invcot (example 3.9)

Time bar (total: 15.6s)

analyze5.0ms (0%)

Memory
8.5MiB live, 8.5MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%49.7%50.3%0%0%0%0
0%0%49.7%50.3%0%0%0%1
0%0%49.7%50.3%0%0%0%2
25%12.4%37.3%50.3%0%0%0%3
62.5%31.1%18.6%50.3%0%0%0%4
81.3%40.4%9.3%50.3%0%0%0%5
90.6%45%4.7%50.3%0%0%0%6
95.3%47.4%2.3%50.3%0%0%0%7
97.7%48.5%1.2%50.3%0%0%0%8
98.8%49.1%0.6%50.3%0%0%0%9
99.4%49.4%0.3%50.3%0%0%0%10
99.7%49.5%0.1%50.3%0%0%0%11
99.9%49.6%0.1%50.3%0%0%0%12
Compiler

Compiled 16 to 12 computations (25% saved)

sample9.4s (59.8%)

Memory
110.4MiB live, 10 391.7MiB allocated
Samples
7.4s3 809×2valid
1.5s4 371×1valid
7.0ms76×0valid
Precisions
Click to see histograms. Total time spent on operations: 8.6s
ival-tan: 7.3s (84.4% of total)
ival-div: 519.0ms (6% of total)
adjust: 345.0ms (4% of total)
const: 289.0ms (3.4% of total)
ival-sub: 128.0ms (1.5% of total)
ival-<: 44.0ms (0.5% of total)
ival-and: 12.0ms (0.1% of total)
exact: 5.0ms (0.1% of total)
ival-assert: 3.0ms (0% of total)
Bogosity

preprocess28.0ms (0.2%)

Memory
-25.0MiB live, 51.4MiB allocated
Algorithm
egg-herbie
Rules
112×lower-fma.f64
112×lower-fma.f32
80×lower-*.f64
80×lower-*.f32
48×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0821
12119
25416
313116
420416
522816
623016
068
0108
1148
2228
3318
4438
5638
61028
71348
81928
92258
102478
02478
Stop Event
iter limit
saturated
iter limit
saturated
Calls
Call 1
Inputs
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Outputs
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
Symmetry

(negabs x)

explain688.0ms (4.4%)

Memory
33.5MiB live, 821.4MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2560-0-(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
00-0-(/.f64 #s(literal 1 binary64) x)
00-0-#s(literal 1 binary64)
00-0-(tan.f64 x)
00-0-(/.f64 #s(literal 1 binary64) (tan.f64 x))
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))cancellation2560
Confusion
Predicted +Predicted -
+2560
-00
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+25600
-000
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
1256
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
367.0ms232×2valid
87.0ms280×1valid
Compiler

Compiled 60 to 28 computations (53.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 417.0ms
ival-tan: 377.0ms (90.3% of total)
ival-div: 22.0ms (5.3% of total)
adjust: 11.0ms (2.6% of total)
ival-sub: 7.0ms (1.7% 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
0.4MiB live, 0.4MiB allocated
Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory
1.5MiB live, 1.5MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
5.9%
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify13.0ms (0.1%)

Memory
-20.6MiB live, 17.9MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(tan.f64 x)
cost-diff0
(/.f64 #s(literal 1 binary64) (tan.f64 x))
cost-diff0
(/.f64 #s(literal 1 binary64) x)
cost-diff0
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Rules
112×lower-fma.f64
112×lower-fma.f32
80×lower-*.f64
80×lower-*.f32
48×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0619
01019
11419
22219
33119
44319
56319
610219
713419
819219
922519
1024719
024719
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(/.f64 #s(literal 1 binary64) (tan.f64 x))
(tan.f64 x)
Outputs
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(/.f64 #s(literal 1 binary64) (tan.f64 x))
(tan.f64 x)

localize278.0ms (1.8%)

Memory
-2.4MiB live, 323.0MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(/.f64 #s(literal 1 binary64) x)
accuracy100.0%
(tan.f64 x)
accuracy100.0%
(/.f64 #s(literal 1 binary64) (tan.f64 x))
accuracy5.9%
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Samples
226.0ms116×2valid
43.0ms140×1valid
Compiler

Compiled 21 to 8 computations (61.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 257.0ms
ival-tan: 237.0ms (92.1% of total)
ival-div: 11.0ms (4.3% of total)
adjust: 6.0ms (2.3% of total)
ival-sub: 3.0ms (1.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series4.0ms (0%)

Memory
6.7MiB live, 6.7MiB allocated
Counts
4 → 48
Calls
Call 1
Inputs
#<alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))>
#<alt (/.f64 #s(literal 1 binary64) x)>
#<alt (/.f64 #s(literal 1 binary64) (tan.f64 x))>
#<alt (tan.f64 x)>
Outputs
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))>
#<alt (* -1 (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (* -1 (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin 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 (* -1/3 (pow x 2))) x)>
#<alt (/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)>
#<alt (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
Calls

12 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(- (/ 1 x) (/ 1 (tan x)))
1.0ms
x
@inf
(- (/ 1 x) (/ 1 (tan x)))
1.0ms
x
@0
(- (/ 1 x) (/ 1 (tan x)))
0.0ms
x
@-inf
(/ 1 (tan x))
0.0ms
x
@inf
(/ 1 (tan x))

simplify737.0ms (4.7%)

