Details

Time bar (total: 3.9s)

sample36.0ms

Algorithm
intervals
Results
16.0ms285×body80valid
4.0ms94×body80nan

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

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: 27.4b

Counts
2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* z z) (* t a))
5.7b
(* (* x y) z)
11.1b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
26.9b
(sqrt (- (* z z) (* t a)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
11×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity
9×sqrt-prod
6×times-frac prod-exp associate-/r* cbrt-unprod add-log-exp
4×sqrt-div
3×cbrt-undiv flip3-- div-exp associate-*r* pow-prod-down flip--
2×associate-/r/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*l* clear-num *-commutative div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
4.0ms
(* (* x y) z)
9.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
3.0ms
(sqrt (- (* z z) (* t a)))

series191.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(- (* z z) (* t a))
22.0ms
(* (* x y) z)
79.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
60.0ms
(sqrt (- (* z z) (* t a)))

simplify51.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0346584
11863515
25002510

prune198.0ms

Filtered
88 candidates to 60 candidates (68.2%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New80888
Fresh000
Picked011
Done000
Total80989

Merged error: 3.8b

Counts
89 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
1.2b
(- (* z z) (* t a))
3.1b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
26.9b
(sqrt (- (* z z) (* t a)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
47×add-sqr-sqrt
46×add-cube-cbrt *-un-lft-identity
33×sqrt-prod
25×associate-/r*
18×add-exp-log add-cbrt-cube
7×cbrt-undiv div-exp associate-/l*
6×add-log-exp
5×pow1
4×sqrt-div div-inv
3×flip3-- flip--
2×frac-2neg prod-exp clear-num cbrt-unprod associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/r/
Counts
4 → 132
Calls
4 calls:
6.0ms
(/ (sqrt (- (* z z) (* t a))) z)
4.0ms
(- (* z z) (* t a))
9.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
3.0ms
(sqrt (- (* z z) (* t a)))

series240.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(/ (sqrt (- (* z z) (* t a))) z)
31.0ms
(- (* z z) (* t a))
79.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
60.0ms
(sqrt (- (* z z) (* t a)))

simplify63.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05191327
123801230
250011214

prune294.0ms

Filtered
144 candidates to 98 candidates (68.1%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1404144
Fresh257
Picked011
Done011
Total14211153

Merged error: 3.8b

Counts
153 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* z z) (* t a))
26.9b
(sqrt (- (* z z) (* t a)))
26.9b
(sqrt (- (* z z) (* t a)))
26.9b
(sqrt (- (* z z) (* t a)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div add-log-exp
4×add-exp-log flip3-- add-cbrt-cube flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg diff-log
Counts
4 → 57
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series208.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(- (* z z) (* t a))
60.0ms
(sqrt (- (* z z) (* t a)))
60.0ms
(sqrt (- (* z z) (* t a)))
56.0ms
(sqrt (- (* z z) (* t a)))

simplify51.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 3 (45.0ms)

IterNodesCost
0142423
1469403
21500397
35001394

prune265.0ms

Filtered
69 candidates to 55 candidates (79.7%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New69069
Fresh088
Picked011
Done022
Total691180

Merged error: 3.8b

Counts
80 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* z z) (* t a))
3.1b
(/ (* x y) (/ (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))) z))
26.9b
(sqrt (- (* z z) (* t a)))
26.9b
(sqrt (- (* z z) (* t a)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
13×times-frac
12×add-sqr-sqrt
10×cbrt-undiv add-cube-cbrt *-un-lft-identity div-exp
7×associate-/r*
6×pow1 sqrt-prod add-log-exp
5×prod-exp cbrt-unprod
4×sqrt-div
3×flip3-- flip-- div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg frac-2neg diff-log clear-num associate-/r/ associate-/l*
Counts
4 → 80
Calls
4 calls:
4.0ms
(- (* z z) (* t a))
14.0ms
(/ (* x y) (/ (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))) z))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series236.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* z z) (* t a))
81.0ms
(/ (* x y) (/ (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))) z))
57.0ms
(sqrt (- (* z z) (* t a)))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify49.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0405959
11934739
25001737

prune221.0ms

Filtered
92 candidates to 65 candidates (70.7%)
Pruning

11 alts after pruning (7 fresh and 4 done)

PrunedKeptTotal
New92092
Fresh077
Picked011
Done033
Total9211103

Merged error: 3.8b

Counts
103 → 11

regimes509.0ms

Accuracy

87.3% (2.3b remaining)

Error of 5.9b against oracle of 3.5b and baseline of 21.8b

bsearch104.0ms

Steps
ItersRangePoint
7
5.376678376664494e+124
1.091924279238501e+126
7.819156595013911e+125
11
-6.092583856546455e+156
-2.986567729303712e+135
-1.8368805238595863e+147

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03228
13828
23828

end0.0ms

sample1.0s

Algorithm
intervals
Results
465.0ms8830×body80valid
148.0ms2891×body80nan