary64))
x
1/2
#s(literal 1/2 binary64)
(* (log -1) 1/2)
(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal -1 binary64)))
(log -1)
(log.f64 #s(literal -1 binary64))
-1
#s(literal -1 binary64)
1/2
#s(literal 1/2 binary64)

localize28.0ms (0.4%)

Memory
5.9MiB live, 45.0MiB allocated
Localize:

Found 5 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 (log.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))
✓accuracy100.0%
(log.f64 #s(literal -1 binary64))
✓accuracy100.0%
(*.f64 x #s(literal 1/2 binary64))
✓accuracy100.0%
(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
✓accuracy100.0%
(log.f64 (*.f64 x #s(literal 1/2 binary64)))
Samples
18.0ms256×0invalid
Compiler

Compiled 24 to 10 computations (58.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-log: 5.0ms (51.3% of total)
ival-mult: 3.0ms (30.8% of total)
ival-neg: 1.0ms (10.3% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series64.0ms (0.9%)

Memory
-3.6MiB live, 53.5MiB allocated
Counts
5 → 36
Calls
Call 1
Inputs
#<alt (neg (log (* x 1/2)))>
#<alt (log (* x 1/2))>
#<alt (* x 1/2)>
#<alt (* (log -1) 1/2)>
#<alt (log -1)>
Outputs
#<alt (* -1 (+ (log 1/2) (log x)))>
#<alt (* -1 (+ (log 1/2) (log x)))>
#<alt (* -1 (+ (log 1/2) (log x)))>
#<alt (* -1 (+ (log 1/2) (log x)))>
#<alt (* -1 (+ (log 1/2) (* -1 (log (/ 1 x)))))>
#<alt (* -1 (+ (log 1/2) (* -1 (log (/ 1 x)))))>
#<alt (* -1 (+ (log 1/2) (* -1 (log (/ 1 x)))))>
#<alt (* -1 (+ (log 1/2) (* -1 (log (/ 1 x)))))>
#<alt (* -1 (+ (log -1/2) (* -1 (log (/ -1 x)))))>
#<alt (* -1 (+ (log -1/2) (* -1 (log (/ -1 x)))))>
#<alt (* -1 (+ (log -1/2) (* -1 (log (/ -1 x)))))>
#<alt (* -1 (+ (log -1/2) (* -1 (log (/ -1 x)))))>
#<alt (+ (log 1/2) (log x))>
#<alt (+ (log 1/2) (log x))>
#<alt (+ (log 1/2) (log x))>
#<alt (+ (log 1/2) (log x))>
#<alt (+ (log 1/2) (* -1 (log (/ 1 x))))>
#<alt (+ (log 1/2) (* -1 (log (/ 1 x))))>
#<alt (+ (log 1/2) (* -1 (log (/ 1 x))))>
#<alt (+ (log 1/2) (* -1 (log (/ 1 x))))>
#<alt (+ (log -1/2) (* -1 (log (/ -1 x))))>
#<alt (+ (log -1/2) (* -1 (log (/ -1 x))))>
#<alt (+ (log -1/2) (* -1 (log (/ -1 x))))>
#<alt (+ (log -1/2) (* -1 (log (/ -1 x))))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
Calls

9 calls:

TimeVariablePointExpression
46.0ms
x
@-inf
(neg (log (* x 1/2)))
12.0ms
x
@0
(neg (log (* x 1/2)))
5.0ms
x
@inf
(neg (log (* x 1/2)))
0.0ms
x
@0
(log (* x 1/2))
0.0ms
x
@inf
(log (* x 1/2))

rewrite193.0ms (2.7%)