Memory
-6.2MiB live, 425.4MiB allocated
Algorithm
egg-herbie
Rules
18 970×lower-fma.f64
18 970×lower-fma.f32
3 656×lower-*.f64
3 656×lower-*.f32
3 436×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067324
1179324
2458318
31321318
42085318
53083318
63670318
73941318
85080318
97268318
08431300
Stop Event
iter limit
node limit
Counts
48 → 47
Calls
Call 1
Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin 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 (* -1/3 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
x
(* x (+ 1 (* 1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* -1 (/ (cos x) (sin x)))
(/.f64 (cos.f64 x) (sin.f64 (neg.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* -1 (/ (cos x) (sin x)))
(/.f64 (cos.f64 x) (sin.f64 (neg.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 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 (* -1/3 (pow x 2))) x)
(/.f64 (fma.f64 x (*.f64 x #s(literal -1/3 binary64)) #s(literal 1 binary64)) x)
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)
(/.f64 (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64)) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)
(/.f64 (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)) #s(literal 1 binary64)) x)
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
x
(* x (+ 1 (* 1/3 (pow x 2))))
(fma.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(fma.f64 x (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64))) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(fma.f64 x (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) #s(literal 1/3 binary64))) x)
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))

rewrite386.0ms (2.5%)

Memory
41.8MiB live, 193.8MiB allocated
Algorithm
batch-egg-rewrite
Rules
3 072×lower-fma.f64
3 072×lower-fma.f32
2 002×lower-*.f64
2 002×lower-*.f32
1 374×frac-times
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0617
01017
14917
245417
3570617
0920317
Stop Event
iter limit
node limit
iter limit
Counts
4 → 277
Calls
Call 1
Inputs
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) (tan.f64 x))
(tan.f64 x)
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))))) #s(literal -1 binary64)))
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) x))
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x))) (*.f64 x (*.f64 x x)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x))))))
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 x x))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))))))
(+.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x))) (*.f64 x (*.f64 x x)))) (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x)))))
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 x x))) (/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))))
(-.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) x))
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(exp.f64 (*.f64 (neg.f64 (log.f64 x)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (log.f64 x) #s(literal -1/2 binary64) (*.f64 (log.f64 x) #s(literal -1/2 binary64))))
(exp.f64 (+.f64 (log.f64 (tan.f64 x)) (*.f64 (log.f64 (*.f64 (tan.f64 x) x)) #s(literal -1 binary64))))
(exp.f64 (+.f64 (log.f64 (tan.f64 x)) (neg.f64 (log.f64 (*.f64 (tan.f64 x) x)))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) x))
(neg.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (tan.f64 x) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (tan.f64 x) x) (tan.f64 x)))
(/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(/.f64 (tan.f64 x) (*.f64 (tan.f64 x) x))
(/.f64 (tan.f64 x) (*.f64 (*.f64 (tan.f64 x) x) #s(literal -1 binary64)))
(/.f64 (sin.f64 x) (*.f64 (*.f64 (tan.f64 x) x) (cos.f64 x)))
(/.f64 (sin.f64 x) (*.f64 (*.f64 (tan.f64 x) x) (neg.f64 (cos.f64 x))))
(/.f64 #s(literal -1 binary64) x)
(/.f64 (/.f64 (tan.f64 x) x) (tan.f64 x))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(pow.f64 x #s(literal -1 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (*.f64 (tan.f64 x) x)) #s(literal -1 binary64))
(pow.f64 (*.f64 (*.f64 (tan.f64 x) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 (tan.f64 x) x) (tan.f64 x)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))
(*.f64 (tan.f64 x) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) x)))
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 (tan.f64 x) x))
(*.f64 (sin.f64 x) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (tan.f64 x) x)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (tan.f64 x) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(*.f64 (/.f64 (sin.f64 x) (tan.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) x))
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (tan.f64 x)))
(*.f64 (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (/.f64 (tan.f64 x) (*.f64 (sin.f64 x) x)) (cos.f64 x))
(exp.f64 (neg.f64 (log.f64 (tan.f64 x))))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 (tan.f64 x))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (tan.f64 x))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 x))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (tan.f64 x)) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (*.f64 (tan.f64 x) x)) #s(literal -1 binary64))))
(exp.f64 (+.f64 (log.f64 x) (neg.f64 (log.f64 (*.f64 (tan.f64 x) x)))))
(exp.f64 (fma.f64 (log.f64 (tan.f64 x)) #s(literal -1/2 binary64) (*.f64 (log.f64 (tan.f64 x)) #s(literal -1/2 binary64))))
(+.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 #s(literal 1 binary64) (tan.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (tan.f64 x) x) x))
(/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (tan.f64 x) x) (/.f64 #s(literal 1 binary64) x)))
(/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64))
(/.f64 (cos.f64 x) (sin.f64 x))
(/.f64 #s(literal -1 binary64) (tan.f64 x))
(/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))))
(/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 x (*.f64 (tan.f64 x) x))
(/.f64 x (*.f64 (*.f64 (tan.f64 x) x) #s(literal -1 binary64)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(/.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
(/.f64 (/.f64 x (tan.f64 x)) x)
(pow.f64 (tan.f64 x) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 (*.f64 (tan.f64 x) x) x) #s(literal -1 binary64))
(pow.f64 (*.f64 (*.f64 (tan.f64 x) x) (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 (tan.f64 x) x)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (tan.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal -1 binary64))
(*.f64 (cos.f64 x) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(*.f64 x (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) x)))
(*.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (cos.f64 x))
(*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (cos.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 x))))
(*.f64 (/.f64 x (tan.f64 x)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (neg.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64))) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)))
(*.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x))) (cos.f64 x))
(*.f64 (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64))) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)))
(*.f64 (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x))) (cos.f64 x))
(*.f64 (/.f64 x (*.f64 (sin.f64 x) x)) (cos.f64 x))
(exp.f64 (log.f64 (tan.f64 x)))
(exp.f64 (*.f64 (log.f64 (tan.f64 x)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 x))) #s(literal -1 binary64)))
(+.f64 #s(literal 0 binary64) (tan.f64 x))
(-.f64 #s(literal 0 binary64) (tan.f64 x))
(tan.f64 x)
(neg.f64 (tan.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 (tan.f64 x) #s(literal 1 binary64))
(/.f64 (tan.f64 x) #s(literal -1 binary64))
(/.f64 (sin.f64 x) (cos.f64 x))
(/.f64 (sin.f64 x) (neg.f64 (cos.f64 x)))
(/.f64 (sin.f64 x) (*.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))))
(/.f64 (sin.f64 x) (*.f64 #s(literal -1 binary64) (neg.f64 (cos.f64 x))))
(/.f64 (sin.f64 x) (neg.f64 (neg.f64 (cos.f64 x))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (tan.f64 x)))))
(/.f64 (/.f64 (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x))
(/.f64 (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x))) (cos.f64 x))
(pow.f64 (tan.f64 x) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) #s(literal -2 binary64))
(pow.f64 (*.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64))) #s(literal 2 binary64))
(pow.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (tan.f64 x)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (tan.f64 x))
(*.f64 (tan.f64 x) #s(literal 1 binary64))
(*.f64 (tan.f64 x) #s(literal -1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))))
(*.f64 (sin.f64 x) (neg.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x))))
(*.f64 (sin.f64 x) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))
(*.f64 (sin.f64 x) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))
(*.f64 #s(literal -1 binary64) (tan.f64 x))
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

