Rust f64::acosh

Time bar (total: 3.6s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated; 0ms collecting garbage
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%25%75%0%0%0%0
100%25%0%75%0%0%0%1
Compiler

Compiled 6 to 5 computations (16.7% saved)

sample845.0ms (23.6%)

Memory
63.2MiB live, 998.7MiB allocated; 284ms collecting garbage
Samples
554.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 217.0ms
ival-acosh: 172.0ms (79.2% of total)
ival->=: 31.0ms (14.3% of total)
exact: 7.0ms (3.2% of total)
ival-assert: 4.0ms (1.8% of total)
adjust: 3.0ms (1.4% of total)
Bogosity

explain128.0ms (3.6%)

Memory
-5.5MiB live, 130.7MiB allocated; 33ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1120-0-(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))
00-0-(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
00-0-#s(literal 1 binary64)
00-0-(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
00-0-(*.f64 x x)
00-0-(-.f64 (*.f64 x x) #s(literal 1 binary64))
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
sqrt.f64(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))oflow-rescue1120
↳(-.f64 (*.f64 x x) #s(literal 1 binary64))overflow112
↳(*.f64 x x)overflow112
Confusion
Predicted +Predicted -
+1120
-0144
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+11200
-00144
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
0144
1112
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
37.0ms512×0valid
Compiler

Compiled 79 to 25 computations (68.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 24.0ms
ival-log: 10.0ms (41.8% of total)
ival-mult: 4.0ms (16.7% of total)
ival-sqrt: 4.0ms (16.7% of total)
ival-add: 3.0ms (12.5% of total)
ival-sub: 3.0ms (12.5% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

preprocess778.0ms (21.7%)

Memory
-95.3MiB live, 89.7MiB allocated; 1.1s collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
047
079
0129
1229
2499
31219
43839
523359
678899
080198
Stop Event
1×iter limit
1×node limit
1×iter limit
1×saturated
Calls
Call 1
Inputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
Outputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
Compiler

Compiled 9 to 7 computations (22.2% saved)

eval0.0ms (0%)

Memory
0.1MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.9MiB live, 0.9MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶57.6%
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify151.0ms (4.2%)

Memory
-1.3MiB live, 188.4MiB allocated; 29ms collecting garbage
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))
cost-diff0
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
cost-diff0
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
cost-diff1
(-.f64 (*.f64 x x) #s(literal 1 binary64))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0733
01233
12233
24933
312133
438333
5233533
6788933
0801929
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
x
(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(-.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
#s(literal 1 binary64)
Outputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
(+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)
x
(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))
(-.f64 (*.f64 x x) #s(literal 1 binary64))
(fma.f64 x x #s(literal -1 binary64))
(*.f64 x x)
#s(literal 1 binary64)

localize48.0ms (1.3%)

Memory
9.5MiB live, 101.3MiB allocated; 5ms collecting garbage
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
accuracy0.00390625
(-.f64 (*.f64 x x) #s(literal 1 binary64))
accuracy0.0078125
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
accuracy26.06898042201995
(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))
Samples
37.0ms256×0valid
Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-log: 3.0ms (30% of total)
ival-mult: 2.0ms (20% of total)
ival-sqrt: 2.0ms (20% of total)
ival-add: 1.0ms (10% of total)
ival-sub: 1.0ms (10% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series13.0ms (0.4%)

Memory
-21.8MiB live, 32.2MiB allocated; 7ms collecting garbage
Counts
4 → 39
Calls
Call 1
Inputs
(-.f64 (*.f64 x x) #s(literal 1 binary64))
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))
Outputs
-1
(- (pow x 2) 1)
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* 2 x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(* -1 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
Calls

3 calls:

TimeVariablePointExpression
7.0ms
x
@-inf
((- (* x x) 1) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)))
3.0ms
x
@0
((- (* x x) 1) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)))
3.0ms
x
@inf
((- (* x x) 1) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)))

simplify251.0ms (7%)