Memory
-14.0MiB live, 179.6MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
2 296×accelerator-lowering-fma.f32
2 296×accelerator-lowering-fma.f64
2 124×*-lowering-*.f32
2 124×*-lowering-*.f64
1 196×pow-lowering-pow.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0819
11917
27217
349717
4455917
0934417
Stop Event
1×iter limit
1×node limit
Counts
5 → 510
Calls
Call 1
Inputs
(neg (log (* x 1/2)))
(log (* x 1/2))
(* x 1/2)
(* (log -1) 1/2)
(log -1)
Outputs
(log.f64 (*.f64 x #s(literal 1/2 binary64)))
(+.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 0 binary64))
(+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (*.f64 x #s(literal -1/2 binary64))))
(+.f64 (log.f64 x) (log.f64 #s(literal 1/2 binary64)))
(+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64)))
(+.f64 (log.f64 x) (*.f64 #s(literal 1 binary64) (log.f64 #s(literal 1/2 binary64))))
(+.f64 (log.f64 x) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal -1 binary64)))
(+.f64 (log.f64 x) (+.f64 (log.f64 #s(literal 2 binary64)) #s(literal 0 binary64)))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(+.f64 #s(literal 0 binary64) (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+.f64 (log.f64 (*.f64 x #s(literal -1/2 binary64))) (log.f64 #s(literal -1 binary64)))
(+.f64 (/.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 1/2 binary64))))))
(+.f64 (*.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) (*.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64)))
(+.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (neg.f64 x)))
(+.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (/.f64 x #s(literal -1 binary64))))
(+.f64 (log.f64 (neg.f64 x)) (log.f64 #s(literal -1/2 binary64)))
(+.f64 (log.f64 (neg.f64 x)) (log.f64 #s(literal -2 binary64)))
(+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (neg.f64 x)))
(+.f64 (+.f64 (log.f64 #s(literal 2 binary64)) #s(literal 0 binary64)) (log.f64 x))
(+.f64 (-.f64 #s(literal 0 binary64) (log.f64 #s(literal 2 binary64))) (log.f64 x))
(+.f64 (-.f64 #s(literal 0 binary64) (log.f64 #s(literal -1 binary64))) (log.f64 (*.f64 x #s(literal -1/2 binary64))))
(+.f64 (-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 1/2 binary64))))) (/.f64 (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 1/2 binary64)))))
(+.f64 (log.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) (*.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64)))
(exp.f64 (log.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64)))))
(exp.f64 (*.f64 (log.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal -1 binary64)))
(-.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 0 binary64))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (*.f64 x #s(literal -1/2 binary64))))
(-.f64 (log.f64 x) (log.f64 #s(literal 1/2 binary64)))
(-.f64 (log.f64 x) (log.f64 #s(literal 2 binary64)))
(-.f64 (log.f64 x) (-.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 0 binary64)))
(-.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(-.f64 #s(literal 0 binary64) (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(-.f64 (log.f64 (*.f64 x #s(literal -1/2 binary64))) (log.f64 #s(literal -1 binary64)))
(-.f64 (/.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 1/2 binary64)))) (-.f64 (/.f64 (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 0 binary64)))
(-.f64 (/.f64 (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 1/2 binary64)))))
(-.f64 (*.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) (*.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64)))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (neg.f64 x)))
(-.f64 (log.f64 (neg.f64 x)) (log.f64 #s(literal -1/2 binary64)))
(-.f64 (log.f64 (neg.f64 x)) (log.f64 #s(literal -2 binary64)))
(-.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (neg.f64 x)))
(-.f64 (/.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 3 binary64)) (fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(-.f64 (+.f64 (log.f64 #s(literal 2 binary64)) #s(literal 0 binary64)) (log.f64 x))
(-.f64 (+.f64 #s(literal 0 binary64) (/.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 1/2 binary64))))) (/.f64 (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 1/2 binary64)))))
(-.f64 (+.f64 #s(literal 0 binary64) (log.f64 #s(literal -1 binary64))) (log.f64 (*.f64 x #s(literal -1/2 binary64))))
(-.f64 (-.f64 #s(literal 0 binary64) (log.f64 #s(literal 2 binary64))) (log.f64 x))
(-.f64 (log.f64 (*.f64 (neg.f64 x) #s(literal 1 binary64))) (log.f64 #s(literal -1/2 binary64)))
(fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64)))
(fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (*.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal -1 binary64) (log.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal 0 binary64))
(fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 (exp.f64 #s(literal -1 binary64))) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (log.f64 x) (log.f64 #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1 binary64) (log.f64 x) (log.f64 #s(literal 2 binary64)))
(fma.f64 #s(literal -1 binary64) (log.f64 x) (*.f64 #s(literal 1 binary64) (log.f64 #s(literal 1/2 binary64))))
(fma.f64 #s(literal -1 binary64) (log.f64 x) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal -1 binary64)))
(fma.f64 #s(literal -1 binary64) (log.f64 x) (+.f64 (log.f64 #s(literal 2 binary64)) #s(literal 0 binary64)))
(fma.f64 #s(literal -1 binary64) (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(fma.f64 #s(literal -1 binary64) (log.f64 (*.f64 x #s(literal -1/2 binary64))) (log.f64 #s(literal -1 binary64)))
(fma.f64 #s(literal 1 binary64) (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 0 binary64))
(fma.f64 (log.f64 x) #s(literal -1 binary64) (log.f64 #s(literal 1/2 binary64)))
