Hyperbolic arcsine

Time bar (total: 2.9s)

start0.0ms (0%)

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

analyze91.0ms (3.2%)

Memory
-2.6MiB live, 120.7MiB allocated; 76ms collecting garbage
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
25%25%75%0%0%0%0%3
50%50%50%0%0%0%0%4
62.5%62.5%37.5%0%0%0%0%5
68.8%68.7%31.2%0%0%0%0%6
71.9%71.8%28.1%0%0%0%0%7
73.4%73.4%26.5%0%0%0%0%8
74.2%74.2%25.8%0%0%0%0%9
74.6%74.6%25.4%0%0%0%0%10
74.8%74.8%25.2%0%0%0%0%11
74.9%74.9%25.1%0%0%0%0%12
Compiler

Compiled 11 to 7 computations (36.4% saved)

sample2.2s (75.7%)

Memory
90.2MiB live, 1 616.6MiB allocated; 964ms collecting garbage
Samples
1000.0ms1 679×2valid
760.0ms4 460×1valid
126.0ms2 117×0valid
Precisions
Click to see histograms. Total time spent on operations: 1.7s
ival-log: 771.0ms (45.8% of total)
ival-hypot: 745.0ms (44.3% of total)
adjust: 121.0ms (7.2% of total)
ival-add!: 46.0ms (2.7% of total)
Bogosity

preprocess72.0ms (2.5%)

Memory
-54.0MiB live, 51.4MiB allocated; 20ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0147
1457
21007
32177
49507
Stop Event
1×node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶28.6%
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))
Symmetry

(negabs x)

Compiler

Compiled 18 to 14 computations (22.2% saved)

series5.0ms (0.2%)

Memory
11.6MiB live, 11.6MiB allocated; 0ms collecting garbage
Counts
7 → 37
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
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(hole binary64 x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 1))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (+ 1 x)))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (+ 1 (* x (+ 1 (* 1/2 x))))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))))
#s(approx (sqrt (+ (* x x) 1)) #s(hole binary64 (+ 1 (* 1/2 (pow x 2)))))
#s(approx (sqrt (+ (* x x) 1)) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))))
#s(approx (sqrt (+ (* x x) 1)) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))))
#s(approx (+ (* x x) 1) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(hole binary64 (+ (log 2) (* -1 (log (/ 1 x))))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(hole binary64 (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2)))))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(hole binary64 (- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(hole binary64 (- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (* 2 x)))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))))
#s(approx (sqrt (+ (* x x) 1)) #s(hole binary64 (* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (sqrt (+ (* x x) 1)) #s(hole binary64 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))))
#s(approx (sqrt (+ (* x x) 1)) #s(hole binary64 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))))
#s(approx (+ (* x x) 1) #s(hole binary64 (* (pow x 2) (+ 1 (/ 1 (pow x 2))))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(hole binary64 (+ (log 1/2) (log (/ -1 x)))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(hole binary64 (- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(hole binary64 (- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(hole binary64 (- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (/ -1/2 x)))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))))
#s(approx (sqrt (+ (* x x) 1)) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (+ (* x x) 1)) #s(hole binary64 (* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))))
#s(approx (sqrt (+ (* x x) 1)) #s(hole binary64 (* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))))
#s(approx (sqrt (+ (* x x) 1)) #s(hole binary64 (* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))))
Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@inf
((log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) x (sqrt (+ (* x x) 1)) (+ (* x x) 1) (* x x) 1)
1.0ms
x
@-inf
((log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) x (sqrt (+ (* x x) 1)) (+ (* x x) 1) (* x x) 1)
1.0ms
x
@0
((log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) x (sqrt (+ (* x x) 1)) (+ (* x x) 1) (* x x) 1)

rewrite180.0ms (6.3%)

