Details

sample46.0ms

Algorithm

intervals

Results

24.0ms

282×

body

valid

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b)
0.1b	(fma (fma z 3.13060547623 11.1667541262) z t)
0.9b	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
26.3b	(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 (fma z 3.13060547623 11.1667541262) z t) z a) z b)
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)

series973.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b)
29.0ms	(fma (fma z 3.13060547623 11.1667541262) z t)
110.0ms	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
742.0ms	(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)

simplify116.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (104.0ms)

Iter	Nodes	Cost
0	269	578
1	828	514
2	3590	508
3	5001	504

prune400.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

3.7b	(/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
7.9b	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
7.9b	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
26.3b	(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)

series1.1s

Counts

4 → 12

Calls

4 calls:

179.0ms	(/ y (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))
104.0ms	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
742.0ms	(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)

simplify121.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (106.0ms)

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

prune498.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

7.9b	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
7.9b	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
15.6b	(log1p (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
26.3b	(fma (/ (/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (expm1 (log1p (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)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
5×	`expm1-log1p-u`
4×	`add-exp-log` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`log1p-udef` `log1p-expm1` `fma-udef`

Counts

4 → 51

Calls

4 calls:

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	(log1p (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))) (expm1 (log1p (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)

series1.9s

Counts

4 → 12

Calls

4 calls:

103.0ms	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
113.0ms	(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
207.0ms	(log1p (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
1.5s	(fma (/ (/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (expm1 (log1p (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)

simplify92.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	260	649
1	785	568
2	3215	549
3	5002	538

prune400.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 3.13060547623 (/ t (pow z 2)))
3.1b	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
7.6b	(/ 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))

series106.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ 3.13060547623 (/ t (pow z 2)))
55.0ms	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
23.0ms	(/ t (pow z 2))

simplify138.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (131.0ms)

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

prune222.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes926.0ms

Accuracy

96.2% (1.1b remaining)

Error of 1.4b against oracle of 0.3b and baseline of 28.2b

bsearch241.0ms

Steps

Iters	Range		Point
8	6.164442305765328e+42	2.961988255022833e+45	6.26170278955736e+42
7	-3.46426322368225e+23	-4.0040270767390007e+21	-7.68831514327899e+21

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	22
1	62	22

end0.0ms

sample945.0ms

Algorithm

intervals

Results

636.0ms

8877×

body

valid