(fma.f64 (log.f64 x) #s(literal -1 binary64) (log.f64 #s(literal 2 binary64)))
(fma.f64 (log.f64 x) #s(literal -1 binary64) (*.f64 #s(literal 1 binary64) (log.f64 #s(literal 1/2 binary64))))
(fma.f64 (log.f64 x) #s(literal -1 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal -1 binary64)))
(fma.f64 (log.f64 x) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) #s(literal 0 binary64)))
(fma.f64 (log.f64 x) (/.f64 (log.f64 x) (log.f64 (*.f64 x #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 1/2 binary64))))))
(fma.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal -1 binary64) (log.f64 x))
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(pow.f64 (exp.f64 (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 3 binary64)))) (*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)))) #s(literal -1 binary64)))
(pow.f64 (exp.f64 (fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (*.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64))))))
(pow.f64 (exp.f64 (fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (/.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(pow.f64 (exp.f64 (/.f64 #s(literal -1 binary64) (log.f64 (*.f64 x #s(literal 1/2 binary64))))) (pow.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(pow.f64 (exp.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64))))) (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 3 binary64))))
(pow.f64 (exp.f64 (/.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 3 binary64))))) (/.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64))))))
(pow.f64 (exp.f64 (pow.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1/2 binary64))) (pow.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 (/.f64 (pow.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (log.f64 (*.f64 x #s(literal 1/2 binary64)))))
(pow.f64 (exp.f64 (/.f64 (pow.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 3 binary64))))) (fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64))))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(pow.f64 (exp.f64 (/.f64 (pow.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3 binary64)) (+.f64 (pow.f64 (log.f64 x) #s(literal 6 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 6 binary64))))) (pow.f64 (fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64)))
(pow.f64 (exp.f64 (/.f64 (pow.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3 binary64)) (*.f64 (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 3 binary64))) (pow.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))))) (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 3 binary64))))
(pow.f64 (exp.f64 (pow.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -3 binary64))) (pow.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 4 binary64)))
(pow.f64 (exp.f64 (/.f64 (pow.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3 binary64)) (*.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 3 binary64)))))) (fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64))))
(pow.f64 (exp.f64 (/.f64 (pow.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3 binary64)))) (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(pow.f64 (exp.f64 (/.f64 (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (log.f64 x) #s(literal 6 binary64)) (pow.f64 (*.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 #s(literal 1/2 binary64))) #s(literal 3 binary64))))) (fma.f64 (*.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 #s(literal 1/2 binary64))) (-.f64 (*.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 #s(literal 1/2 binary64))) (pow.f64 (log.f64 x) #s(literal 2 binary64))) (pow.f64 (log.f64 x) #s(literal 4 binary64))))
(pow.f64 (exp.f64 (/.f64 (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 3 binary64))) (pow.f64 (fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64)))) (fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64))))
(pow.f64 (exp.f64 (pow.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -2 binary64))) (pow.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3 binary64)))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 x #s(literal 2 binary64))
(*.f64 x (exp.f64 (+.f64 (log.f64 #s(literal 2 binary64)) #s(literal 0 binary64))))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(*.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 2 binary64) x)
(*.f64 (neg.f64 x) #s(literal -1/2 binary64))
(*.f64 (neg.f64 x) #s(literal -2 binary64))
(*.f64 #s(literal -1/2 binary64) (neg.f64 x))
(*.f64 #s(literal -1/2 binary64) (/.f64 x #s(literal -1 binary64)))
(*.f64 #s(literal -2 binary64) (neg.f64 x))
(*.f64 (pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 1/2 binary64))))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 1/2 binary64)))))))
(*.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (log.f64 #s(literal 2 binary64)))) x)
(*.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (log.f64 #s(literal -1 binary64)))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 (exp.f64 (/.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 1/2 binary64))))) (exp.f64 (neg.f64 (/.f64 (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 1/2 binary64)))))))
(*.f64 (exp.f64 (-.f64 #s(literal 0 binary64) (log.f64 #s(literal 2 binary64)))) x)
(*.f64 (exp.f64 (-.f64 #s(literal 0 binary64) (log.f64 #s(literal -1 binary64)))) (*.f64 x #s(literal -1/2 binary64)))
(*.f64 (exp.f64 (+.f64 (log.f64 #s(literal 2 binary64)) #s(literal 0 binary64))) x)
(*.f64 (exp.f64 (-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 1/2 binary64)))))) (exp.f64 (/.f64 (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 1/2 binary64))))))
(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal -1 binary64)))
(*.f64 (log.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))
(log.f64 #s(literal -1 binary64))