Memory
18.1MiB live, 216.5MiB allocated; 42ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0172864
0179628
11006615
08312581
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
44 → 131
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)
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(hole binary64 x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 1))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (+ 1 x)))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (+ 1 (* x (+ 1 (* 1/2 x))))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))))
#s(approx (sqrt (+ (* x x) 1)) #s(hole binary64 (+ 1 (* 1/2 (pow x 2)))))
#s(approx (sqrt (+ (* x x) 1)) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))))
#s(approx (sqrt (+ (* x x) 1)) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))))
#s(approx (+ (* x x) 1) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(hole binary64 (+ (log 2) (* -1 (log (/ 1 x))))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(hole binary64 (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2)))))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(hole binary64 (- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(hole binary64 (- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (* 2 x)))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))))
#s(approx (sqrt (+ (* x x) 1)) #s(hole binary64 (* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (sqrt (+ (* x x) 1)) #s(hole binary64 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))))
#s(approx (sqrt (+ (* x x) 1)) #s(hole binary64 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))))
#s(approx (+ (* x x) 1) #s(hole binary64 (* (pow x 2) (+ 1 (/ 1 (pow x 2))))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(hole binary64 (+ (log 1/2) (log (/ -1 x)))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(hole binary64 (- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(hole binary64 (- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(hole binary64 (- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (/ -1/2 x)))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))))
#s(approx (sqrt (+ (* x x) 1)) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (+ (* x x) 1)) #s(hole binary64 (* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))))
#s(approx (sqrt (+ (* x x) 1)) #s(hole binary64 (* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))))
#s(approx (sqrt (+ (* x x) 1)) #s(hole binary64 (* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))))
Outputs
(asinh.f64 x)
(-.f64 (log.f64 (-.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)))) (log.f64 (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
(-.f64 (log.f64 (fma.f64 (*.f64 x x) x (*.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64))))) (log.f64 (fma.f64 x x (-.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))
(/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))
(/.f64 (fma.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64)) (*.f64 (*.f64 x x) x)) (+.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 (*.f64 x x) (*.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)))) (neg.f64 (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) x (*.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64))))) (neg.f64 (fma.f64 x x (-.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(/.f64 (-.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64))) (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (fma.f64 (*.f64 x x) x (*.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64)))) (fma.f64 x x (-.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
(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)
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
(+.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x x (-.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (/.f64 (*.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x (-.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)
(+.f64 x (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
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)))
(pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1 binary64))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64))))))
(/.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 (+.f64 (exp.f64 (asinh.f64 x)) (exp.f64 (neg.f64 (asinh.f64 x)))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/2 binary64)))
(cosh.f64 (neg.f64 (asinh.f64 x)))
(cosh.f64 (asinh.f64 (fabs.f64 x)))
(cosh.f64 (asinh.f64 (neg.f64 x)))
(cosh.f64 (asinh.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)))
(*.f64 (fabs.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) (fabs.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
(*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64)) (*.f64 x x))
(*.f64 (*.f64 x x) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(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 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #s(literal 2 binary64))
(pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1 binary64))) (neg.f64 (fma.f64 x x #s(literal -1 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)))) (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64))))))
(/.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal 1 binary64))) (neg.f64 (fma.f64 (*.f64 x x) (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)))))