Memory
15.0MiB live, 245.6MiB allocated; 29ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0150525
1470499
21771482
07736463
Stop Event
1×iter limit
1×iter limit
1×node limit
Counts
39 → 38
Calls
Call 1
Inputs
-1
(- (pow x 2) 1)
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* 2 x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(* -1 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
Outputs
-1
#s(literal -1 binary64)
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64))) x (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal 3/40 binary64) x) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/6 binary64) (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64)))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ x (sqrt -1))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) x #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(fma.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x x) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal 1/16 binary64) x) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x) x)
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64)))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(-.f64 (-.f64 (+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (-.f64 (+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 5/96 binary64) (*.f64 x x)) #s(literal -3/32 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(*.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x)
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(*.f64 (-.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x)
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(*.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 2 binary64))) x)
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) x x)
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f64 (/.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) x)
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x x)
(+ (log -1/2) (log (/ -1 x)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -1/2 binary64)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(-.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(-.f64 (-.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (/.f64 #s(literal -3/32 binary64) (pow.f64 x #s(literal 4 binary64))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(-.f64 (-.f64 (-.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (/.f64 #s(literal -3/32 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal -5/96 binary64) (pow.f64 x #s(literal 6 binary64))))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(/.f64 (+.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) #s(literal -1/8 binary64)) x) x) #s(literal 1/2 binary64)) x)
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal -5/128 binary64) (*.f64 x x)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))) (neg.f64 x))
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64)) x)
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(*.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64)))) x)
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
(*.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64))) x)

rewrite117.0ms (3.3%)

Memory
7.6MiB live, 97.4MiB allocated; 14ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0728
01215
15315
040014
Stop Event
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
4 → 64
Calls
Call 1
Inputs
(-.f64 (*.f64 x x) #s(literal 1 binary64))
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))
Outputs
(*.f64 (+.f64 (neg.f64 x) #s(literal 1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))
(*.f64 (+.f64 (fabs.f64 x) #s(literal 1 binary64)) (-.f64 (fabs.f64 x) #s(literal 1 binary64)))
(*.f64 (neg.f64 (sinh.f64 (acosh.f64 x))) (neg.f64 (sinh.f64 (acosh.f64 x))))
(*.f64 (fabs.f64 (sinh.f64 (acosh.f64 x))) (fabs.f64 (sinh.f64 (acosh.f64 x))))
(*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal -1 binary64)))
(*.f64 (-.f64 x #s(literal -1 binary64)) (-.f64 x #s(literal 1 binary64)))
(*.f64 (sinh.f64 (acosh.f64 x)) (sinh.f64 (acosh.f64 x)))
(pow.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) #s(literal 1/2 binary64))
(pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 2 binary64))
(pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (+.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))))
(fma.f64 (*.f64 (neg.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 (*.f64 (fabs.f64 x) #s(literal 1 binary64)) (*.f64 (fabs.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 (*.f64 x #s(literal 1 binary64)) (*.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) #s(literal -1 binary64))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) #s(literal -1 binary64))
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) #s(literal -1 binary64))
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 (neg.f64 x) (neg.f64 x) #s(literal -1 binary64))
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 (fabs.f64 x) (fabs.f64 x) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 x x) #s(literal -1 binary64))
(fma.f64 (*.f64 x x) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 x (*.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 x x #s(literal -1 binary64))
(expm1.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (*.f64 x x) #s(literal 1 binary64))
(+.f64 (*.f64 x x) #s(literal -1 binary64))
(acosh.f64 x)
(-.f64 (log.f64 (-.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)))) (log.f64 (-.f64 x (sinh.f64 (acosh.f64 x)))))
(-.f64 (log.f64 (+.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (log.f64 (fma.f64 (sinh.f64 (acosh.f64 x)) (-.f64 (sinh.f64 (acosh.f64 x)) x) (*.f64 x x))))
(log.f64 (+.f64 (sinh.f64 (acosh.f64 x)) x))
(/.f64 (-.f64 (fma.f64 x x #s(literal -1 binary64)) (*.f64 x x)) (-.f64 (sinh.f64 (acosh.f64 x)) x))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)))) (neg.f64 (-.f64 x (sinh.f64 (acosh.f64 x)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (sinh.f64 (acosh.f64 x)) (-.f64 (sinh.f64 (acosh.f64 x)) x) (*.f64 x x))))
(/.f64 (-.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64))) (-.f64 x (sinh.f64 (acosh.f64 x))))
(/.f64 (+.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (*.f64 x x) (*.f64 (sinh.f64 (acosh.f64 x)) x))))
(/.f64 (+.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (sinh.f64 (acosh.f64 x)) (-.f64 (sinh.f64 (acosh.f64 x)) x) (*.f64 x x)))
(fma.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1/4 binary64)) x)
(fma.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))) x)
(fma.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) x)
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (sinh.f64 (acosh.f64 x)))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 x (sinh.f64 (acosh.f64 x)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (sinh.f64 (acosh.f64 x)) (-.f64 (sinh.f64 (acosh.f64 x)) x) (*.f64 x x))) (/.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (fma.f64 (sinh.f64 (acosh.f64 x)) (-.f64 (sinh.f64 (acosh.f64 x)) x) (*.f64 x x))))
(+.f64 (sinh.f64 (acosh.f64 x)) x)
(+.f64 x (sinh.f64 (acosh.f64 x)))
(*.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(*.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (sqrt.f64 (+.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (exp.f64 (acosh.f64 x)) (exp.f64 (neg.f64 (acosh.f64 x)))) #s(literal 2 binary64))
(sinh.f64 (acosh.f64 (neg.f64 x)))
(sinh.f64 (acosh.f64 (fabs.f64 x)))
(sinh.f64 (acosh.f64 x))
(sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (fma.f64 x x #s(literal -1 binary64))) #s(literal 1/2 binary64)))