simplify17.0ms (0.2%)

Memory
20.9MiB live, 20.9MiB allocated
Algorithm
1×egg-herbie
Rules
160×accelerator-lowering-fma.f32
160×accelerator-lowering-fma.f64
100×*-lowering-*.f32
100×*-lowering-*.f64
64×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
021192
154184
278180
3118180
4189180
5252180
6275180
7283180
0283180
Stop Event
1×iter limit
1×saturated
Counts
36 → 36
Calls
Call 1
Inputs
(* -1 (+ (log 1/2) (log x)))
(* -1 (+ (log 1/2) (log x)))
(* -1 (+ (log 1/2) (log x)))
(* -1 (+ (log 1/2) (log x)))
(* -1 (+ (log 1/2) (* -1 (log (/ 1 x)))))
(* -1 (+ (log 1/2) (* -1 (log (/ 1 x)))))
(* -1 (+ (log 1/2) (* -1 (log (/ 1 x)))))
(* -1 (+ (log 1/2) (* -1 (log (/ 1 x)))))
(* -1 (+ (log -1/2) (* -1 (log (/ -1 x)))))
(* -1 (+ (log -1/2) (* -1 (log (/ -1 x)))))
(* -1 (+ (log -1/2) (* -1 (log (/ -1 x)))))
(* -1 (+ (log -1/2) (* -1 (log (/ -1 x)))))
(+ (log 1/2) (log x))
(+ (log 1/2) (log x))
(+ (log 1/2) (log x))
(+ (log 1/2) (log x))
(+ (log 1/2) (* -1 (log (/ 1 x))))
(+ (log 1/2) (* -1 (log (/ 1 x))))
(+ (log 1/2) (* -1 (log (/ 1 x))))
(+ (log 1/2) (* -1 (log (/ 1 x))))
(+ (log -1/2) (* -1 (log (/ -1 x))))
(+ (log -1/2) (* -1 (log (/ -1 x))))
(+ (log -1/2) (* -1 (log (/ -1 x))))
(+ (log -1/2) (* -1 (log (/ -1 x))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
Outputs
(* -1 (+ (log 1/2) (log x)))
(-.f64 (neg.f64 (log.f64 x)) (log.f64 #s(literal 1/2 binary64)))
(* -1 (+ (log 1/2) (log x)))
(-.f64 (neg.f64 (log.f64 x)) (log.f64 #s(literal 1/2 binary64)))
(* -1 (+ (log 1/2) (log x)))
(-.f64 (neg.f64 (log.f64 x)) (log.f64 #s(literal 1/2 binary64)))
(* -1 (+ (log 1/2) (log x)))
(-.f64 (neg.f64 (log.f64 x)) (log.f64 #s(literal 1/2 binary64)))
(* -1 (+ (log 1/2) (* -1 (log (/ 1 x)))))
(-.f64 (neg.f64 (log.f64 x)) (log.f64 #s(literal 1/2 binary64)))
(* -1 (+ (log 1/2) (* -1 (log (/ 1 x)))))
(-.f64 (neg.f64 (log.f64 x)) (log.f64 #s(literal 1/2 binary64)))
(* -1 (+ (log 1/2) (* -1 (log (/ 1 x)))))
(-.f64 (neg.f64 (log.f64 x)) (log.f64 #s(literal 1/2 binary64)))
(* -1 (+ (log 1/2) (* -1 (log (/ 1 x)))))
(-.f64 (neg.f64 (log.f64 x)) (log.f64 #s(literal 1/2 binary64)))
(* -1 (+ (log -1/2) (* -1 (log (/ -1 x)))))
(-.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -1/2 binary64)))
(* -1 (+ (log -1/2) (* -1 (log (/ -1 x)))))
(-.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -1/2 binary64)))
(* -1 (+ (log -1/2) (* -1 (log (/ -1 x)))))
(-.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -1/2 binary64)))
(* -1 (+ (log -1/2) (* -1 (log (/ -1 x)))))
(-.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -1/2 binary64)))
(+ (log 1/2) (log x))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(+ (log 1/2) (log x))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(+ (log 1/2) (log x))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(+ (log 1/2) (log x))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(+ (log 1/2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(+ (log 1/2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(+ (log 1/2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(+ (log 1/2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(+ (log -1/2) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(+ (log -1/2) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(+ (log -1/2) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(+ (log -1/2) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)

