Details

Time bar (total: 3.9s)

sample20.0ms

Algorithm
intervals
Results
10.0ms277×body80valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0217
1407
2567
3767
4907
5947
6947

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: 29.2b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.5b
(- (* b c) (* a d))
28.7b
(/ (- (* 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 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg fma-def frac-2neg fma-neg diff-log div-sub div-exp prod-diff clear-num sum-log div-inv
Counts
3 → 64
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)))

series157.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(+ (* c c) (* d d))
39.0ms
(- (* b c) (* a d))
89.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify39.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0314555
11341496
25001481

prune167.0ms

Filtered
73 candidates to 59 candidates (80.8%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New69473
Fresh000
Picked011
Done000
Total69574

Merged error: 11.7b

Counts
74 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (* (hypot c d) 1))
0.3b
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
0.5b
(- (* b c) (* a d))
15.0b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
83×add-exp-log
38×prod-exp
32×add-cbrt-cube
29×div-exp
28×add-sqr-sqrt
25×times-frac
23×add-cube-cbrt *-un-lft-identity
18×1-exp
13×associate-*r*
10×cbrt-undiv
9×pow1 rec-exp cbrt-unprod
7×associate-*l*
6×associate-/l* add-log-exp
4×expm1-log1p-u associate-/r* log1p-expm1-u div-inv
2×flip3-- pow-flip frac-2neg pow-prod-down clear-num flip-- associate-/l/ unswap-sqr
1×frac-times sub-neg fma-neg diff-log div-sub associate-*r/ prod-diff associate-*l/ *-commutative inv-pow
Counts
4 → 143
Calls
4 calls:
4.0ms
(/ 1 (* (hypot c d) 1))
12.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
3.0ms
(- (* b c) (* a d))
6.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series400.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ 1 (* (hypot c d) 1))
193.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
38.0ms
(- (* b c) (* a d))
115.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify63.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05531207
123041003
25001995

prune286.0ms

Filtered
155 candidates to 94 candidates (60.6%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1478155
Fresh123
Picked101
Done101
Total15010160

Merged error: 4.0b

Counts
160 → 10

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
0.5b
(- (* b c) (* a d))
15.0b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
53×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
10×add-exp-log add-cbrt-cube
6×associate-/r* div-inv
5×add-log-exp
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u div-sub log1p-expm1-u associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg fma-neg diff-log prod-diff
Counts
3 → 121
Calls
3 calls:
7.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
3.0ms
(- (* b c) (* a d))
6.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series265.0ms

Counts
3 → 9
Calls
3 calls:
112.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
40.0ms
(- (* b c) (* a d))
112.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify52.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04491408
116571307
250011298

prune275.0ms

Filtered
130 candidates to 97 candidates (74.6%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1246130
Fresh459
Picked101
Done000
Total12911140

Merged error: 4.0b

Counts
140 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 (/ (hypot c d) (- (* b c) (* a d)))) (hypot c d))
0.2b
(/ 1 (/ (hypot c d) (- (* b c) (* a d))))
0.5b
(- (* b c) (* a d))
15.0b
(/ (hypot c d) (- (* b c) (* a d)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
528×times-frac
255×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
56×associate-/l*
39×associate-/r/
36×add-exp-log
23×div-inv
22×div-exp
21×associate-/r*
20×add-cbrt-cube
18×flip3-- flip--
10×cbrt-undiv
6×add-log-exp
5×pow1
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u
3×frac-2neg clear-num
1×sub-neg pow-flip fma-neg diff-log prod-diff associate-/l/ inv-pow
Counts
4 → 359
Calls
4 calls:
15.0ms
(/ (/ 1 (/ (hypot c d) (- (* b c) (* a d)))) (hypot c d))
8.0ms
(/ 1 (/ (hypot c d) (- (* b c) (* a d))))
4.0ms
(- (* b c) (* a d))
5.0ms
(/ (hypot c d) (- (* b c) (* a d)))

series414.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(/ (/ 1 (/ (hypot c d) (- (* b c) (* a d)))) (hypot c d))
111.0ms
(/ 1 (/ (hypot c d) (- (* b c) (* a d))))
38.0ms
(- (* b c) (* a d))
89.0ms
(/ (hypot c d) (- (* b c) (* a d)))

simplify74.0ms

Algorithm
egg-herbie
Counts
371 → 371
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012945404
150024894

prune666.0ms

Filtered
371 candidates to 228 candidates (61.5%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New3701371
Fresh2810
Picked011
Done000
Total37210382

Merged error: 4.0b

Counts
382 → 10

regimes205.0ms

Accuracy

33.9% (8.3b remaining)

Error of 12.9b against oracle of 4.6b and baseline of 17.2b

bsearch142.0ms

Steps
ItersRangePoint
8
1.5184330169621066e+139
6.324854275423776e+142
4.6230231189603044e+141
9
4.60987506426565e+76
1.4293103507126414e+82
2.54946443013026e+79
7
4.563194349605498e-107
7.312504672026838e-106
6.698957894855029e-106
7
-8.906213487170025e+95
-3.3207123533803692e+94
-5.122757241376907e+95

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04130
14230
24230

end0.0ms

sample503.0ms

Algorithm
intervals
Results
299.0ms8490×body80valid

Profiling

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