(/.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal 1 binary64)) (fma.f64 (*.f64 x x) (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(fma.f64 (*.f64 (fabs.f64 x) #s(literal 1 binary64)) (*.f64 (fabs.f64 x) #s(literal 1 binary64)) #s(literal 1 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 #s(literal 1 binary64) (fabs.f64 x)) (*.f64 #s(literal 1 binary64) (fabs.f64 x)) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (*.f64 #s(literal 1 binary64) (neg.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 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) #s(literal 1 binary64))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) #s(literal 1 binary64))
(fma.f64 (fabs.f64 x) (fabs.f64 x) #s(literal 1 binary64))
(fma.f64 (neg.f64 x) (neg.f64 x) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 x x #s(literal 1 binary64))
(sqrt.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(-.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(-.f64 (*.f64 x x) (*.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 x x)))
(-.f64 (*.f64 x x) (*.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(-.f64 (*.f64 x x) #s(literal -1 binary64))
(-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x))
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64))))) (/.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64))))))
(+.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (fma.f64 (*.f64 x x) (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 (*.f64 (fabs.f64 x) #s(literal 1 binary64)) (*.f64 (fabs.f64 x) #s(literal 1 binary64)))
(*.f64 (*.f64 (neg.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 x) #s(literal 1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (*.f64 #s(literal 1 binary64) (fabs.f64 x)))
(*.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (*.f64 #s(literal 1 binary64) (neg.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 x x)
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (*.f64 x x) #s(literal -1 binary64)))
(neg.f64 (*.f64 #s(literal -1 binary64) (*.f64 x x)))
(neg.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) #s(literal 0 binary64)))
(exp.f64 (+.f64 #s(literal 0 binary64) (*.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))))
#s(literal 1 binary64)
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) x)
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 3/40 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -5/112 binary64) (*.f64 x x) #s(literal 3/40 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(literal 1 binary64))
#s(approx (+ x (sqrt (+ (* x x) 1))) (-.f64 x #s(literal -1 binary64)))
#s(approx (+ x (sqrt (+ (* x x) 1))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
#s(approx (+ x (sqrt (+ (* x x) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
#s(approx (sqrt (+ (* x x) 1)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (sqrt (+ (* x x) 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (sqrt (+ (* x x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (+ (* x x) 1) (fma.f64 x x #s(literal 1 binary64)))
#s(approx (* x x) (*.f64 x x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (log.f64 (+.f64 x x)))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (+.f64 (log.f64 (+.f64 x x)) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (-.f64 (+.f64 (log.f64 (+.f64 x x)) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 3/32 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (-.f64 (+.f64 (log.f64 (+.f64 x x)) (fma.f64 (pow.f64 x #s(literal -6 binary64)) #s(literal 5/96 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (/.f64 #s(literal 3/32 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))
#s(approx (+ x (sqrt (+ (* x x) 1))) (+.f64 x x))
#s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 2 binary64)) x))
#s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 (+.f64 #s(literal 2 binary64) (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) (/.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))) x))
#s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 (-.f64 (+.f64 (fma.f64 (pow.f64 x #s(literal -6 binary64)) #s(literal 1/16 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 2 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) x))
#s(approx (sqrt (+ (* x x) 1)) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64)) x))
#s(approx (sqrt (+ (* x x) 1)) (*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) x))
#s(approx (sqrt (+ (* x x) 1)) (*.f64 (-.f64 (-.f64 (fma.f64 (pow.f64 x #s(literal -6 binary64)) #s(literal 1/16 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) x))
#s(approx (+ (* x x) 1) (fma.f64 x x #s(literal 1 binary64)))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (log.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (-.f64 (log.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (-.f64 (+.f64 (log.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64))) (/.f64 #s(literal 3/32 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (-.f64 (-.f64 (+.f64 (log.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64))) (/.f64 #s(literal 3/32 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 5/96 binary64) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)))))
#s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x))
#s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))
#s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) (neg.f64 x)))
#s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) (/.f64 #s(literal 5/128 binary64) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)))) (neg.f64 x)))
#s(approx (sqrt (+ (* x x) 1)) (neg.f64 x))
#s(approx (sqrt (+ (* x x) 1)) (*.f64 (neg.f64 x) (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64))))
#s(approx (sqrt (+ (* x x) 1)) (*.f64 (neg.f64 x) (-.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))))
#s(approx (sqrt (+ (* x x) 1)) (*.f64 (neg.f64 x) (-.f64 (-.f64 (fma.f64 (pow.f64 x #s(literal -6 binary64)) #s(literal 1/16 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))))