eval83.0ms (1.1%)

Memory
17.0MiB live, 92.5MiB allocated
Compiler

Compiled 8 945 to 1 050 computations (88.3% saved)

prune93.0ms (1.3%)

Memory
-9.8MiB live, 108.0MiB allocated
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New5451546
Fresh000
Picked112
Done022
Total5464550
Accuracy
100.0%
Counts
550 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓98.9%
(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
✓99.4%
(log.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x))
✓100.0%
(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))
▶1.5%
(log.f64 (*.f64 x #s(literal 1/2 binary64)))
Compiler

Compiled 33 to 24 computations (27.3% saved)

simplify3.0ms (0%)

Memory
4.9MiB live, 4.9MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 x #s(literal 1/2 binary64))
✓cost-diff0
(log.f64 (*.f64 x #s(literal 1/2 binary64)))
Rules
4×*-lowering-*.f32
4×*-lowering-*.f64
2×*-commutative
2×log-lowering-log.f64
2×log-lowering-log.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
049
159
059
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(log (* x 1/2))
(* x 1/2)
x
1/2
Outputs
(log (* x 1/2))
(log.f64 (*.f64 x #s(literal 1/2 binary64)))
(* x 1/2)
(*.f64 x #s(literal 1/2 binary64))
x
1/2
#s(literal 1/2 binary64)

localize18.0ms (0.2%)

Memory
-12.5MiB live, 26.0MiB allocated
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 x #s(literal 1/2 binary64))
✓accuracy100.0%
(log.f64 (*.f64 x #s(literal 1/2 binary64)))
Samples
12.0ms256×0valid
Compiler

Compiled 11 to 6 computations (45.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
ival-log: 3.0ms (45.7% of total)
ival-mult: 3.0ms (45.7% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Counts
2 → 24
Calls
Call 1
Inputs
#<alt (log (* x 1/2))>
#<alt (* x 1/2)>
Outputs
#<alt (+ (log 1/2) (log x))>
#<alt (+ (log 1/2) (log x))>
#<alt (+ (log 1/2) (log x))>
#<alt (+ (log 1/2) (log x))>
#<alt (+ (log 1/2) (* -1 (log (/ 1 x))))>
#<alt (+ (log 1/2) (* -1 (log (/ 1 x))))>
#<alt (+ (log 1/2) (* -1 (log (/ 1 x))))>
#<alt (+ (log 1/2) (* -1 (log (/ 1 x))))>
#<alt (+ (log -1/2) (* -1 (log (/ -1 x))))>
#<alt (+ (log -1/2) (* -1 (log (/ -1 x))))>
#<alt (+ (log -1/2) (* -1 (log (/ -1 x))))>
#<alt (+ (log -1/2) (* -1 (log (/ -1 x))))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
Calls