eval133.0ms (0.8%)

Memory
-15.0MiB live, 63.0MiB allocated
Compiler

Compiled 6 028 to 755 computations (87.5% saved)

prune102.0ms (0.7%)

Memory
-11.4MiB live, 63.9MiB allocated
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New3222324
Fresh000
Picked101
Done000
Total3232325
Accuracy
99.5%
Counts
325 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.5%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
99.3%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
Compiler

Compiled 15 to 9 computations (40% saved)

simplify30.0ms (0.2%)

Memory
32.1MiB live, 32.1MiB allocated
Algorithm
egg-herbie
Localize:

Found 6 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x #s(literal 1/45 binary64))
cost-diff0
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
cost-diff0
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
cost-diff0
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
cost-diff0
(*.f64 #s(literal 1/3 binary64) x)
cost-diff0
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
Rules
536×lower-fma.f32
534×lower-fma.f64
360×lower-*.f32
354×lower-*.f64
170×associate-*r*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01454
01954
13554
25054
36354
47654
59654
613554
716554
829554
969354
1091454
1192754
092754
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
(*.f64 #s(literal 1/3 binary64) x)
#s(literal 1/3 binary64)
x
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
x
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(*.f64 x #s(literal 1/45 binary64))
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)
Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 x #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
x
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
x
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
(*.f64 x #s(literal 1/45 binary64))
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)

localize505.0ms (3.2%)

Memory
-11.2MiB live, 236.0MiB allocated
Localize:

Found 6 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
accuracy100.0%
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
accuracy99.6%
(*.f64 x #s(literal 1/45 binary64))
accuracy99.5%
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
accuracy99.7%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
accuracy99.5%
(*.f64 #s(literal 1/3 binary64) x)
Samples
435.0ms116×2valid
51.0ms140×1valid
Compiler

Compiled 45 to 15 computations (66.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 471.0ms
ival-tan: 402.0ms (85.3% of total)
const: 36.0ms (7.6% of total)
ival-div: 10.0ms (2.1% of total)
ival-mult: 9.0ms (1.9% of total)
adjust: 8.0ms (1.7% of total)
ival-sub: 3.0ms (0.6% of total)
ival-add: 2.0ms (0.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series4.0ms (0%)

Memory
3.4MiB live, 3.4MiB allocated
Counts
6 → 72
Calls
Call 1
Inputs
#<alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))>
#<alt (*.f64 #s(literal 1/3 binary64) x)>
#<alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))>
#<alt (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))>
#<alt (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))>
#<alt (*.f64 x #s(literal 1/45 binary64))>
Outputs
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))>
#<alt (* -1 (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (* -1 (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))>
#<alt (* -1 (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (* -1 (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt 1/3>
#<alt (+ 1/3 (* 1/45 (pow x 2)))>
#<alt (+ 1/3 (* 1/45 (pow x 2)))>
#<alt (+ 1/3 (* 1/45 (pow x 2)))>
#<alt (* 1/45 (pow x 2))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/45 (pow x 2))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/45 x)>
#<alt (* 1/45 x)>
#<alt (* 1/45 x)>
#<alt (* 1/45 x)>
#<alt (* 1/45 x)>
#<alt (* 1/45 x)>
#<alt (* 1/45 x)>
#<alt (* 1/45 x)>
#<alt (* 1/45 x)>
#<alt (* 1/45 x)>
#<alt (* 1/45 x)>
#<alt (* 1/45 x)>
Calls

18 calls:

TimeVariablePointExpression
1.0ms
x
@0
(* 1/3 x)
0.0ms
x
@inf
(* x (+ (* x (* x 1/45)) 1/3))
0.0ms
x
@0
(* x (+ (* x (* x 1/45)) 1/3))
0.0ms
x
@-inf
(* 1/3 x)
0.0ms
x
@inf
(* 1/3 x)

simplify286.0ms (1.8%)

Memory
-17.7MiB live, 214.7MiB allocated
Algorithm
egg-herbie
Rules
4 348×lower-*.f64
4 348×lower-*.f32
4 316×lower-fma.f64
4 316×lower-fma.f32
2 366×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
040468
1114468
2282468
3644468
41219468
52796468
63279468
74012468
87328468
08840438
Stop Event
iter limit
node limit
Counts
72 → 72
Calls
Call 1
Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (pow x 2)))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64))) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 1/4725 binary64) #s(literal 2/945 binary64))) #s(literal 1/45 binary64))) #s(literal 1/3 binary64)))
(* -1 (/ (cos x) (sin x)))
(/.f64 (cos.f64 x) (sin.f64 (neg.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* -1 (/ (cos x) (sin x)))
(/.f64 (cos.f64 x) (sin.f64 (neg.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64))) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 1/4725 binary64) #s(literal 2/945 binary64))) #s(literal 1/45 binary64))) #s(literal 1/3 binary64)))
(* -1 (/ (cos x) (sin x)))
(/.f64 (cos.f64 x) (sin.f64 (neg.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* -1 (/ (cos x) (sin x)))
(/.f64 (cos.f64 x) (sin.f64 (neg.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* 1/45 (pow x 2))
(*.f64 #s(literal 1/45 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* 1/45 (pow x 2))
(*.f64 #s(literal 1/45 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))

rewrite254.0ms (1.6%)

