Details

sample39.0ms

Algorithm

intervals

Results

19.0ms

293×

body

valid

simplify58.0ms

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.9b

localize24.0ms

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)
1.4b	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
26.5b	(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)

series929.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)
36.0ms	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
115.0ms	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
721.0ms	(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)

simplify106.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (97.0ms)

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

prune410.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
0.0b	(/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.6b	(* y (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
26.5b	(fma (* y (/ 1 (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)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
7×	`pow1`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `fma-udef` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 91

Calls

4 calls:

0.0ms	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
2.0ms	(/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
8.0ms	(* y (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
0.0ms	(fma (* y (/ 1 (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:

41.0ms	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
75.0ms	(/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
111.0ms	(* y (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
910.0ms	(fma (* y (/ 1 (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)

simplify50.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	379	876
1	1498	763
2	5001	729

prune443.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
0.0b	(/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.6b	(* y (expm1 (log1p (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))))
26.5b	(fma (* y (expm1 (log1p (/ 1 (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

16×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-exp-log`
9×	`times-frac`
8×	`add-cbrt-cube`
7×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l` `associate-/r` `associate-/l`
2×	`div-exp` `fma-udef`
1×	`cbrt-undiv` `rec-exp` `pow-flip` `frac-2neg` `1-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `inv-pow` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

0.0ms	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
2.0ms	(/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
3.0ms	(* y (expm1 (log1p (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))))
0.0ms	(fma (* y (expm1 (log1p (/ 1 (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:

41.0ms	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
77.0ms	(/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
188.0ms	(* y (expm1 (log1p (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))))
861.0ms	(fma (* y (expm1 (log1p (/ 1 (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)

simplify44.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	329	792
1	1209	676
2	5001	650

prune434.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.7b

localize32.0ms

Local error

Found 4 expressions with local error:

1.6b	(* y (expm1 (log1p (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))))
26.5b	(fma (* y (expm1 (log1p (/ 1 (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)
26.5b	(fma (* y (expm1 (log1p (/ 1 (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)
26.5b	(fma (* y (expm1 (log1p (/ 1 (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)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l` `fma-udef`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 50

Calls

4 calls:

6.0ms	(* y (expm1 (log1p (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))))
0.0ms	(fma (* y (expm1 (log1p (/ 1 (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)
0.0ms	(fma (* y (expm1 (log1p (/ 1 (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)
0.0ms	(fma (* y (expm1 (log1p (/ 1 (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)

series2.8s

Counts

4 → 12

Calls

4 calls:

189.0ms	(* y (expm1 (log1p (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))))
867.0ms	(fma (* y (expm1 (log1p (/ 1 (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)
871.0ms	(fma (* y (expm1 (log1p (/ 1 (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)
860.0ms	(fma (* y (expm1 (log1p (/ 1 (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)

simplify109.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	191	809
1	710	689
2	3533	670
3	5002	664

prune452.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.7b

regimes468.0ms

Accuracy

97.2% (0.8b remaining)

Error of 1.2b against oracle of 0.4b and baseline of 28.8b

bsearch262.0ms

Steps

Iters	Range		Point
10	206990874932.61172	1.2565267625942284e+28	6.283218624731784e+21
9	-4.7805415039378135e+20	-2766341173278078.0	-1.0993814227302263e+18

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	14
1	38	14

end0.0ms

sample889.0ms

Algorithm

intervals

Results

577.0ms

8875×

body

valid