6 calls:

TimeVariablePointExpression
0.0ms
x
@0
(log (* x 1/2))
0.0ms
x
@inf
(log (* x 1/2))
0.0ms
x
@-inf
(log (* x 1/2))
0.0ms
x
@inf
(* x 1/2)
0.0ms
x
@-inf
(* x 1/2)

rewrite363.0ms (5%)

Memory
-4.2MiB live, 430.8MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
7 112×accelerator-lowering-fma.f32
7 112×accelerator-lowering-fma.f64
4 162×*-lowering-*.f32
4 162×*-lowering-*.f64
4 134×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
047
187
2227
31347
412517
088077
Stop Event
1×iter limit
1×node limit
Counts
2 → 192
Calls
Call 1
Inputs
(log (* x 1/2))
(* x 1/2)
Outputs
(log.f64 (*.f64 x #s(literal 1/2 binary64)))
(log.f64 (/.f64 x #s(literal 2 binary64)))
(+.f64 (log.f64 x) (log.f64 #s(literal 1/2 binary64)))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) (log.f64 x)))
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(*.f64 (-.f64 (pow.f64 (log.f64 x) #s(literal 6 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (+.f64 (pow.f64 (log.f64 x) #s(literal 4 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))) (pow.f64 (*.f64 (log.f64 x) (log.f64 #s(literal 1/2 binary64))) #s(literal 2 binary64))) (log.f64 (*.f64 x #s(literal 2 binary64))))))
(*.f64 (-.f64 (pow.f64 (log.f64 x) #s(literal 4 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (log.f64 (*.f64 x #s(literal 2 binary64))) (+.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64))))))
(*.f64 (-.f64 (pow.f64 (log.f64 x) #s(literal 4 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64))) (log.f64 (*.f64 x #s(literal 2 binary64))))))
(*.f64 #s(literal -1 binary64) (neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64)))))
(*.f64 (-.f64 (*.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 2 binary64)))) (*.f64 (log.f64 (*.f64 x #s(literal 2 binary64))) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
(*.f64 (-.f64 (/.f64 (pow.f64 (log.f64 x) #s(literal 6 binary64)) (pow.f64 (log.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 3 binary64))) (/.f64 (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 6 binary64)) (pow.f64 (log.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (/.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64)) (*.f64 (/.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 2 binary64)))) (/.f64 (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 2 binary64)))))))))
(*.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 2 binary64)))) (/.f64 (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 2 binary64))))) (log.f64 (*.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 2 binary64)))) (/.f64 (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 2 binary64)))))))
(*.f64 (/.f64 (+.f64 (pow.f64 (log.f64 x) #s(literal 9 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 9 binary64))) (fma.f64 (log.f64 x) (log.f64 (*.f64 x #s(literal 2 binary64))) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (pow.f64 (log.f64 x) #s(literal 6 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 6 binary64))) (pow.f64 (*.f64 (log.f64 x) (log.f64 #s(literal 1/2 binary64))) #s(literal 3 binary64)))))
(*.f64 (/.f64 (-.f64 (pow.f64 (log.f64 x) #s(literal 6 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 6 binary64))) (fma.f64 (log.f64 x) (log.f64 (*.f64 x #s(literal 2 binary64))) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)))))
(*.f64 (/.f64 (-.f64 (pow.f64 (log.f64 x) #s(literal 6 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 6 binary64))) (log.f64 (*.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (pow.f64 (log.f64 x) #s(literal 4 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))) (pow.f64 (*.f64 (log.f64 x) (log.f64 #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(*.f64 (/.f64 (-.f64 (pow.f64 (log.f64 x) #s(literal 4 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))) (log.f64 (*.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(*.f64 (/.f64 (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (log.f64 x) #s(literal 6 binary64)) (pow.f64 (*.f64 (log.f64 #s(literal 1/2 binary64)) (neg.f64 (log.f64 (*.f64 x #s(literal 2 binary64))))) #s(literal 3 binary64)))) (fma.f64 (*.f64 (log.f64 #s(literal 1/2 binary64)) (neg.f64 (log.f64 (*.f64 x #s(literal 2 binary64))))) (-.f64 (*.f64 (log.f64 #s(literal 1/2 binary64)) (neg.f64 (log.f64 (*.f64 x #s(literal 2 binary64))))) (pow.f64 (log.f64 x) #s(literal 2 binary64))) (pow.f64 (log.f64 x) #s(literal 4 binary64))))
(*.f64 (/.f64 (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 3 binary64))) (-.f64 (pow.f64 (log.f64 x) #s(literal 4 binary64)) (pow.f64 (*.f64 (log.f64 #s(literal 1/2 binary64)) (neg.f64 (log.f64 (*.f64 x #s(literal 2 binary64))))) #s(literal 2 binary64)))) (+.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (*.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 (*.f64 x #s(literal 2 binary64))))))
(*.f64 (/.f64 (*.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 (*.f64 x #s(literal 2 binary64)))) (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)))) (fma.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 (*.f64 x #s(literal 1/2 binary64))) (pow.f64 (log.f64 x) #s(literal 2 binary64))))
(*.f64 (pow.f64 (/.f64 (fma.f64 (log.f64 x) (log.f64 (*.f64 x #s(literal 2 binary64))) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64))) (+.f64 (pow.f64 (log.f64 x) #s(literal 9 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 9 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (pow.f64 (log.f64 x) #s(literal 6 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 6 binary64))) (pow.f64 (*.f64 (log.f64 x) (log.f64 #s(literal 1/2 binary64))) #s(literal 3 binary64)))))
(*.f64 (pow.f64 (/.f64 (fma.f64 (log.f64 x) (log.f64 (*.f64 x #s(literal 2 binary64))) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64))) (-.f64 (pow.f64 (log.f64 x) #s(literal 6 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 6 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)))))
(*.f64 (pow.f64 (/.f64 (log.f64 (*.f64 x #s(literal 2 binary64))) (-.f64 (pow.f64 (log.f64 x) #s(literal 6 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 6 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (pow.f64 (log.f64 x) #s(literal 4 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))) (pow.f64 (*.f64 (log.f64 x) (log.f64 #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (/.f64 (log.f64 (*.f64 x #s(literal 2 binary64))) (-.f64 (pow.f64 (log.f64 x) #s(literal 4 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)