Memory
34.9MiB live, 425.9MiB allocated
Algorithm
batch-egg-rewrite
Rules
5 010×lower-fma.f32
5 008×lower-fma.f64
3 848×lower-*.f32
3 842×lower-*.f64
3 116×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01449
01949
18449
264149
3757249
0805549
Stop Event
iter limit
node limit
iter limit
Counts
6 → 181
Calls
Call 1
Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
(*.f64 #s(literal 1/3 binary64) x)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(*.f64 x #s(literal 1/45 binary64))
Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal 1 binary64))
(/.f64 (*.f64 (neg.f64 x) #s(literal 1/3 binary64)) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 1/3 binary64) (neg.f64 x)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/3 binary64)))
(*.f64 x #s(literal 1/3 binary64))
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal 1 binary64))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
(+.f64 (*.f64 x #s(literal 1/3 binary64)) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(+.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64)))) (*.f64 x #s(literal 1/3 binary64)))
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64))) (*.f64 x x)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))) (/.f64 (*.f64 #s(literal 1/9 binary64) (*.f64 x x)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))))
(fma.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/3 binary64)) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64)))) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 x #s(literal 1/3 binary64) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64))) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 #s(literal 1/3 binary64) x (*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 #s(literal 1/45 binary64) (*.f64 x (*.f64 x x)) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 (*.f64 x #s(literal 1/45 binary64)) (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 (*.f64 x (*.f64 x #s(literal 1/45 binary64))) x (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64)))) #s(literal 1 binary64) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/45 binary64)) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64))) (*.f64 x x) (*.f64 #s(literal 1/9 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x #s(literal 1/135 binary64))))) (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/91125 binary64))) (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/27 binary64) (*.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))) (*.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)) (*.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)) (*.f64 x (fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)))))
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
(/.f64 x (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))
(/.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) #s(literal 1 binary64)))
(/.f64 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) #s(literal 1 binary64))
(/.f64 (neg.f64 x) (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))
(/.f64 (neg.f64 x) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) #s(literal -1 binary64)))
(/.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/91125 binary64))) (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/27 binary64) (*.f64 x (*.f64 x x)))) (-.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64))) (*.f64 x x) (*.f64 #s(literal 1/9 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x #s(literal 1/135 binary64))))))
(/.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/91125 binary64))) (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/27 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) (-.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64))) (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x #s(literal 1/135 binary64)))))))
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(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/4100625 binary64) #s(literal -1/81 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))) (fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 1/2025 binary64) #s(literal 1/9 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))))
(*.f64 (fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))
(*.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)))))
(*.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal 1/3 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))) (fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)))
(*.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 x #s(literal 1/45 binary64))))))
(*.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) (fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(*.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64))) (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1/8303765625 binary64)))) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)) (-.f64 (fma.f64 (*.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)))) (*.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/4100625 binary64))))
(*.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64)) (*.f64 (fma.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)) (+.f64 (fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) (*.f64 x (*.f64 x #s(literal 1/135 binary64)))))) (+.f64 (fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) (*.f64 x (*.f64 x #s(literal 1/135 binary64)))))
(*.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/91125 binary64)) #s(literal -1/27 binary64))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) (fma.f64 x (*.f64 x #s(literal 1/135 binary64)) #s(literal 1/9 binary64))))
(/.f64 #s(literal 1/45 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 x #s(literal 1/45 binary64)) #s(literal 1 binary64))
(/.f64 (*.f64 #s(literal 1/45 binary64) (neg.f64 x)) #s(literal -1 binary64))
(/.f64 (*.f64 (neg.f64 x) #s(literal 1/45 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/45 binary64)))
(*.f64 x #s(literal 1/45 binary64))
(*.f64 #s(literal 1/45 binary64) x)
(*.f64 (*.f64 x #s(literal 1/45 binary64)) #s(literal 1 binary64))

eval28.0ms (0.2%)

Memory
-11.1MiB live, 66.3MiB allocated
Compiler

Compiled 5 627 to 527 computations (90.6% saved)

prune24.0ms (0.2%)

Memory
-20.9MiB live, 59.6MiB allocated
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New2503253
Fresh000
Picked022
Done000
Total2505255
Accuracy
100.0%
Counts
255 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.5%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
100.0%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))
99.2%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))
99.5%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
99.3%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
Compiler

Compiled 46 to 29 computations (37% saved)

simplify48.0ms (0.3%)

Memory
4.5MiB live, 82.1MiB allocated
Algorithm
egg-herbie
Localize:

Found 11 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x x)
cost-diff0
(*.f64 x (*.f64 x x))
cost-diff0
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
cost-diff320
(fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))
cost-diff0
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
cost-diff0
(/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
cost-diff0
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))
cost-diff1088
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
cost-diff0
(/.f64 #s(literal 1 binary64) x)
cost-diff0
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))
cost-diff1088
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))
Rules
552×lower-fma.f32
548×lower-fma.f64
376×lower-*.f32
368×lower-*.f64
170×associate-*r*
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
021118
033112
152104
270104
394104
4112104
5136104
6171104
7201104
8373104
9850104
101101104
111125104
121127104
131130104
141131104
01131104
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))
#s(literal 1/3 binary64)
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
x
(/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
#s(literal 1 binary64)
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(*.f64 x #s(literal 1/45 binary64))
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
(fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))
(*.f64 x (*.f64 x x))
x
(*.f64 x x)
#s(literal 1/45 binary64)
(*.f64 x #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 x #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
x
(/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
#s(literal 1 binary64)
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(*.f64 x #s(literal 1/45 binary64))
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
(fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(*.f64 x (*.f64 x x))
x
(*.f64 x x)
#s(literal 1/45 binary64)
(*.f64 x #s(literal 1/3 binary64))
#s(literal 1/3 binary64)

localize403.0ms (2.6%)

