Details

sample51.0ms

Algorithm

intervals

Results

28.0ms

287×

body

valid

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	62	11
1	132	11
2	377	10
3	1105	10
4	3599	10
5	5001	10

prune15.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 32.2b

Counts

2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma z 3.13060547623 11.1667541262) z t)
0.1b	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
1.7b	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
31.2b	(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b) x)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `fma-udef` `associate-/l`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 59

Calls

4 calls:

1.0ms	(fma (fma z 3.13060547623 11.1667541262) z t)
1.0ms	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
3.0ms	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.0ms	(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b) x)

series913.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(fma (fma z 3.13060547623 11.1667541262) z t)
40.0ms	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
112.0ms	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
732.0ms	(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b) x)

simplify105.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	270	563
1	830	501
2	3551	493
3	5002	491

prune383.0ms

Filtered

71 candidates to 60 candidates (84.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	65	6	71
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	65	8	73

Merged error: 0.5b

Counts

73 → 8

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 3.13060547623 (/ t (pow z 2)))
3.8b	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
9.3b	(/ t (pow z 2))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
23×	`*-un-lft-identity`
21×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`unpow-prod-down`
8×	`add-exp-log` `associate-/r*`
5×	`add-cbrt-cube` `add-log-exp`
4×	`unpow2` `sqr-pow`
3×	`pow1` `expm1-log1p-u` `fma-def` `div-exp` `log1p-expm1-u` `associate-/l*`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `frac-2neg` `flip3-+` `pow-exp` `clear-num` `sum-log` `flip-+` `fma-udef` `div-inv` `distribute-lft-out`

Counts

3 → 78

Calls

3 calls:

9.0ms	(+ 3.13060547623 (/ t (pow z 2)))
1.0ms	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
5.0ms	(/ t (pow z 2))

series104.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ 3.13060547623 (/ t (pow z 2)))
54.0ms	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
23.0ms	(/ t (pow z 2))

simplify136.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (128.0ms)

Iter	Nodes	Cost
0	255	414
1	847	369
2	4454	360
3	5001	359

prune229.0ms

Filtered

87 candidates to 59 candidates (67.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	82	5	87
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	84	11	95

Merged error: 0.5b

Counts

95 → 11

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 3.13060547623 (/ (/ t z) z))
0.2b	(/ (/ t z) z)
3.8b	(fma y (+ 3.13060547623 (/ (/ t z) z)) x)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
48×	`*-un-lft-identity`
46×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`associate-/l*`
8×	`add-exp-log` `add-cbrt-cube`
5×	`div-inv` `add-log-exp`
3×	`pow1` `cbrt-undiv` `expm1-log1p-u` `fma-def` `div-exp` `associate-/r*` `log1p-expm1-u`
1×	`+-commutative` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+` `fma-udef` `associate-/l/` `distribute-lft-out`

Counts

3 → 99

Calls

3 calls:

12.0ms	(+ 3.13060547623 (/ (/ t z) z))
6.0ms	(/ (/ t z) z)
1.0ms	(fma y (+ 3.13060547623 (/ (/ t z) z)) x)

series105.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ 3.13060547623 (/ (/ t z) z))
22.0ms	(/ (/ t z) z)
54.0ms	(fma y (+ 3.13060547623 (/ (/ t z) z)) x)

simplify46.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	415	619
1	1504	567
2	5001	560

prune257.0ms

Filtered

108 candidates to 79 candidates (73.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	108	11	119

Merged error: 0.5b

Counts

119 → 11

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 3.13060547623 (/ t (pow z 2)))
0.0b	(+ (* y (+ 3.13060547623 (/ t (pow z 2)))) x)
3.8b	(* y (+ 3.13060547623 (/ t (pow z 2))))
9.3b	(/ t (pow z 2))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `times-frac`
12×	`unpow-prod-down`
11×	`add-exp-log`
8×	`associate-/r*` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
4×	`expm1-log1p-u` `fma-def` `associate-r` `log1p-expm1-u` `unpow2` `sqr-pow`
3×	`flip3-+` `div-exp` `associate-l` `flip-+` `associate-/l*`
2×	`+-commutative` `distribute-rgt-in` `associate-+l+` `distribute-lft-in` `associate-*r/` `sum-log` `distribute-lft-out`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 109

Calls

4 calls:

10.0ms	(+ 3.13060547623 (/ t (pow z 2)))
13.0ms	(+ (* y (+ 3.13060547623 (/ t (pow z 2)))) x)
12.0ms	(* y (+ 3.13060547623 (/ t (pow z 2))))
5.0ms	(/ t (pow z 2))

series159.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ 3.13060547623 (/ t (pow z 2)))
59.0ms	(+ (* y (+ 3.13060547623 (/ t (pow z 2)))) x)
45.0ms	(* y (+ 3.13060547623 (/ t (pow z 2))))
27.0ms	(/ t (pow z 2))

simplify49.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	385	614
1	1539	561
2	5001	552

prune235.0ms

Filtered

121 candidates to 82 candidates (67.8%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	121	11	132

Merged error: 0.5b

Counts

132 → 11

regimes943.0ms

Accuracy

96.6% (0.9b remaining)

Error of 1.3b against oracle of 0.4b and baseline of 26.6b

bsearch240.0ms

Steps

Iters	Range		Point
9	5.011416382658859e+47	6.660481980169663e+54	2.4092092336166706e+50
8	-4.439562019202243e+67	-2.457675435220466e+63	-2.50316192346756e+63

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	19
1	43	19

end0.0ms

sample1.1s

Algorithm

intervals

Results

792.0ms

8896×

body

valid