Details

Time bar (total: 3.2s)

sample24.0ms

Algorithm
intervals
Results
12.0ms272×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: 24.1b

Counts
2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.2b
(- (* b c) (* a d))
23.7b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite16.0ms

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))
3.0ms
(- (* b c) (* a d))
8.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series150.0ms

Counts
3 → 9
Calls
3 calls:
25.0ms
(+ (* c c) (* d d))
40.0ms
(- (* b c) (* a d))
84.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify37.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0292541
11273493
25001491

prune167.0ms

Filtered
64 candidates to 50 candidates (78.1%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New55964
Fresh000
Picked101
Done000
Total56965

Merged error: 23.4b

Counts
65 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b c) (* a d))
15.8b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
26.2b
(sqrt (+ (* c c) (* d d)))
26.2b
(sqrt (+ (* c c) (* d d)))

rewrite22.0ms

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)))

series220.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(- (* b c) (* a d))
109.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
34.0ms
(sqrt (+ (* c c) (* d d)))
37.0ms
(sqrt (+ (* c c) (* d d)))

simplify96.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0304910
1990857
23340845
35003845

prune242.0ms

Filtered
98 candidates to 75 candidates (76.5%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New95398
Fresh178
Picked011
Done000
Total9611107

Merged error: 20.7b

Counts
107 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))))
15.8b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
26.2b
(sqrt (+ (* c c) (* d d)))
26.2b
(sqrt (+ (* c c) (* d d)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
28×add-exp-log
24×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
10×sqrt-div
9×div-exp
8×pow1 prod-exp
6×associate-/r* associate-/r/
5×cbrt-undiv flip3-+ flip-+
4×cbrt-unprod add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-/l/
1×frac-times flip3-- frac-2neg div-sub associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative flip--
Counts
4 → 161
Calls
4 calls:
28.0ms
(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (- (* b c) (* a 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)))

series315.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))))
109.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
38.0ms
(sqrt (+ (* c c) (* d d)))
34.0ms
(sqrt (+ (* c c) (* d d)))

simplify77.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
05822518
126382255
250012130

prune354.0ms

Filtered
173 candidates to 112 candidates (64.7%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1721173
Fresh099
Picked011
Done011
Total17212184

Merged error: 20.7b

Counts
184 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.0b
(- (/ (* b c) (+ (* c c) (* d d))) (/ (* a d) (+ (* c c) (* d d))))
15.6b
(/ (* a d) (+ (* c c) (* d d)))
16.5b
(/ (* b c) (+ (* c c) (* d d)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
10×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt associate-/r/ add-log-exp
6×times-frac associate-/r*
5×flip3-+ flip-+
4×pow1 cbrt-undiv div-exp div-inv
3×distribute-rgt-out--
2×frac-2neg prod-exp clear-num cbrt-unprod associate-/l*
1×+-commutative sub-neg flip3-- diff-log sum-log frac-sub flip-- distribute-lft-out-- sub-div difference-of-squares
Counts
4 → 76
Calls
4 calls:
4.0ms
(+ (* c c) (* d d))
13.0ms
(- (/ (* b c) (+ (* c c) (* d d))) (/ (* a d) (+ (* c c) (* d d))))
6.0ms
(/ (* a d) (+ (* c c) (* d d)))
6.0ms
(/ (* b c) (+ (* c c) (* d d)))

series235.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(+ (* c c) (* d d))
117.0ms
(- (/ (* b c) (+ (* c c) (* d d))) (/ (* a d) (+ (* c c) (* d d))))
43.0ms
(/ (* a d) (+ (* c c) (* d d)))
46.0ms
(/ (* b c) (+ (* c c) (* d d)))

simplify45.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0385746
11875664
25002660

prune179.0ms

Filtered
88 candidates to 65 candidates (73.9%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New84488
Fresh639
Picked101
Done112
Total928100

Merged error: 18.9b

Counts
100 → 8

regimes169.0ms

Accuracy

66.4% (0.9b remaining)

Error of 23.0b against oracle of 22.1b and baseline of 24.7b

bsearch70.0ms

Steps
ItersRangePoint
6
1.4692372860321438e+56
1.5715651896237286e+57
9.046605254534478e+56
6
-4.2568175387433725e+35
-5.141442709397297e+34
-1.9332834244083665e+35

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03728
13728

end0.0ms

sample618.0ms

Algorithm
intervals
Results
398.0ms8478×body80valid

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