Details

Time bar (total: 13.1s)

sample16.0ms

Algorithm
intervals
Results
7.0ms274×body80valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0215
1404
2694
31044
41464
51604
61604

prune5.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 4.9b

Counts
2 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

3.0b
(/ (/ (/ 1.0 x) (fma z z 1.0)) y)
3.9b
(/ (/ 1.0 x) (fma z z 1.0))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
468×times-frac
228×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
56×associate-/l*
22×div-inv
16×add-exp-log add-cbrt-cube
9×cbrt-undiv div-exp
6×associate-/r*
2×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u associate-/l/ add-log-exp
Counts
2 → 266
Calls
2 calls:
16.0ms
(/ (/ (/ 1.0 x) (fma z z 1.0)) y)
6.0ms
(/ (/ 1.0 x) (fma z z 1.0))

series125.0ms

Counts
2 → 6
Calls
2 calls:
64.0ms
(/ (/ (/ 1.0 x) (fma z z 1.0)) y)
61.0ms
(/ (/ 1.0 x) (fma z z 1.0))

simplify114.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
011482808
146382733
250022733

prune753.0ms

Filtered
272 candidates to 237 candidates (87.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2648272
Fresh101
Picked101
Done000
Total2668274

Merged error: 4.8b

Counts
274 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (/ (cbrt 1.0) (/ (sqrt (fma z z 1.0)) (cbrt 1.0))) (/ (/ (/ (cbrt 1.0) x) (sqrt (fma z z 1.0))) y))
2.5b
(/ (/ (/ (cbrt 1.0) x) (sqrt (fma z z 1.0))) y)
16.6b
(sqrt (fma z z 1.0))
16.6b
(sqrt (fma z z 1.0))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
3283×times-frac
1881×add-sqr-sqrt
1372×add-cube-cbrt *-un-lft-identity
700×cbrt-prod
641×sqrt-prod
412×associate-*r*
245×associate-*l*
136×associate-/l*
88×unswap-sqr
67×add-exp-log
58×div-inv
51×add-cbrt-cube
36×cbrt-undiv div-exp
12×prod-exp cbrt-unprod
8×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num associate-/r/ *-commutative associate-/l/
Counts
4 → 1379
Calls
4 calls:
1.2s
(* (/ (cbrt 1.0) (/ (sqrt (fma z z 1.0)) (cbrt 1.0))) (/ (/ (/ (cbrt 1.0) x) (sqrt (fma z z 1.0))) y))
33.0ms
(/ (/ (/ (cbrt 1.0) x) (sqrt (fma z z 1.0))) y)
2.0ms
(sqrt (fma z z 1.0))
2.0ms
(sqrt (fma z z 1.0))

series364.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(* (/ (cbrt 1.0) (/ (sqrt (fma z z 1.0)) (cbrt 1.0))) (/ (/ (/ (cbrt 1.0) x) (sqrt (fma z z 1.0))) y))
116.0ms
(/ (/ (/ (cbrt 1.0) x) (sqrt (fma z z 1.0))) y)
54.0ms
(sqrt (fma z z 1.0))
52.0ms
(sqrt (fma z z 1.0))

simplify288.0ms

Algorithm
egg-herbie
Counts
1391 → 1391
Iterations

Useful iterations: 1 (77.0ms)

IterNodesCost
0495323381
1500123377

prune5.0s

Filtered
1391 candidates to 1086 candidates (78.1%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New138831391
Fresh347
Picked101
Done000
Total139271399