eval12.0ms (0.3%)

Memory
28.5MiB live, 28.5MiB allocated; 0ms collecting garbage
Compiler

Compiled 1 699 to 485 computations (71.5% saved)

prune45.0ms (1.2%)

Memory
-41.2MiB live, 26.4MiB allocated; 25ms collecting garbage
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1002102
Fresh000
Picked011
Done000
Total1003103
Accuracy
100.0%
Counts
103 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓57.6%
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
▶98.6%
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
▶99.7%
(acosh.f64 x)
Compiler

Compiled 24 to 19 computations (20.8% saved)

simplify155.0ms (4.3%)

Memory
18.0MiB live, 152.6MiB allocated; 24ms collecting garbage
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 #s(literal 2 binary64) x)
cost-diff0
#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
cost-diff0
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
cost-diff0
(acosh.f64 x)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01133
01433
12733
25933
314933
456233
5396933
0817531
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(acosh.f64 x)
x
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
Outputs
(acosh.f64 x)
x
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x

localize52.0ms (1.5%)

Memory
7.9MiB live, 102.4MiB allocated; 20ms collecting garbage
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 #s(literal 2 binary64) x)
accuracy0.0
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
accuracy0.9744501190496595
#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
accuracy0.17578125
(acosh.f64 x)
Samples
45.0ms256×0valid
Compiler

Compiled 27 to 12 computations (55.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 25.0ms
ival-log: 8.0ms (32.5% of total)
ival-sub: 6.0ms (24.4% of total)
ival-acosh: 4.0ms (16.3% of total)
ival-mult: 3.0ms (12.2% of total)
ival-sqrt: 2.0ms (8.1% of total)
ival-add: 1.0ms (4.1% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory
9.7MiB live, 9.8MiB allocated; 0ms collecting garbage
Counts
4 → 24
Calls
Call 1
Inputs
(acosh.f64 x)
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
Outputs
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(* 2 x)
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
((acosh x) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (* 2 x))
1.0ms
x
@inf
((acosh x) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (* 2 x))
1.0ms
x
@0
((acosh x) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (* 2 x))

simplify246.0ms (6.9%)