simplify15.0ms (0.2%)

Memory
20.2MiB live, 20.2MiB allocated
Algorithm
1×egg-herbie
Rules
160×accelerator-lowering-fma.f32
160×accelerator-lowering-fma.f64
100×*-lowering-*.f32
100×*-lowering-*.f64
64×+-lowering-+.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
018108
129104
237104
363104
490104
5126104
6172104
7205104
8250104
9265104
10273104
0273104
Stop Event
1×iter limit
1×saturated
Counts
24 → 24
Calls
Call 1
Inputs
(+ (log 1/2) (log x))
(+ (log 1/2) (log x))
(+ (log 1/2) (log x))
(+ (log 1/2) (log x))
(+ (log 1/2) (* -1 (log (/ 1 x))))
(+ (log 1/2) (* -1 (log (/ 1 x))))
(+ (log 1/2) (* -1 (log (/ 1 x))))
(+ (log 1/2) (* -1 (log (/ 1 x))))
(+ (log -1/2) (* -1 (log (/ -1 x))))
(+ (log -1/2) (* -1 (log (/ -1 x))))
(+ (log -1/2) (* -1 (log (/ -1 x))))
(+ (log -1/2) (* -1 (log (/ -1 x))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
Outputs
(+ (log 1/2) (log x))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(+ (log 1/2) (log x))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(+ (log 1/2) (log x))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(+ (log 1/2) (log x))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(+ (log 1/2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(+ (log 1/2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(+ (log 1/2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(+ (log 1/2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(+ (log -1/2) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(+ (log -1/2) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(+ (log -1/2) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(+ (log -1/2) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)

eval36.0ms (0.5%)