eval62.0ms (2.2%)

Memory
-23.3MiB live, 22.0MiB allocated; 5ms collecting garbage
Compiler

Compiled 2 278 to 599 computations (73.7% saved)

prune4.0ms (0.2%)

Memory
7.2MiB live, 7.2MiB allocated; 0ms collecting garbage
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1215126
Fresh000
Picked101
Done000
Total1225127
Accuracy
100.0%
Counts
127 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶0.0%
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x)))
▶18.8%
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (-.f64 x #s(literal -1 binary64))))
▶48.9%
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (+.f64 x x)))
▶99.8%
(asinh.f64 x)
▶53.2%
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) x)
Compiler

Compiled 104 to 78 computations (25% saved)

series4.0ms (0.1%)

Memory
4.3MiB live, 4.3MiB allocated; 0ms collecting garbage
Counts
14 → 25
Calls
Call 1
Inputs
(asinh.f64 x)
x
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) x)
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (-.f64 x #s(literal -1 binary64))))
#s(approx (+ x (sqrt (+ (* x x) 1))) (-.f64 x #s(literal -1 binary64)))
(-.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)
(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)
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x)))
#s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x))
(/.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
Outputs
#s(approx (asinh x) #s(hole binary64 x))
#s(approx (asinh x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (asinh x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))))
#s(approx (asinh x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 1))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (+ 1 x)))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (+ 1 (* x (+ 1 (* 1/2 x))))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (/ -1/2 x) #s(hole binary64 (/ -1/2 x)))
#s(approx (asinh x) #s(hole binary64 (+ (log 2) (* -1 (log (/ 1 x))))))
#s(approx (asinh x) #s(hole binary64 (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2)))))))
#s(approx (asinh x) #s(hole binary64 (- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))))
#s(approx (asinh x) #s(hole binary64 (- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))))
#s(approx (- x -1) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (asinh x) #s(hole binary64 (+ (log 1/2) (log (/ -1 x)))))
#s(approx (asinh x) #s(hole binary64 (- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (asinh x) #s(hole binary64 (- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (asinh x) #s(hole binary64 (- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))))
Calls

3 calls:

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

rewrite80.0ms (2.8%)

Memory
-12.9MiB live, 31.1MiB allocated; 5ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0147589
0153487
0844470
Stop Event
1×iter-limit
1×iter-limit
1×node-limit
1×iter-limit
Counts
39 → 47
Calls
Call 1
Inputs
(asinh.f64 x)
x
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) x)
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (-.f64 x #s(literal -1 binary64))))
#s(approx (+ x (sqrt (+ (* x x) 1))) (-.f64 x #s(literal -1 binary64)))
(-.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)
(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)
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x)))
#s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x))
(/.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
#s(approx (asinh x) #s(hole binary64 x))
#s(approx (asinh x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (asinh x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))))
#s(approx (asinh x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 1))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (+ 1 x)))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (+ 1 (* x (+ 1 (* 1/2 x))))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (/ -1/2 x) #s(hole binary64 (/ -1/2 x)))
#s(approx (asinh x) #s(hole binary64 (+ (log 2) (* -1 (log (/ 1 x))))))
#s(approx (asinh x) #s(hole binary64 (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2)))))))
#s(approx (asinh x) #s(hole binary64 (- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))))
#s(approx (asinh x) #s(hole binary64 (- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))))
#s(approx (- x -1) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (asinh x) #s(hole binary64 (+ (log 1/2) (log (/ -1 x)))))
#s(approx (asinh x) #s(hole binary64 (- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (asinh x) #s(hole binary64 (- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (asinh x) #s(hole binary64 (- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(hole binary64 (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))))
Outputs
(asinh.f64 x)
(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))
x
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) x)
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (-.f64 x #s(literal -1 binary64))))
#s(approx (+ x (sqrt (+ (* x x) 1))) (-.f64 x #s(literal -1 binary64)))
(/.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1 binary64)))))
(-.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (+.f64 x x)))
#s(approx (+ x (sqrt (+ (* x x) 1))) (+.f64 x 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))))
(+.f64 x x)
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x)))
#s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x))
(/.f64 #s(literal 1/2 binary64) (neg.f64 x))
(/.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) x)
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 3/40 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -5/112 binary64) (*.f64 x x) #s(literal 3/40 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (+ x (sqrt (+ (* x x) 1))) #s(literal 1 binary64))
#s(approx (+ x (sqrt (+ (* x x) 1))) (+.f64 #s(literal 1 binary64) x))
#s(approx (+ x (sqrt (+ (* x x) 1))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
#s(approx (+ x (sqrt (+ (* x x) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
#s(approx (+ x x) (+.f64 x x))
#s(approx (/ -1/2 x) (/.f64 #s(literal -1/2 binary64) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (+.f64 (neg.f64 (neg.f64 (log.f64 x))) (log.f64 #s(literal 2 binary64))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (+.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (neg.f64 (neg.f64 (log.f64 x)))) (log.f64 #s(literal 2 binary64))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (+.f64 (log.f64 #s(literal 2 binary64)) (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (neg.f64 (neg.f64 (log.f64 x)))) (/.f64 #s(literal 3/32 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (-.f64 (+.f64 (+.f64 (fma.f64 (pow.f64 x #s(literal -6 binary64)) #s(literal 5/96 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (neg.f64 (neg.f64 (log.f64 x)))) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/32 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))
#s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 2 binary64)) x))
#s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 (+.f64 #s(literal 2 binary64) (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) (/.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))) x))
#s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 (-.f64 (+.f64 (fma.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal -6 binary64)) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 2 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) x))
#s(approx (- x -1) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (log.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (-.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (-.f64 (+.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x))) (/.f64 #s(literal 3/32 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (-.f64 (+.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x))) (/.f64 #s(literal 3/32 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (fma.f64 (pow.f64 x #s(literal -6 binary64)) #s(literal 5/96 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))))
#s(approx (+ x (sqrt (+ (* x x) 1))) (neg.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)))
#s(approx (+ x (sqrt (+ (* x x) 1))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) x)))
#s(approx (+ x (sqrt (+ (* x x) 1))) (neg.f64 (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal -6 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) x)))

eval4.0ms (0.1%)