Memory
13.9MiB live, 568.6MiB allocated
Localize:

Found 11 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(*.f64 x x)
accuracy100.0%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
accuracy99.9%
(*.f64 x (*.f64 x x))
accuracy99.5%
(*.f64 x #s(literal 1/3 binary64))
accuracy100.0%
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
accuracy100.0%
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
accuracy100.0%
(/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
accuracy99.6%
(*.f64 x #s(literal 1/45 binary64))
accuracy100.0%
(/.f64 #s(literal 1 binary64) x)
accuracy99.7%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))
accuracy99.4%
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))
Samples
279.0ms116×2valid
89.0ms140×1valid
Compiler

Compiled 96 to 21 computations (78.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 345.0ms
ival-tan: 219.0ms (63.4% of total)
ival-mult: 77.0ms (22.3% of total)
ival-div: 21.0ms (6.1% of total)
adjust: 11.0ms (3.2% of total)
const: 9.0ms (2.6% of total)
ival-add: 4.0ms (1.2% of total)
ival-sub: 3.0ms (0.9% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series5.0ms (0%)

Memory
15.1MiB live, 15.1MiB allocated
Counts
13 → 156
Calls
Call 1
Inputs
#<alt (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))>
#<alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))>
#<alt (/.f64 #s(literal 1 binary64) x)>
#<alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))>
#<alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))>
#<alt (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))>
#<alt (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))>
#<alt (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))>
#<alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))>
#<alt (*.f64 x (*.f64 x x))>
#<alt (*.f64 x x)>
#<alt (*.f64 x #s(literal 1/45 binary64))>
#<alt (*.f64 x #s(literal 1/3 binary64))>
Outputs
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))>
#<alt (* -1 (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (* -1 (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin 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 (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))>
#<alt (* -1 (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (* -1 (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt 3>
#<alt (+ 3 (* -1/5 (pow x 2)))>
#<alt (+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))>
#<alt (+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))>
#<alt (/ 45 (pow x 2))>
#<alt (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))>
#<alt (/ 45 (pow x 2))>
#<alt (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))>
#<alt 1/3>
#<alt (+ 1/3 (* 1/45 (pow x 2)))>
#<alt (+ 1/3 (* 1/45 (pow x 2)))>
#<alt (+ 1/3 (* 1/45 (pow x 2)))>
#<alt (* 1/45 (pow x 2))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/45 (pow x 2))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))>
#<alt (* -1 (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (* -1 (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<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)>
#<alt (* 1/45 x)>
#<alt (* 1/45 x)>
#<alt (* 1/45 x)>
#<alt (* 1/45 x)>
#<alt (* 1/45 x)>
#<alt (* 1/45 x)>
#<alt (* 1/45 x)>
#<alt (* 1/45 x)>
#<alt (* 1/45 x)>
#<alt (* 1/45 x)>
#<alt (* 1/45 x)>
#<alt (* 1/45 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
Calls

39 calls:

TimeVariablePointExpression
1.0ms
x
@0
(* x (* x x))
0.0ms
x
@inf
(+ (* (* x (* x x)) 1/45) (* x 1/3))
0.0ms
x
@-inf
(* x (* x x))
0.0ms
x
@inf
(/ 1 (+ (* x (* x 1/45)) 1/3))
0.0ms
x
@0
(+ (* (* x (* x x)) 1/45) (* x 1/3))

simplify287.0ms (1.8%)

Memory
3.7MiB live, 562.7MiB allocated
Algorithm
egg-herbie
Rules
10 150×lower-fma.f64
10 150×lower-fma.f32
3 108×lower-*.f64
3 108×lower-*.f32
2 516×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077972
1198972
2494972
31160972
42439972
55349972
08394921
Stop Event
iter limit
node limit
Counts
156 → 156
Calls
Call 1
Inputs
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin 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)
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (pow x 2)))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(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)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64))) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* -1 (/ (cos x) (sin x)))
(/.f64 (cos.f64 x) (neg.f64 (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* -1 (/ (cos x) (sin x)))
(/.f64 (cos.f64 x) (neg.f64 (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 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)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64))) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* -1 (/ (cos x) (sin x)))
(/.f64 (cos.f64 x) (neg.f64 (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* -1 (/ (cos x) (sin x)))
(/.f64 (cos.f64 x) (neg.f64 (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
3
#s(literal 3 binary64)
(+ 3 (* -1/5 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 1/75 binary64) #s(literal -1/5 binary64))) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/1125 binary64)) #s(literal 1/75 binary64)) #s(literal -1/5 binary64)) #s(literal 3 binary64))
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (*.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (-.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (/.f64 #s(literal -10125 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 (-.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (/.f64 #s(literal -10125 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (/.f64 #s(literal -151875 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))))) (*.f64 x x))
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (*.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (-.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (/.f64 #s(literal -10125 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 (-.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (/.f64 #s(literal -10125 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (/.f64 #s(literal -151875 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))))) (*.f64 x x))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* 1/45 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/45 binary64)))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* 1/45 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/45 binary64)))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64))) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* -1 (/ (cos x) (sin x)))
(/.f64 (cos.f64 x) (neg.f64 (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* -1 (/ (cos x) (sin x)))
(/.f64 (cos.f64 x) (neg.f64 (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.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)
(pow x 2)
(*.f64 x x)
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)

rewrite353.0ms (2.3%)