Memory
9.9MiB live, 48.0MiB allocated
Compiler

Compiled 6 476 to 490 computations (92.4% saved)

prune47.0ms (0.7%)

Memory
-32.0MiB live, 48.3MiB allocated
Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New2160216
Fresh000
Picked011
Done033
Total2164220
Accuracy
100.0%
Counts
220 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓98.9%
(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
✓99.4%
(log.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x))
✓100.0%
(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))
✓1.5%
(log.f64 (*.f64 x #s(literal 1/2 binary64)))
Compiler

Compiled 87 to 53 computations (39.1% saved)

regimes10.0ms (0.1%)

Memory
20.9MiB live, 20.9MiB allocated
Counts
8 → 1
Calls
Call 1
Inputs
(log.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 (log.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))
(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(log.f64 (/.f64 #s(literal 2 binary64) x))
(log.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x))
(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))
(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
Outputs
(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))
Calls

3 calls:

3.0ms
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
3.0ms
(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
3.0ms
x
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
100.0%1(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
Compiler

Compiled 29 to 18 computations (37.9% saved)

regimes9.0ms (0.1%)

Memory
-20.9MiB live, 18.4MiB allocated
Counts
6 → 1
Calls
Call 1
Inputs
(log.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 (log.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))
(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(log.f64 (/.f64 #s(literal 2 binary64) x))
(log.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x))
Outputs
(log.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x))
Calls

3 calls:

3.0ms
x
3.0ms
(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
3.0ms
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
Results
AccuracySegmentsBranch
99.4%1x
99.4%1(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
99.4%1(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
Compiler

Compiled 29 to 18 computations (37.9% saved)

regimes8.0ms (0.1%)

Memory
15.9MiB live, 15.9MiB allocated
Counts
5 → 1
Calls
Call 1
Inputs
(log.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 (log.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))
(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(log.f64 (/.f64 #s(literal 2 binary64) x))
Outputs
(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
Calls

3 calls:

2.0ms
(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
2.0ms
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
2.0ms
x
Results
AccuracySegmentsBranch
98.9%1x
98.9%1(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
98.9%1(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
Compiler

Compiled 29 to 18 computations (37.9% saved)

regimes5.0ms (0.1%)

Memory
10.1MiB live, 10.1MiB allocated
Accuracy

Total -1.0b remaining (-1.6%)

Threshold costs -1b (-1.6%)

Counts
2 → 1
Calls
Call 1
Inputs
(log.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 (log.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))
Outputs
(log.f64 (*.f64 x #s(literal 1/2 binary64)))
Calls

3 calls:

2.0ms
(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
2.0ms
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
1.0ms
x
Results
AccuracySegmentsBranch
1.5%1x
1.5%1(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
1.5%1(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
Compiler

Compiled 29 to 18 computations (37.9% saved)

simplify25.0ms (0.3%)

Memory
-26.4MiB live, 12.1MiB allocated
Algorithm
1×egg-herbie
Rules
10×*-commutative_binary64
10×+-commutative_binary64
8×sub-neg_binary64
6×neg-sub0_binary64
6×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01829
13229
24029
34529
44729
Stop Event
1×saturated
Calls
Call 1
Inputs
(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))
(log.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x))
(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(log.f64 (*.f64 x #s(literal 1/2 binary64)))
Outputs
(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))
(log.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x))
(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(log.f64 (*.f64 x #s(literal 1/2 binary64)))

soundness688.0ms (9.5%)

Memory
25.0MiB live, 426.7MiB allocated
Rules
17 138×accelerator-lowering-fma.f32
17 138×accelerator-lowering-fma.f64
5 416×accelerator-lowering-fma.f32
5 416×accelerator-lowering-fma.f64
4 520×accelerator-lowering-fma.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0942
16242
261738
3757738
0833538
0155767
1409742
21098722
33202709
47969709
08467680
0819
11917
27217
349717
4455917
0934417
02079
19779
267879
3678879
0916975
Stop Event
1×done
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 75 to 52 computations (30.7% saved)

preprocess35.0ms (0.5%)

Memory
4.0MiB live, 42.7MiB allocated
Compiler

Compiled 88 to 54 computations (38.6% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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