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

Compiled 714 to 179 computations (74.9% saved)

prune3.0ms (0.1%)

Memory
5.7MiB live, 5.7MiB allocated; 0ms collecting garbage
Pruning

5 alts after pruning (0 fresh and 5 done)

PrunedKeptTotal
New32032
Fresh000
Picked055
Done000
Total32537
Accuracy
100.0%
Counts
37 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓0.0%
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x)))
✓18.8%
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (-.f64 x #s(literal -1 binary64))))
✓48.9%
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (+.f64 x x)))
✓99.8%
(asinh.f64 x)
✓53.2%
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) x)
Compiler

Compiled 113 to 65 computations (42.5% saved)

regimes6.0ms (0.2%)

Memory
12.3MiB live, 12.3MiB allocated; 0ms collecting garbage
Counts
6 → 1
Calls
Call 1
Inputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) x)
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (-.f64 x #s(literal -1 binary64))))
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (+.f64 x x)))
(asinh.f64 x)
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x)))
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))
Outputs
(asinh.f64 x)
Calls

3 calls:

2.0ms
x
2.0ms
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))
2.0ms
(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))
Results
AccuracySegmentsBranch
99.8%1(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))
99.8%1(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))
99.8%1x
Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes4.0ms (0.2%)

Memory
10.0MiB live, 10.0MiB allocated; 0ms collecting garbage
Counts
3 → 2
Calls
Call 1
Inputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) x)
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (-.f64 x #s(literal -1 binary64))))
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (+.f64 x x)))
Outputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) x)
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (+.f64 x x)))
Calls

3 calls:

1.0ms
x
1.0ms
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))
1.0ms
(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))
Results
AccuracySegmentsBranch
98.3%2(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))
98.3%2(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))
98.3%2x
Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes18.0ms (0.6%)

Memory
-32.5MiB live, 9.6MiB allocated; 7ms collecting garbage
Counts
2 → 2
Calls
Call 1
Inputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) x)
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (-.f64 x #s(literal -1 binary64))))
Outputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) x)
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (-.f64 x #s(literal -1 binary64))))
Calls

3 calls:

15.0ms
(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))
1.0ms
x
1.0ms
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))
Results
AccuracySegmentsBranch
65.7%2(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))
65.7%2(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))
65.7%2x
Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes3.0ms (0.1%)

Memory
9.3MiB live, 9.3MiB allocated; 0ms collecting garbage
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) x)
Outputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) x)
Calls

3 calls:

1.0ms
x
1.0ms
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))
1.0ms
(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))
Results
AccuracySegmentsBranch
53.2%1x
53.2%1(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))
53.2%1(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))
Compiler

Compiled 18 to 14 computations (22.2% saved)

bsearch8.0ms (0.3%)

Memory
15.9MiB live, 15.9MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
8.0ms
0.49874898351897257
3.3521285529165565
Samples
4.0ms96×0valid
Compiler

Compiled 156 to 123 computations (21.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.0ms
ival-hypot: 2.0ms (75.1% of total)
ival-log: 1.0ms (37.6% of total)
adjust: 0.0ms (0% of total)
ival-add!: 0.0ms (0% of total)

bsearch0.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.48009260203288967
1.9242833154775913
Compiler

Compiled 12 to 11 computations (8.3% saved)

derivations100.0ms (3.5%)

Memory
9.2MiB live, 111.3MiB allocated; 15ms collecting garbage
Stop Event
1×done
Compiler

Compiled 77 to 28 computations (63.6% saved)

preprocess50.0ms (1.7%)

Memory
3.5MiB live, 95.1MiB allocated; 9ms collecting garbage
Remove

(negabs x)

Compiler

Compiled 264 to 139 computations (47.3% saved)

end0.0ms (0%)

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

Profiling

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