Details

Time bar (total: 4.5s)

sample42.0ms

Algorithm
intervals
Results
11.0ms244×body160nan
9.0ms490×body80nan
7.0ms256×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0115
1125
2125

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(log (+ x (sqrt (- (* x x) 1.0))))
0.0b
(+ x (sqrt (- (* x x) 1.0)))
28.5b
(sqrt (- (* x x) 1.0))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-sqr-sqrt
6×add-cube-cbrt
5×pow1 add-log-exp
4×add-exp-log log-prod sqrt-prod
3×expm1-log1p-u fma-def add-cbrt-cube log1p-expm1-u
2×log-div flip3-+ sqrt-div flip-+ distribute-lft-out
1×+-commutative rem-sqrt-square flip3-- sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow flip-- difference-of-squares
Counts
3 → 52
Calls
3 calls:
6.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
6.0ms
(+ x (sqrt (- (* x x) 1.0)))
5.0ms
(sqrt (- (* x x) 1.0))

series313.0ms

Counts
3 → 9
Calls
3 calls:
191.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
67.0ms
(+ x (sqrt (- (* x x) 1.0)))
55.0ms
(sqrt (- (* x x) 1.0))

simplify34.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0339436
11140401
25001389

prune152.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.0b
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.5b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
15×sqrt-prod
13×*-un-lft-identity
12×sqrt-div
9×add-cube-cbrt associate-*r*
8×pow1
7×associate-*l*
6×add-exp-log
5×flip3-+ add-cbrt-cube flip-+ add-log-exp
4×frac-times unswap-sqr
3×expm1-log1p-u log-prod flip3-- fma-def pow-prod-down flip-- log1p-expm1-u
2×log-div sqrt-pow1 pow1/2 associate-*r/ associate-*l/ difference-of-squares
1×+-commutative sqrt-unprod rem-log-exp prod-exp sum-log log-pow *-commutative cbrt-unprod distribute-lft-out distribute-lft-out--
Counts
3 → 76
Calls
3 calls:
2.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
3.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
12.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series647.0ms

Counts
3 → 9
Calls
3 calls:
289.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
153.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
204.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify46.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04671012
11665907
25001894

prune249.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))
0.0b
(log (exp (log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))))
0.1b
(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
5.8b
(exp (log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
15×log-prod
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
8×pow1 exp-prod log-pow
6×exp-sum
5×add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×rem-log-exp
1×fma-udef rem-exp-log
Counts
4 → 62
Calls
4 calls:
1.0ms
(log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))
3.0ms
(log (exp (log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))))
1.0ms
(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
2.0ms
(exp (log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)))

series1.3s

Counts
4 → 12
Calls
4 calls:
421.0ms
(log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))
429.0ms
(log (exp (log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))))
251.0ms
(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
248.0ms
(exp (log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)))

simplify45.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
03771057
11242932
25002884

prune236.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes13.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0139
1139

end0.0ms

sample1.3s

Algorithm
intervals
Results
348.0ms7745×body160nan
331.0ms16329×body80nan
228.0ms8000×body80valid