Memory
12.7MiB live, 681.7MiB allocated
Algorithm
batch-egg-rewrite
Rules
9 850×lower-fma.f32
9 846×lower-fma.f64
5 194×lower-*.f32
5 186×lower-*.f64
2 890×lower-/.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
021108
033102
113394
297894
0859894
Stop Event
iter limit
node limit
iter limit
Counts
13 → 448
Calls
Call 1
Inputs
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) x)
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))
(/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
(*.f64 x (*.f64 x x))
(*.f64 x x)
(*.f64 x #s(literal 1/45 binary64))
(*.f64 x #s(literal 1/3 binary64))
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/3 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 x #s(literal -1/3 binary64)))
(neg.f64 (*.f64 x #s(literal -1/3 binary64)))
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/3 binary64))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/3 binary64))))
(/.f64 #s(literal -1/3 binary64) (/.f64 #s(literal -1 binary64) x))
(pow.f64 (/.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/3 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) x))
(*.f64 x #s(literal 1/3 binary64))
(*.f64 (*.f64 #s(literal 1/3 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/3 binary64)))
(*.f64 #s(literal -1/3 binary64) (neg.f64 x))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/3 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/3 binary64))) #s(literal -1/2 binary64)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
(exp.f64 (neg.f64 (log.f64 x)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) x))
(neg.f64 (/.f64 #s(literal -1 binary64) x))
(neg.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) x)
(/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 x))
(/.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64))
(pow.f64 x #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))) #s(literal -1 binary64)))
(+.f64 (*.f64 #s(literal 1/3 binary64) x) (*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(+.f64 (*.f64 #s(literal 1/3 binary64) x) (*.f64 (*.f64 (*.f64 x x) #s(literal -1/45 binary64)) (neg.f64 x)))
(+.f64 (*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x))) (*.f64 #s(literal 1/3 binary64) x))
(+.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))) (neg.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/9 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))))
(+.f64 (*.f64 (neg.f64 x) #s(literal -1/3 binary64)) (*.f64 (neg.f64 x) (*.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(+.f64 (*.f64 (neg.f64 x) (*.f64 (*.f64 x x) #s(literal -1/45 binary64))) (*.f64 (neg.f64 x) #s(literal -1/3 binary64)))
(+.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -1/45 binary64)) (neg.f64 x)) (*.f64 #s(literal 1/3 binary64) x))
(-.f64 (*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x))) (*.f64 x #s(literal -1/3 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64))))
(-.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/9 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))))
(-.f64 (/.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))) #s(literal 1 binary64)) (/.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/9 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64)))) (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64))))
(-.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/9 binary64)) (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) #s(literal -1/45 binary64))))) (/.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)))) (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) #s(literal -1/45 binary64))))))
(fma.f64 #s(literal 1/3 binary64) x (*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(fma.f64 #s(literal 1/3 binary64) x (*.f64 (*.f64 (*.f64 x x) #s(literal -1/45 binary64)) (neg.f64 x)))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) x) (*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) x) (*.f64 (*.f64 (*.f64 x x) #s(literal -1/45 binary64)) (neg.f64 x)))
(fma.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x))) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 x #s(literal 1/3 binary64) (*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) #s(literal -1/45 binary64)) (neg.f64 x)))
(fma.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal 1/45 binary64) (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (*.f64 x #s(literal 1/45 binary64)) (*.f64 x x) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/45 binary64)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (*.f64 #s(literal 1/3 binary64) x) #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(fma.f64 (*.f64 #s(literal 1/3 binary64) x) #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) #s(literal -1/45 binary64)) (neg.f64 x)))
(fma.f64 (*.f64 #s(literal 1/45 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x))) #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal -1 binary64) (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/45 binary64))) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/3 binary64)) (*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(fma.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/3 binary64)) (*.f64 (*.f64 (*.f64 x x) #s(literal -1/45 binary64)) (neg.f64 x)))
(fma.f64 #s(literal -1/3 binary64) (neg.f64 x) (*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(fma.f64 #s(literal -1/3 binary64) (neg.f64 x) (*.f64 (*.f64 (*.f64 x x) #s(literal -1/45 binary64)) (neg.f64 x)))
(fma.f64 (neg.f64 x) #s(literal -1/3 binary64) (*.f64 (neg.f64 x) (*.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(fma.f64 (neg.f64 x) (*.f64 (*.f64 x x) #s(literal -1/45 binary64)) (*.f64 (neg.f64 x) #s(literal -1/3 binary64)))
(fma.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)))) (/.f64 #s(literal -1 binary64) (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal 1/3 binary64)))) (neg.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/9 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))))
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/45 binary64)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (*.f64 (*.f64 x x) #s(literal -1/45 binary64)) (neg.f64 x) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (/.f64 x x) (/.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))) (neg.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/9 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))))
(fma.f64 (/.f64 #s(literal 1/45 binary64) x) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x))))) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))) (neg.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/9 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))))
(fma.f64 (/.f64 (*.f64 x x) x) (/.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64))) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))) (neg.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/9 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))))
(fma.f64 (/.f64 (*.f64 x (*.f64 x x)) x) (/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2025 binary64))) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))) (neg.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/9 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))))
(fma.f64 (/.f64 (*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x))) x) (/.f64 (*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x))) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))) (neg.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/9 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))))
(fma.f64 (/.f64 #s(literal 1/2025 binary64) x) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))) (neg.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/9 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))))
(fma.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) x) (/.f64 #s(literal 1/2025 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))) (neg.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/9 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))))
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(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))) (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/9 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/9 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))))) (+.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/9 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))))
(pow.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(*.f64 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) x)
(*.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) #s(literal 1 binary64))
(*.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) (*.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))) (/.f64 #s(literal -1 binary64) (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal 1/3 binary64))))))
(*.f64 #s(literal -1 binary64) (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64)) (neg.f64 x))
(*.f64 (neg.f64 x) (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64)))
(*.f64 (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/91125 binary64))) #s(literal 1/27 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/9 binary64)) (*.f64 (*.f64 x x) #s(literal -1/135 binary64)))) x))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/91125 binary64))) #s(literal 1/27 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/9 binary64))) (*.f64 x (*.f64 x (*.f64 x (*.f64 x #s(literal 1/135 binary64))))))))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/91125 binary64))) #s(literal 1/27 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/9 binary64)) (*.f64 (*.f64 x (*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x)))) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))))
(*.f64 (-.f64 (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/9 binary64))) (*.f64 x (*.f64 x (*.f64 x (*.f64 x #s(literal 1/135 binary64)))))) (*.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/9 binary64))) (*.f64 x (*.f64 x (*.f64 x (*.f64 x #s(literal 1/135 binary64)))))))))
(*.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/9 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))) x))
(*.f64 (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/9 binary64))) (/.f64 #s(literal -1 binary64) (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal 1/3 binary64)))))
(*.f64 (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/91125 binary64))) #s(literal 1/27 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/9 binary64)) (*.f64 (*.f64 x x) #s(literal -1/135 binary64)))))
(*.f64 (*.f64 x (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/9 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))
(*.f64 (neg.f64 (*.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/91125 binary64))) #s(literal 1/27 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/9 binary64))) (*.f64 x (*.f64 x (*.f64 x (*.f64 x #s(literal 1/135 binary64)))))))))
(*.f64 (neg.f64 (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/9 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal 1/3 binary64)))))
(*.f64 (*.f64 (*.f64 x x) (-.f64 #s(literal 1/9 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64))))) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) #s(literal -1/45 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) #s(literal -1/2 binary64))) (/.f64 x (pow.f64 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) #s(literal -1/2 binary64))))
(*.f64 (/.f64 x (pow.f64 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) #s(literal -1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/91125 binary64))) #s(literal 1/27 binary64)))) (/.f64 x (+.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/9 binary64)) (*.f64 (*.f64 x x) #s(literal -1/135 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/9 binary64)))) (/.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))
(*.f64 (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/91125 binary64))) #s(literal 1/27 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/9 binary64)) (*.f64 (*.f64 x x) #s(literal -1/135 binary64)))))
(*.f64 (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/9 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) #s(literal -1/2 binary64))) (/.f64 (neg.f64 x) (pow.f64 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) #s(literal -1/2 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/91125 binary64))) #s(literal 1/27 binary64)))) (/.f64 (neg.f64 x) (+.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/9 binary64)) (*.f64 (*.f64 x x) #s(literal -1/135 binary64)))))
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/9 binary64)))) (/.f64 (neg.f64 x) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))
(*.f64 (/.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) x) (/.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) #s(literal -1/2 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/91125 binary64))) #s(literal 1/27 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/9 binary64))) (*.f64 x (*.f64 x (*.f64 x (*.f64 x #s(literal 1/135 binary64))))))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))
(/.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 x (*.f64 x x)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x x))))
(/.f64 (neg.f64 (*.f64 x (*.f64 x x))) #s(literal -1 binary64))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))
(*.f64 x (*.f64 x x))
(*.f64 (*.f64 x x) x)
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 (*.f64 x (*.f64 x x))))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(*.f64 (*.f64 (*.f64 x x) #s(literal -1 binary64)) (neg.f64 x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(neg.f64 (*.f64 x (neg.f64 x)))
(/.f64 x (/.f64 #s(literal 1 binary64) x))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 x x)
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (*.f64 x (neg.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(/.f64 #s(literal 1/45 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/45 binary64)))
(*.f64 x #s(literal 1/45 binary64))
(*.f64 #s(literal 1/45 binary64) x)
(*.f64 (*.f64 x #s(literal 1/45 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) #s(literal 1/45 binary64)))
(*.f64 #s(literal -1/45 binary64) (neg.f64 x))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/3 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 x #s(literal -1/3 binary64)))
(neg.f64 (*.f64 x #s(literal -1/3 binary64)))
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/3 binary64))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/3 binary64))))
(/.f64 #s(literal -1/3 binary64) (/.f64 #s(literal -1 binary64) x))
(pow.f64 (/.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/3 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) x))
(*.f64 x #s(literal 1/3 binary64))
(*.f64 (*.f64 #s(literal 1/3 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/3 binary64)))
(*.f64 #s(literal -1/3 binary64) (neg.f64 x))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/3 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/3 binary64))) #s(literal -1/2 binary64)))

