Details

Time bar (total: 6.8s)

sample74.0ms

Algorithm
intervals
Results
24.0ms238×body160nan
21.0ms495×body80nan
13.0ms256×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: 31.4b

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))))
29.2b
(sqrt (- (* x x) 1.0))

rewrite25.0ms

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:
9.0ms
(+ x (sqrt (- (* x x) 1.0)))
9.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
6.0ms
(sqrt (- (* x x) 1.0))

series513.0ms

Counts
3 → 9
Calls
3 calls:
64.0ms
(+ x (sqrt (- (* x x) 1.0)))
395.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
53.0ms
(sqrt (- (* x x) 1.0))

simplify36.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0339436
11140401
25001389

prune155.0ms

Pruning

2 alts after pruning (2 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))))

rewrite40.0ms

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
(+ 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))))))
34.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series632.0ms

Counts
3 → 9
Calls
3 calls:
150.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
287.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
195.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify48.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04671012
11665907
25001894

prune239.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

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)))
0.2b
(/ (pow (sqrt 1.0) 4) (pow x 4))
0.5b
(/ (* 1/4 1.0) (pow x 2))

rewrite65.0ms

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:
0.0ms
(fma 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)) (/ (* 1/4 1.0) (pow x 2)))
35.0ms
(- (- (log 2) (fma 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)) (/ (* 1/4 1.0) (pow x 2)))) (log (/ 1 x)))
8.0ms
(/ (pow (sqrt 1.0) 4) (pow x 4))
5.0ms
(/ (* 1/4 1.0) (pow x 2))

series470.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(fma 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)) (/ (* 1/4 1.0) (pow x 2)))
154.0ms
(- (- (log 2) (fma 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)) (/ (* 1/4 1.0) (pow x 2)))) (log (/ 1 x)))
104.0ms
(/ (pow (sqrt 1.0) 4) (pow x 4))
25.0ms
(/ (* 1/4 1.0) (pow x 2))

simplify118.0ms

Algorithm
egg-herbie
Counts
264 → 264
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
08293752
133942759
250022659

prune709.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt x) (cbrt x))
0.5b
(cbrt x)
0.5b
(cbrt x)
0.5b
(cbrt x)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
6.0ms
(* (cbrt x) (cbrt x))
0.0ms
(cbrt x)
0.0ms
(cbrt x)
1.0ms
(cbrt x)

series748.0ms

Counts
4 → 12
Calls
4 calls:
207.0ms
(* (cbrt x) (cbrt x))
178.0ms
(cbrt x)
185.0ms
(cbrt x)
178.0ms
(cbrt x)

simplify89.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
0119308
1477281
22972258
35001255

prune504.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes15.0ms

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
0139
1139

end0.0ms

sample2.2s

Algorithm
intervals
Results
705.0ms16487×body80nan
667.0ms7753×body160nan
424.0ms8000×body80valid