Details

Time bar (total: 4.2s)

sample62.0ms

Algorithm
intervals
Results
37.0ms80×body1280valid
9.0ms46×body640valid
3.0ms30×body320valid
2.0ms87×body80valid
2.0ms103×body80nan
1.0ms13×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
052
152

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 39.5b

Counts
2 → 1

localize7.0ms

Local error

Found 1 expressions with local error:

3.9b
(log (+ 1.0 x))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
4×log-prod *-un-lft-identity
2×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt log-div
1×expm1-log1p-u flip3-+ rem-log-exp log-pow add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out add-log-exp
Counts
1 → 17
Calls
1 calls:
3.0ms
(log (+ 1.0 x))

series44.0ms

Counts
1 → 3
Calls
1 calls:
44.0ms
(log (+ 1.0 x))

simplify40.0ms

Algorithm
egg-herbie
Counts
20 → 20
Iterations

Useful iterations: 3 (37.0ms)

IterNodesCost
013199
136389
2129286
3500281

prune43.0ms

Filtered
20 candidates to 15 candidates (75.0%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New18220
Fresh000
Picked011
Done000
Total18321

Merged error: 0.1b

Counts
21 → 3

localize10.0ms

Local error

Found 1 expressions with local error:

0.0b
(* 1/2 (/ (pow x 2) (pow 1.0 2)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
80×times-frac
69×add-sqr-sqrt
68×associate-*r*
56×unpow-prod-down
35×add-cube-cbrt *-un-lft-identity
24×add-exp-log unpow2 sqr-pow
17×unswap-sqr
10×prod-exp
9×div-exp
6×pow-to-exp pow-exp add-cbrt-cube
3×pow1 associate-*l*
2×cbrt-unprod
1×cbrt-undiv expm1-log1p-u associate-*r/ pow-prod-down *-commutative log1p-expm1-u div-inv add-log-exp
Counts
1 → 112
Calls
1 calls:
20.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))

series57.0ms

Counts
1 → 3
Calls
1 calls:
56.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))

simplify56.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0535648
12311536
25001535

prune216.0ms

Filtered
115 candidates to 70 candidates (60.9%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1150115
Fresh011
Picked011
Done011
Total1153118

Merged error: 0.1b

Counts
118 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* 1.0 1.0) (* x x))
0.0b
(- (log (- (* 1.0 1.0) (* x x))) (log (- 1.0 x)))
1.6b
(log (- (* 1.0 1.0) (* x x)))
3.9b
(log (- 1.0 x))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
23×add-sqr-sqrt
19×pow1
18×log-prod
17×add-cube-cbrt prod-diff
15×log-pow
8×log-div
6×add-exp-log flip3-- flip-- distribute-lft-out-- add-log-exp difference-of-squares
5×fma-neg associate--r+
4×expm1-log1p-u associate--l+ add-cbrt-cube log1p-expm1-u
2×associate--l- sub-neg diff-log rem-log-exp associate--r-
Counts
4 → 104
Calls
4 calls:
4.0ms
(- (* 1.0 1.0) (* x x))
13.0ms
(- (log (- (* 1.0 1.0) (* x x))) (log (- 1.0 x)))
4.0ms
(log (- (* 1.0 1.0) (* x x)))
4.0ms
(log (- 1.0 x))

series313.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(- (* 1.0 1.0) (* x x))
114.0ms
(- (log (- (* 1.0 1.0) (* x x))) (log (- 1.0 x)))
116.0ms
(log (- (* 1.0 1.0) (* x x)))
43.0ms
(log (- 1.0 x))

simplify57.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04481111
11512811
25001717

prune215.0ms

Filtered
116 candidates to 82 candidates (70.7%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1142116
Fresh000
Picked101
Done022
Total1154119

Merged error: 0.0b

Counts
119 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b
(fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))
9.2b
(fma 1/3 (/ (pow x 3) (pow 1.0 3)) (- (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (* 1.0 (pow x 2))))
11.6b
(- (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (* 1.0 (pow x 2)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
80×times-frac
74×add-sqr-sqrt
68×associate-*r*
56×unpow-prod-down
40×add-cube-cbrt *-un-lft-identity
27×add-exp-log
24×unpow2 sqr-pow
17×unswap-sqr
10×prod-exp
9×div-exp add-cbrt-cube
6×pow1 pow-to-exp pow-exp add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×fma-neg associate-*l* prod-diff fma-udef
2×cbrt-unprod
1×cbrt-undiv sub-neg flip3-- diff-log associate-*r/ pow-prod-down associate--l+ *-commutative flip-- div-inv
Counts
4 → 153
Calls
4 calls:
19.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
1.0ms
(fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))
1.0ms
(fma 1/3 (/ (pow x 3) (pow 1.0 3)) (- (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (* 1.0 (pow x 2))))
3.0ms
(- (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (* 1.0 (pow x 2)))

series566.0ms

Counts
4 → 12
Calls
4 calls:
254.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
96.0ms
(fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))
69.0ms
(fma 1/3 (/ (pow x 3) (pow 1.0 3)) (- (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (* 1.0 (pow x 2))))
147.0ms
(- (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (* 1.0 (pow x 2)))

simplify76.0ms

Algorithm
egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06791241
13327998
25002995

prune459.0ms

Filtered
165 candidates to 111 candidates (67.3%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1641165
Fresh011
Picked101
Done022
Total1654169

Merged error: 0.0b

Counts
169 → 4

regimes79.0ms

Accuracy

99.1% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 21.3b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01810
11810

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.0s2234×body1280valid
364.0ms1683×body640valid
101.0ms896×body320valid
62.0ms2774×body80valid
38.0ms2702×body80nan
27.0ms413×body160valid