Details

Time bar (total: 5.3s)

sample45.0ms

Algorithm
intervals
Results
11.0ms473×body80nan
10.0ms256×body80valid
10.0ms206×body160nan

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0115
1125
2125

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
0.2b
(log (+ x (sqrt (- (* x x) 1.0))))
28.6b
(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
(+ x (sqrt (- (* x x) 1.0)))
6.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
5.0ms
(sqrt (- (* x x) 1.0))

series314.0ms

Counts
3 → 9
Calls
3 calls:
69.0ms
(+ x (sqrt (- (* x x) 1.0)))
190.0ms
(log (+ 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

prune167.0ms

Filtered
61 candidates to 53 candidates (86.9%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.2b
(log (+ 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:
3.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
2.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
12.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series636.0ms

Counts
3 → 9
Calls
3 calls:
149.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
282.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
205.0ms
(* (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

prune256.0ms

Filtered
85 candidates to 69 candidates (81.2%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b
(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
0.2b
(log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
3×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt log-prod *-un-lft-identity
2×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
1×rem-log-exp log-pow fma-udef
Counts
2 → 24
Calls
2 calls:
1.0ms
(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
1.0ms
(log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))

series713.0ms

Counts
2 → 6
Calls
2 calls:
281.0ms
(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
432.0ms
(log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))

simplify38.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0334452
11176394
25001379

prune115.0ms

Filtered
30 candidates to 26 candidates (86.7%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)) (/ (* 1/4 1.0) (pow x 2)))
0.2b
(- (- (log 2) (fma 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)) (/ (* 1/4 1.0) (pow x 2)))) (log (/ 1 x)))
0.6b
(/ (* 1/4 1.0) (pow x 2))
0.9b
(/ (pow (sqrt 1.0) 4) (pow x 4))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
114×*-un-lft-identity
98×add-sqr-sqrt
87×unpow-prod-down times-frac
82×add-cube-cbrt
48×prod-diff
33×log-pow
31×pow1
29×add-exp-log
24×sqrt-prod distribute-lft-out--
21×sqr-pow
20×associate--l+
16×log-prod
15×div-exp associate-/r*
13×associate--r+
11×add-cbrt-cube associate-/l*
8×pow-to-exp pow-exp difference-of-squares
6×pow-flip fma-neg inv-pow add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv diff-log prod-exp div-inv
2×sub-neg frac-2neg clear-num unpow2
1×associate--l- log-div flip3-- flip-- cbrt-unprod fma-udef associate--r-
Counts
4 → 252
Calls
4 calls:
1.0ms
(fma 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)) (/ (* 1/4 1.0) (pow x 2)))
13.0ms
(- (- (log 2) (fma 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)) (/ (* 1/4 1.0) (pow x 2)))) (log (/ 1 x)))
9.0ms
(/ (* 1/4 1.0) (pow x 2))
7.0ms
(/ (pow (sqrt 1.0) 4) (pow x 4))

series644.0ms

Counts
4 → 12
Calls
4 calls:
364.0ms
(fma 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)) (/ (* 1/4 1.0) (pow x 2)))
147.0ms
(- (- (log 2) (fma 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)) (/ (* 1/4 1.0) (pow x 2)))) (log (/ 1 x)))
30.0ms
(/ (* 1/4 1.0) (pow x 2))
102.0ms
(/ (pow (sqrt 1.0) 4) (pow x 4))

simplify103.0ms

Algorithm
egg-herbie
Counts
264 → 264
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
08293752
133972750
250012648

prune676.0ms

Filtered
264 candidates to 142 candidates (53.8%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes14.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0158
1178
2178

end0.0ms

sample1.3s

Algorithm
intervals
Results
369.0ms15807×body80nan
358.0ms7453×body160nan
232.0ms8000×body80valid