Details

Time bar (total: 3.4s)

analyze532.0ms

Algorithm
search

sample25.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
1.0ms16×body80invalid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1367
2487
3667
4727
5727

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 24.6b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.0b
(- (* b c) (* a d))
24.2b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite17.0ms

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:
4.0ms
(+ (* c c) (* d d))
4.0ms
(- (* b c) (* a d))
8.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series44.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ (* c c) (* d d))
10.0ms
(- (* b c) (* a d))
28.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify42.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0292541
11273493
25001491

prune112.0ms

Filtered
50 candidates to 64 candidates (-28.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New56864
Fresh000
Picked101
Done000
Total57865

Merged error: 23.8b

Counts
65 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
14.5b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
28.5b
(sqrt (+ (* c c) (* d d)))
28.5b
(sqrt (+ (* c c) (* d d)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
164×add-sqr-sqrt
162×add-cube-cbrt *-un-lft-identity
156×sqrt-prod
27×associate-/l*
22×sqrt-div
18×associate-/r/
12×associate-/r*
11×add-exp-log flip3-+ add-cbrt-cube flip-+
9×div-inv
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×div-sub associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×flip3-- flip--
Counts
4 → 266
Calls
4 calls:
16.0ms
(/ (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
9.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
3.0ms
(sqrt (+ (* c c) (* d d)))
4.0ms
(sqrt (+ (* c c) (* d d)))

series80.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
40.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
6.0ms
(sqrt (+ (* c c) (* d d)))
6.0ms
(sqrt (+ (* c c) (* d d)))

simplify100.0ms

Algorithm
egg-herbie
Counts
278 → 278
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
07455703
128885224
250015172

prune196.0ms

Filtered
148 candidates to 278 candidates (-87.8%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2735278
Fresh437
Picked011
Done000
Total2779286

Merged error: 22.6b

Counts
286 → 9

localize30.0ms

Local error

Found 4 expressions with local error:

14.5b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
28.5b
(sqrt (+ (* c c) (* d d)))
28.5b
(sqrt (+ (* c c) (* d d)))
28.5b
(sqrt (+ (* c c) (* d d)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
21×sqrt-prod
18×times-frac
8×sqrt-div
7×pow1
6×add-exp-log associate-/r* add-cbrt-cube
4×flip3-+ flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l*
2×associate-/r/ associate-/l/
1×cbrt-undiv flip3-- frac-2neg div-sub div-exp clear-num flip-- div-inv
Counts
4 → 89
Calls
4 calls:
10.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
3.0ms
(sqrt (+ (* c c) (* d d)))
4.0ms
(sqrt (+ (* c c) (* d d)))
4.0ms
(sqrt (+ (* c c) (* d d)))

series55.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
6.0ms
(sqrt (+ (* c c) (* d d)))
6.0ms
(sqrt (+ (* c c) (* d d)))
6.0ms
(sqrt (+ (* c c) (* d d)))

simplify85.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
0269932
1854883
22635870
35001870

prune119.0ms

Filtered
79 candidates to 101 candidates (-27.8%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1010101
Fresh077
Picked011
Done011
Total1019110

Merged error: 22.6b

Counts
110 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

15.0b
(cbrt (- (* b c) (* a d)))
15.0b
(cbrt (- (* b c) (* a d)))
15.0b
(cbrt (- (* b c) (* a d)))
15.7b
(* (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))) (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))

rewrite34.0ms

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:
3.0ms
(cbrt (- (* b c) (* a d)))
3.0ms
(cbrt (- (* b c) (* a d)))
3.0ms
(cbrt (- (* b c) (* a d)))
21.0ms
(* (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))) (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))

series146.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(cbrt (- (* b c) (* a d)))
40.0ms
(cbrt (- (* b c) (* a d)))
38.0ms
(cbrt (- (* b c) (* a d)))
31.0ms
(* (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))) (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))

simplify73.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
06161940
123811751
250011668

prune117.0ms

Filtered
92 candidates to 114 candidates (-23.9%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1140114
Fresh066
Picked011
Done022
Total1149123

Merged error: 22.6b

Counts
123 → 9

regimes309.0ms

Accuracy

0% (3.0b remaining)

Error of 26.6b against oracle of 23.7b and baseline of 26.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01613
11613

end0.0ms

analyze526.0ms

Algorithm
search

sample594.0ms

Algorithm
intervals
Results
358.0ms8000×body80valid
21.0ms481×body80invalid

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