Details

sample53.0ms

Algorithm

intervals

Results

32.0ms

278×

body

valid

simplify62.0ms

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

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)
0.0b	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
1.3b	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
26.7b	(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)

rewrite4.0ms

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:

0.0ms	(fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)
0.0ms	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
2.0ms	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
0.0ms	(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)

series925.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)
35.0ms	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
118.0ms	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
714.0ms	(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)

simplify113.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (104.0ms)

Iter	Nodes	Cost
0	274	590
1	845	530
2	3490	520
3	5001	517

prune419.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 3.13060547623 (/ t (pow z 2)))
4.4b	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
9.9b	(/ t (pow z 2))

rewrite18.0ms

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:

12.0ms	(+ 3.13060547623 (/ t (pow z 2)))
0.0ms	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
4.0ms	(/ t (pow z 2))

series110.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ 3.13060547623 (/ t (pow z 2)))
51.0ms	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
26.0ms	(/ t (pow z 2))

simplify142.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (135.0ms)

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

prune242.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 3.13060547623 (* (/ 1 z) (/ t z)))
0.2b	(* (/ 1 z) (/ t z))
4.4b	(fma y (+ 3.13060547623 (* (/ 1 z) (/ t z))) x)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
25×	`add-exp-log` `times-frac`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt`
15×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
8×	`div-exp` `prod-exp`
6×	`unswap-sqr`
5×	`pow1` `add-log-exp`
4×	`cbrt-undiv` `cbrt-unprod`
3×	`expm1-log1p-u` `fma-def` `log1p-expm1-u`
2×	`rec-exp` `1-exp` `div-inv`
1×	`+-commutative` `frac-times` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `sum-log` `*-commutative` `flip-+` `fma-udef`

Counts

3 → 84

Calls

3 calls:

2.0ms	(+ 3.13060547623 (* (/ 1 z) (/ t z)))
15.0ms	(* (/ 1 z) (/ t z))
0.0ms	(fma y (+ 3.13060547623 (* (/ 1 z) (/ t z))) x)

series78.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(+ 3.13060547623 (* (/ 1 z) (/ t z)))
16.0ms	(* (/ 1 z) (/ t z))
46.0ms	(fma y (+ 3.13060547623 (* (/ 1 z) (/ t z))) x)

simplify56.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	426	495
1	1969	421
2	5001	381

prune258.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.3b

localize30.0ms

Local error

Found 4 expressions with local error:

15.8b	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
15.8b	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
15.8b	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
26.7b	(fma (/ (/ y (* (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))) (cbrt (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)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

0.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
0.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
0.0ms	(fma (/ (/ y (* (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))) (cbrt (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)

series1.2s

Counts

4 → 12

Calls

4 calls:

146.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
153.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
156.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
731.0ms	(fma (/ (/ y (* (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))) (cbrt (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)

simplify60.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	181	755
1	472	661
2	1648	642
3	5002	619

prune418.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.3b

regimes665.0ms

Accuracy

96.6% (0.9b remaining)

Error of 1.1b against oracle of 0.3b and baseline of 26.2b

bsearch302.0ms

Steps

Iters	Range		Point
10	257763.20554958374	1.6866726669846925e+18	1.6627493328873475e+18
10	-1.117469858314241e+21	-5076924889.451885	-4.2825168323351446e+19

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	15
1	42	15

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s

8962×

body

valid