Details

Time bar (total: 3.3s)

sample22.0ms

Algorithm
intervals
Results
12.0ms277×body80valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1367
2487
3667
4727
5727

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: 28.4b

Counts
2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.3b
(- (* b c) (* a d))
27.9b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
7×add-log-exp
5×add-exp-log add-cbrt-cube
3×pow1 associate-/r* associate-/l*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg frac-2neg diff-log div-sub div-exp clear-num sum-log div-inv
Counts
3 → 55
Calls
3 calls:
3.0ms
(+ (* c c) (* d d))
3.0ms
(- (* b c) (* a d))
7.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series154.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (* c c) (* d d))
39.0ms
(- (* b c) (* a d))
88.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify41.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0292541
11273493
25002491

prune169.0ms

Filtered
64 candidates to 50 candidates (78.1%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New56864
Fresh000
Picked011
Done000
Total56965

Merged error: 27.7b

Counts
65 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (* b c) (* a d))
16.4b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
30.8b
(sqrt (+ (* c c) (* d d)))
30.8b
(sqrt (+ (* c c) (* d d)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
6×pow1 add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
3×flip3-+ flip-+ associate-/l*
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-/r/ flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
4 → 86
Calls
4 calls:
3.0ms
(- (* b c) (* a d))
9.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
3.0ms
(sqrt (+ (* c c) (* d d)))
3.0ms
(sqrt (+ (* c c) (* d d)))

series224.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(- (* b c) (* a d))
112.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
39.0ms
(sqrt (+ (* c c) (* d d)))
35.0ms
(sqrt (+ (* c c) (* d d)))

simplify99.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0304910
1990857
23354845
35001845

prune230.0ms

Filtered
98 candidates to 75 candidates (76.5%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New94498
Fresh167
Picked101
Done011
Total9611107

Merged error: 24.8b

Counts
107 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (* b c) (* a d))
16.4b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
30.8b
(sqrt (+ (* c c) (* d d)))
30.8b
(sqrt (+ (* c c) (* d d)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
6×pow1 add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
3×flip3-+ flip-+ associate-/l*
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-/r/ flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
4 → 86
Calls
4 calls:
3.0ms
(- (* b c) (* a d))
8.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
3.0ms
(sqrt (+ (* c c) (* d d)))
3.0ms
(sqrt (+ (* c c) (* d d)))

series234.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* b c) (* a d))
112.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
40.0ms
(sqrt (+ (* c c) (* d d)))
36.0ms
(sqrt (+ (* c c) (* d d)))

simplify104.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0304910
1990857
23354845
35001845

prune242.0ms

Filtered
98 candidates to 75 candidates (76.5%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New98098
Fresh099
Picked011
Done011
Total9811109

Merged error: 24.8b

Counts
109 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

14.6b
(* (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))) (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))
17.1b
(cbrt (- (* b c) (* a d)))
17.1b
(cbrt (- (* b c) (* a d)))
17.1b
(cbrt (- (* b c) (* a d)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
30×cbrt-div
25×add-sqr-sqrt
24×associate-*r*
20×add-cube-cbrt *-un-lft-identity times-frac
19×cbrt-prod
16×add-exp-log frac-times
15×flip3-- flip--
12×associate-*l/
10×add-cbrt-cube
9×pow1
6×prod-exp cbrt-unprod
5×associate-*r/
4×add-log-exp
3×pow1/3 pow-prod-down unswap-sqr
2×cbrt-undiv div-exp associate-/r/
1×flip3-+ associate-*l* *-commutative flip-+ div-inv
Counts
4 → 102
Calls
4 calls:
19.0ms
(* (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))) (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))
3.0ms
(cbrt (- (* b c) (* a d)))
3.0ms
(cbrt (- (* b c) (* a d)))
3.0ms
(cbrt (- (* b c) (* a d)))

series439.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(* (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))) (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))
115.0ms
(cbrt (- (* b c) (* a d)))
119.0ms
(cbrt (- (* b c) (* a d)))
116.0ms
(cbrt (- (* b c) (* a d)))

simplify66.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
06191928
123631739
250011650

prune309.0ms

Filtered
114 candidates to 90 candidates (78.9%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New1140114
Fresh088
Picked011
Done022
Total11411125

Merged error: 24.8b

Counts
125 → 11

regimes239.0ms

Accuracy

22.7% (2.4b remaining)

Error of 25.5b against oracle of 23.1b and baseline of 26.2b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03027
13227
23227

end0.0ms

sample571.0ms

Algorithm
intervals
Results
361.0ms8502×body80valid