eval67.0ms (0.4%)

Memory
-6.9MiB live, 146.9MiB allocated
Compiler

Compiled 12 044 to 927 computations (92.3% saved)

prune43.0ms (0.3%)

Memory
10.1MiB live, 90.1MiB allocated
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New6031604
Fresh000
Picked213
Done022
Total6054609
Accuracy
100.0%
Counts
609 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.5%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
99.7%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
99.5%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
99.3%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
Compiler

Compiled 33 to 19 computations (42.4% saved)

simplify39.0ms (0.2%)

Memory
-5.6MiB live, 32.6MiB allocated
Algorithm
egg-herbie
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
cost-diff0
#s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))
cost-diff0
(/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))
cost-diff0
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
Rules
360×lower-fma.f64
360×lower-fma.f32
280×lower-*.f64
280×lower-*.f32
120×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01648
01748
12648
23548
34448
45748
57748
611648
714748
823748
942248
1055548
1165448
1277348
1381048
1484148
1585948
1686448
1786548
086545
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
(/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))
x
#s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))
#s(literal 3 binary64)
Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
(/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))
x
#s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))
#s(literal 3 binary64)

localize264.0ms (1.7%)

Memory
9.0MiB live, 289.2MiB allocated
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
accuracy100.0%
(/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))
accuracy99.7%
#s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))
Samples
191.0ms116×2valid
57.0ms140×1valid
Compiler

Compiled 32 to 16 computations (50% saved)