Memory
-28.2MiB live, 203.6MiB allocated; 84ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0124339
1386321
21414310
07718301
Stop Event
1×iter limit
1×iter limit
1×node limit
Counts
24 → 24
Calls
Call 1
Inputs
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(* 2 x)
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
Outputs
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64))) x (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal 3/40 binary64) x) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/6 binary64) (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64)))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ x (sqrt -1))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) x #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64)))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(-.f64 (-.f64 (+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (-.f64 (+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 5/96 binary64) (*.f64 x x)) #s(literal -3/32 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(*.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x)
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(*.f64 (-.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x)
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(*.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 2 binary64))) x)
(+ (log -1/2) (log (/ -1 x)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -1/2 binary64)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(-.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(-.f64 (-.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (/.f64 #s(literal -3/32 binary64) (pow.f64 x #s(literal 4 binary64))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(-.f64 (-.f64 (-.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (/.f64 #s(literal -3/32 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal -5/96 binary64) (pow.f64 x #s(literal 6 binary64))))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(/.f64 (+.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) #s(literal -1/8 binary64)) x) x) #s(literal 1/2 binary64)) x)
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal -5/128 binary64) (*.f64 x x)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))) (neg.f64 x))

rewrite120.0ms (3.3%)

Memory
6.1MiB live, 154.1MiB allocated; 20ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01130
01424
15724
042124
Stop Event
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
4 → 15
Calls
Call 1
Inputs
(acosh.f64 x)
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
Outputs
(acosh.f64 x)
(-.f64 (log.f64 (-.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)))) (log.f64 (-.f64 x (sinh.f64 (acosh.f64 x)))))
(-.f64 (log.f64 (+.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (log.f64 (fma.f64 (sinh.f64 (acosh.f64 x)) (-.f64 (sinh.f64 (acosh.f64 x)) x) (*.f64 x x))))
(log.f64 (+.f64 (sinh.f64 (acosh.f64 x)) x))
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(/.f64 (-.f64 (*.f64 x x) (*.f64 x x)) (-.f64 x x))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 (*.f64 x x) (*.f64 x x))))
(fma.f64 #s(literal 1 binary64) x (*.f64 #s(literal 1 binary64) x))
(fma.f64 x #s(literal 1 binary64) (*.f64 x #s(literal 1 binary64)))
(+.f64 (*.f64 #s(literal 1 binary64) x) (*.f64 #s(literal 1 binary64) x))
(+.f64 (*.f64 x #s(literal 1 binary64)) (*.f64 x #s(literal 1 binary64)))
(+.f64 x x)

eval4.0ms (0.1%)

Memory
16.2MiB live, 16.2MiB allocated; 0ms collecting garbage
Compiler

Compiled 689 to 194 computations (71.8% saved)

prune2.0ms (0.1%)

Memory
7.9MiB live, 7.9MiB allocated; 0ms collecting garbage
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New38139
Fresh000
Picked112
Done011
Total39342
Accuracy
100.0%
Counts
42 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓57.6%
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
▶98.6%
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x)))
✓99.7%
(acosh.f64 x)
Compiler

Compiled 24 to 18 computations (25% saved)

simplify193.0ms (5.4%)

Memory
-30.3MiB live, 164.1MiB allocated; 48ms collecting garbage
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 x x)
cost-diff0
#s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x))
cost-diff0
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0929
01129
12329
25229
313029
443129
5267729
6690229
0819327
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x))
(+.f64 x x)
x
Outputs
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x)))
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x))
#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
(+.f64 x x)
(*.f64 #s(literal 2 binary64) x)
x

localize23.0ms (0.6%)

Memory
33.8MiB live, 33.8MiB allocated; 0ms collecting garbage
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(+.f64 x x)
accuracy0.0
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x)))
accuracy0.9744501190496595
#s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x))
Samples
16.0ms256×0valid
Compiler

Compiled 23 to 10 computations (56.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-log: 3.0ms (28.3% of total)
ival-add: 2.0ms (18.9% of total)
ival-mult: 2.0ms (18.9% of total)
ival-sqrt: 2.0ms (18.9% of total)
ival-sub: 1.0ms (9.4% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series11.0ms (0.3%)