Merged error: 4.8b

Counts
1399 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 (sqrt (fma z z 1.0))) y)
0.8b
(* (/ (* (cbrt 1.0) (/ (cbrt 1.0) x)) (/ (sqrt (fma z z 1.0)) (cbrt 1.0))) (/ (/ 1 (sqrt (fma z z 1.0))) y))
16.6b
(sqrt (fma z z 1.0))
16.6b
(sqrt (fma z z 1.0))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
343×times-frac
193×add-exp-log
190×add-sqr-sqrt
171×*-un-lft-identity
169×add-cube-cbrt
103×div-exp
90×add-cbrt-cube
89×sqrt-prod
70×associate-*r*
57×cbrt-undiv
55×prod-exp
45×associate-*l*
33×cbrt-unprod
22×associate-/l*
18×cbrt-prod
11×div-inv
8×pow1 rec-exp 1-exp
6×unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num associate-/r/ *-commutative associate-/l/
Counts
4 → 331
Calls
4 calls:
9.0ms
(/ (/ 1 (sqrt (fma z z 1.0))) y)
72.0ms
(* (/ (* (cbrt 1.0) (/ (cbrt 1.0) x)) (/ (sqrt (fma z z 1.0)) (cbrt 1.0))) (/ (/ 1 (sqrt (fma z z 1.0))) y))
2.0ms
(sqrt (fma z z 1.0))
2.0ms
(sqrt (fma z z 1.0))

series401.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(/ (/ 1 (sqrt (fma z z 1.0))) y)
142.0ms
(* (/ (* (cbrt 1.0) (/ (cbrt 1.0) x)) (/ (sqrt (fma z z 1.0)) (cbrt 1.0))) (/ (/ 1 (sqrt (fma z z 1.0))) y))
56.0ms
(sqrt (fma z z 1.0))
57.0ms
(sqrt (fma z z 1.0))

simplify77.0ms

Algorithm
egg-herbie
Counts
343 → 343
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
015984670
150024111

prune846.0ms

Filtered
343 candidates to 200 candidates (58.3%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New3430343
Fresh066
Picked011
Done000
Total3437350

Merged error: 4.8b

Counts
350 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (* (cbrt 1.0) (/ (/ (/ (cbrt 1.0) x) (sqrt (fma z z 1.0))) y)) (/ (sqrt (fma z z 1.0)) (cbrt 1.0)))
2.5b
(/ (/ (/ (cbrt 1.0) x) (sqrt (fma z z 1.0))) y)
16.6b
(sqrt (fma z z 1.0))
16.6b
(sqrt (fma z z 1.0))

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
1480×times-frac
687×add-sqr-sqrt
685×add-cube-cbrt *-un-lft-identity
306×sqrt-prod
252×cbrt-prod
137×associate-/l*
58×add-exp-log
43×associate-/r*
42×add-cbrt-cube
33×cbrt-undiv div-exp
32×div-inv
8×prod-exp cbrt-unprod
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
1×associate-*r/ associate-/r/
Counts
4 → 711
Calls
4 calls:
48.0ms
(/ (* (cbrt 1.0) (/ (/ (/ (cbrt 1.0) x) (sqrt (fma z z 1.0))) y)) (/ (sqrt (fma z z 1.0)) (cbrt 1.0)))
36.0ms
(/ (/ (/ (cbrt 1.0) x) (sqrt (fma z z 1.0))) y)
2.0ms
(sqrt (fma z z 1.0))
2.0ms
(sqrt (fma z z 1.0))

series386.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(/ (* (cbrt 1.0) (/ (/ (/ (cbrt 1.0) x) (sqrt (fma z z 1.0))) y)) (/ (sqrt (fma z z 1.0)) (cbrt 1.0)))
117.0ms
(/ (/ (/ (cbrt 1.0) x) (sqrt (fma z z 1.0))) y)
57.0ms
(sqrt (fma z z 1.0))
62.0ms
(sqrt (fma z z 1.0))

simplify150.0ms

Algorithm
egg-herbie
Counts
723 → 723
Iterations

Useful iterations: 1 (48.0ms)

IterNodesCost
0273510904
1500110552

prune2.2s

Filtered
723 candidates to 495 candidates (68.5%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New7230723
Fresh055
Picked011
Done011
Total7237730

Merged error: 4.8b

Counts
730 → 7

regimes130.0ms

Accuracy

0% (1.1b remaining)

Error of 5.9b against oracle of 4.8b and baseline of 5.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01914
11914

end0.0ms

sample428.0ms

Algorithm
intervals
Results
242.0ms8629×body80valid