Precisions
Click to see histograms. Total time spent on operations: 233.0ms
ival-tan: 183.0ms (78.4% of total)
ival-div: 17.0ms (7.3% of total)
adjust: 9.0ms (3.9% of total)
ival-sub: 9.0ms (3.9% of total)
const: 9.0ms (3.9% of total)
ival-add: 3.0ms (1.3% of total)
ival-mult: 3.0ms (1.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series1.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated
Counts
3 → 36
Calls
Call 1
Inputs
#<alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))>
#<alt (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))>
#<alt #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))>
Outputs
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))>
#<alt (* -1 (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (* -1 (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt 3>
#<alt (+ 3 (* -1/5 (pow x 2)))>
#<alt (+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))>
#<alt (+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))>
#<alt (/ 45 (pow x 2))>
#<alt (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))>
#<alt (/ 45 (pow x 2))>
#<alt (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))>
Calls

9 calls:

TimeVariablePointExpression
0.0ms
x
@0
(- (/ 1 x) (/ 1 (tan x)))
0.0ms
x
@inf
(- (/ 1 x) (/ 1 (tan x)))
0.0ms
x
@-inf
(- (/ 1 x) (/ 1 (tan x)))
0.0ms
x
@-inf
(/ x (/ 1 (+ (* x (* x 1/45)) 1/3)))
0.0ms
x
@inf
(/ x (/ 1 (+ (* x (* x 1/45)) 1/3)))

simplify315.0ms (2%)

Memory
9.1MiB live, 434.1MiB allocated
Algorithm
egg-herbie
Rules
13 282×lower-fma.f64
13 282×lower-fma.f32
4 394×lower-*.f64
4 394×lower-*.f32
2 430×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
075360
1189360
2475360
31130360
42196360
53753360
66185360
08436339
Stop Event
iter limit
node limit
Counts
36 → 36
Calls
Call 1
Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* -1 (/ (cos x) (sin x)))
(neg.f64 (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* -1 (/ (cos x) (sin x)))
(neg.f64 (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
3
#s(literal 3 binary64)
(+ 3 (* -1/5 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/75 binary64) #s(literal -1/5 binary64)) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/1125 binary64)) #s(literal 1/75 binary64)) #s(literal -1/5 binary64)) #s(literal 3 binary64))
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (*.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (/.f64 #s(literal 10125 binary64) (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 10125 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (/.f64 #s(literal -151875 binary64) (*.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))))))) (*.f64 x x))
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (*.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (/.f64 #s(literal 10125 binary64) (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 10125 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (/.f64 #s(literal -151875 binary64) (*.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))))))) (*.f64 x x))

rewrite302.0ms (1.9%)

Memory
-1.2MiB live, 280.4MiB allocated
Algorithm
batch-egg-rewrite
Rules
4 876×lower-fma.f64
4 876×lower-fma.f32
3 764×lower-*.f64
3 764×lower-*.f32
3 130×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01646
01746
18646
266846
3764246
0827143
Stop Event
iter limit
node limit
iter limit
Counts
3 → 36
Calls
Call 1
Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
(/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))
#s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))
Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)) x)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))) (neg.f64 (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))))
(neg.f64 (neg.f64 (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)) x))
(/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))
(/.f64 x (*.f64 (neg.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) #s(literal -1 binary64)))
(/.f64 (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)) x)))
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) (neg.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))))
(/.f64 (neg.f64 x) (neg.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
(/.f64 (neg.f64 x) (*.f64 #s(literal 1 binary64) (neg.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))))
(/.f64 (neg.f64 x) (*.f64 (neg.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) #s(literal 1 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))) #s(literal -1 binary64))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) (neg.f64 x)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)) x) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
(*.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
(*.f64 (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))))
(*.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) x)
(*.f64 (/.f64 #s(literal -1 binary64) #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) (neg.f64 x))
(*.f64 (pow.f64 (/.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)) x) #s(literal -1/2 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
(neg.f64 (neg.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
(/.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)) #s(literal 1 binary64))
(/.f64 (neg.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) #s(literal -1 binary64))
#s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))
(*.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))
(*.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))

eval10.0ms (0.1%)

Memory
-29.1MiB live, 15.3MiB allocated
Compiler

Compiled 745 to 128 computations (82.8% saved)

prune7.0ms (0%)

Memory
18.3MiB live, 18.3MiB allocated
Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New72072
Fresh000
Picked011
Done033
Total72476
Accuracy
100.0%
Counts
76 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.5%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
99.7%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
99.5%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
99.3%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
Compiler

Compiled 88 to 40 computations (54.5% saved)

regimes5.0ms (0%)

Memory
10.8MiB live, 10.8MiB allocated
Counts
7 → 1
Calls
Call 1
Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))
Calls

2 calls:

3.0ms
x
2.0ms
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes4.0ms (0%)

Memory
9.1MiB live, 9.1MiB allocated
Counts
5 → 1
Calls
Call 1
Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))
Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
Calls

2 calls:

2.0ms
x
2.0ms
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Results
AccuracySegmentsBranch
99.7%1x
99.7%1(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes3.0ms (0%)

Memory
-33.0MiB live, 6.0MiB allocated
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
Calls

2 calls:

2.0ms
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
1.0ms
x
Results
AccuracySegmentsBranch
99.3%1x
99.3%1(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify5.0ms (0%)

Memory
11.9MiB live, 11.9MiB allocated
Algorithm
egg-herbie
Rules
*-commutative_binary64
1-exp_binary64
1-exp_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02353
12853
Stop Event
saturated
Calls
Call 1
Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))

soundness543.0ms (3.5%)

Memory
11.9MiB live, 349.6MiB allocated
Rules
18 970×lower-fma.f64
18 970×lower-fma.f32
10 150×lower-fma.f64
10 150×lower-fma.f32
5 010×lower-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01449
01949
18449
264149
3757249
0805549
077972
1198972
2494972
31160972
42439972
55349972
08394921
067324
1179324
2458318
31321318
42085318
53083318
63670318
73941318
85080318
97268318
08431300
Stop Event
done
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
Compiler

Compiled 68 to 41 computations (39.7% saved)

preprocess83.0ms (0.5%)

Memory
13.4MiB live, 127.7MiB allocated
Remove

(negabs x)

Compiler

Compiled 158 to 100 computations (36.7% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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