Memory
-43.9MiB live, 2.7MiB allocated; 5ms collecting garbage
Counts
3 → 24
Calls
Call 1
Inputs
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x))
(+.f64 x x)
Outputs
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(* 2 x)
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
Calls

3 calls:

TimeVariablePointExpression
10.0ms
x
@inf
((log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (+ x x))
1.0ms
x
@-inf
((log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (+ x x))
0.0ms
x
@0
((log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (+ x x))

simplify205.0ms (5.7%)

Memory
51.7MiB live, 232.8MiB allocated; 42ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0124339
1386321
21414310
07718301
Stop Event
1×iter limit
1×iter limit
1×node limit
Counts
24 → 24
Calls
Call 1
Inputs
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(* 2 x)
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
Outputs
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64))) x (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal 3/40 binary64) x) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/6 binary64) (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64)))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ x (sqrt -1))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) x #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64)))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(-.f64 (-.f64 (+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (-.f64 (+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 5/96 binary64) (*.f64 x x)) #s(literal -3/32 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(*.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x)
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(*.f64 (-.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x)
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(*.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 2 binary64))) x)
(+ (log -1/2) (log (/ -1 x)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -1/2 binary64)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(-.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(-.f64 (-.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (/.f64 #s(literal -3/32 binary64) (pow.f64 x #s(literal 4 binary64))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(-.f64 (-.f64 (-.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (/.f64 #s(literal -3/32 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal -5/96 binary64) (pow.f64 x #s(literal 6 binary64))))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(/.f64 (+.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) #s(literal -1/8 binary64)) x) x) #s(literal 1/2 binary64)) x)
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal -5/128 binary64) (*.f64 x x)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))) (neg.f64 x))

rewrite42.0ms (1.2%)

Memory
-18.1MiB live, 28.2MiB allocated; 4ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0928
01122
15922
048922
Stop Event
1×iter limit
1×iter limit
1×node limit
1×iter limit
Counts
3 → 10
Calls
Call 1
Inputs
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x))
(+.f64 x x)
Outputs
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(-.f64 (/.f64 (*.f64 x x) #s(literal 0 binary64)) (/.f64 (*.f64 x x) #s(literal 0 binary64)))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 0 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 0 binary64))))
(+.f64 x x)

eval4.0ms (0.1%)

Memory
7.6MiB live, 7.5MiB allocated; 0ms collecting garbage
Compiler

Compiled 713 to 174 computations (75.6% saved)

prune2.0ms (0.1%)

Memory
5.4MiB live, 5.4MiB allocated; 0ms collecting garbage
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New34034
Fresh000
Picked011
Done022
Total34337
Accuracy
100.0%
Counts
37 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓57.6%
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
✓98.6%
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x)))
✓99.7%
(acosh.f64 x)
Compiler

Compiled 61 to 38 computations (37.7% saved)

regimes35.0ms (1%)

Memory
-9.8MiB live, 47.4MiB allocated; 9ms collecting garbage
Accuracy

Total -27.9b remaining (-15879.9%)

Threshold costs -27.9b (-15879.9%)

Counts
4 → 1
Calls
Call 1
Inputs
(acosh.f64 x)
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x)))
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
Outputs
(acosh.f64 x)
Calls

3 calls:

14.0ms
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
2.0ms
x
2.0ms
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
Results
AccuracySegmentsBranch
99.7%1(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
99.7%1(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
99.7%1x
Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify13.0ms (0.4%)

Memory
-22.1MiB live, 22.3MiB allocated; 6ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
022
Stop Event
1×saturated
Calls
Call 1
Inputs
(acosh.f64 x)
Outputs
(acosh.f64 x)

derivations67.0ms (1.9%)

Memory
21.2MiB live, 104.2MiB allocated; 22ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0728
01215
15315
040014
Stop Event
1×done
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Compiler

Compiled 2 to 2 computations (0% saved)

preprocess16.0ms (0.4%)

Memory
28.6MiB live, 28.6MiB allocated; 0ms collecting garbage
Compiler

Compiled 46 to 36 computations (21.7% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

Profiling

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