Details

sample43.0ms

Algorithm

intervals

Results

19.0ms

295×

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

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.2b

localize27.0ms

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)
0.1b	(fma (fma z 3.13060547623 11.1667541262) z t)
1.3b	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
29.7b	(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 3.13060547623 11.1667541262) z t)
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)

series940.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)
34.0ms	(fma (fma z 3.13060547623 11.1667541262) z t)
114.0ms	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
740.0ms	(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)

simplify115.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (105.0ms)

Iter	Nodes	Cost
0	265	578
1	824	514
2	3565	508
3	5001	506

prune428.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 2 expressions with local error:

2.7b	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
7.7b	(/ t (pow z 2))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
8×	`associate-/r*`
7×	`add-exp-log`
4×	`add-cbrt-cube` `unpow2` `sqr-pow`
3×	`div-exp` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 61

Calls

2 calls:

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

series80.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
23.0ms	(/ t (pow z 2))

simplify123.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	191	332
1	664	290
2	3660	281
3	5001	281

prune198.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

7.7b	(/ t (pow z 2))
12.1b	(cbrt (fma y (+ 3.13060547623 (/ t (pow z 2))) x))
12.1b	(cbrt (fma y (+ 3.13060547623 (/ t (pow z 2))) x))
12.1b	(cbrt (fma y (+ 3.13060547623 (/ t (pow z 2))) x))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
12×	`unpow-prod-down`
9×	`add-exp-log` `cbrt-prod`
8×	`associate-/r*`
6×	`add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
3×	`pow1/3` `div-exp` `associate-/l*`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`

Counts

4 → 90

Calls

4 calls:

4.0ms	(/ t (pow z 2))
0.0ms	(cbrt (fma y (+ 3.13060547623 (/ t (pow z 2))) x))
1.0ms	(cbrt (fma y (+ 3.13060547623 (/ t (pow z 2))) x))
1.0ms	(cbrt (fma y (+ 3.13060547623 (/ t (pow z 2))) x))

series959.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ t (pow z 2))
310.0ms	(cbrt (fma y (+ 3.13060547623 (/ t (pow z 2))) x))
309.0ms	(cbrt (fma y (+ 3.13060547623 (/ t (pow z 2))) x))
317.0ms	(cbrt (fma y (+ 3.13060547623 (/ t (pow z 2))) x))

simplify45.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	281	682
1	935	622
2	5001	601

prune397.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

5.2b	(/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
8.0b	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
8.0b	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
29.7b	(fma (/ (/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (sqrt (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)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

3.0ms	(/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
1.0ms	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.0ms	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
0.0ms	(fma (/ (/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (sqrt (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)

series1.3s

Counts

4 → 12

Calls

4 calls:

181.0ms	(/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
101.0ms	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
102.0ms	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
935.0ms	(fma (/ (/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (sqrt (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)

simplify120.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	312	978
1	980	880
2	4076	857
3	5001	855

prune472.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

regimes669.0ms

Accuracy

96.8% (0.9b remaining)

Error of 1.1b against oracle of 0.3b and baseline of 27.2b

bsearch275.0ms

Steps

Iters	Range		Point
8	1.2564570459059827e+18	1.9712404559034665e+21	1.497253047305232e+19
10	-6.6313037056385885e+35	-1.88993376364928e+24	-1.7503197233736622e+25

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	22
1	62	22

end0.0ms

sample894.0ms

Algorithm

intervals

Results

591.0ms

8906×

body

valid