Details

sample119.0ms

Algorithm

intervals

Results

47.0ms	93×	body	1280	valid
24.0ms	81×	body	640	valid
16.0ms	259×	body	80	valid
7.0ms	39×	body	320	valid
4.0ms	29×	body	160	valid

simplify379.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	8
1	44	8
2	91	8
3	195	8
4	332	8
5	652	8
6	1279	8
7	1694	8
8	4980	8
9	5001	8

prune8.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 16.6b

Counts

2 → 1

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(* J (- (exp l) (exp (- l))))
0.0b	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
5.5b	(- (exp l) (exp (- l)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
27×	`prod-diff`
24×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
5×	`pow1` `add-exp-log` `associate-r` `add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `sub-neg` `fma-neg` `associate-l` `log1p-expm1-u`
2×	`flip3--` `associate-*r/` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

3 → 84

Calls

3 calls:

8.0ms	(* J (- (exp l) (exp (- l))))
1.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
6.0ms	(- (exp l) (exp (- l)))

series262.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(* J (- (exp l) (exp (- l))))
168.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
36.0ms	(- (exp l) (exp (- l)))

simplify42.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	318	1176
1	1096	780
2	5001	725

prune245.0ms

Filtered

93 candidates to 56 candidates (60.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	3	94

Merged error: 0.1b

Counts

94 → 3

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
0.0b	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
0.1b	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

1.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
4.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
1.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

series569.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
132.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
381.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

simplify110.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	176	451
1	760	390
2	4095	382
3	5001	382

prune200.0ms

Filtered

51 candidates to 39 candidates (76.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	47	7	54

Merged error: 0.0b

Counts

54 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)) (cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)))
0.7b	(cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U))
0.7b	(cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U))
0.7b	(cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

6.0ms	(* (cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)) (cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)))
1.0ms	(cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U))
1.0ms	(cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U))
1.0ms	(cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U))

series2.0s

Counts

4 → 12

Calls

4 calls:

803.0ms	(* (cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)) (cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)))
417.0ms	(cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U))
406.0ms	(cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U))
411.0ms	(cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U))

simplify165.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	294	1835
1	989	1685
2	4974	1549
3	5001	1549

prune460.0ms

Filtered

93 candidates to 72 candidates (77.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	92	8	100

Merged error: 0.0b

Counts

100 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* J (cbrt (pow (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) 3)))
0.1b	(pow (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) 3)
0.1b	(fma (* J (cbrt (pow (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) 3))) (cos (/ K 2.0)) U)
38.7b	(cbrt (pow (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) 3))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
24×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
10×	`unpow-prod-down` `cube-prod`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`cube-mult` `pow-unpow` `unpow3` `associate-l`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `fma-udef` `rem-cube-cbrt`

Counts

4 → 94

Calls

4 calls:

12.0ms	(* J (cbrt (pow (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) 3)))
2.0ms	(pow (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) 3)
1.0ms	(fma (* J (cbrt (pow (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) 3))) (cos (/ K 2.0)) U)
2.0ms	(cbrt (pow (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) 3))

series514.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* J (cbrt (pow (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) 3)))
81.0ms	(pow (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) 3)
246.0ms	(fma (* J (cbrt (pow (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) 3))) (cos (/ K 2.0)) U)
54.0ms	(cbrt (pow (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) 3))

simplify60.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	321	1019
1	1297	939
2	5003	919

prune314.0ms

Filtered

106 candidates to 66 candidates (62.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	106	8	114

Merged error: 0.0b

Counts

114 → 8

regimes302.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.2s	2656×	body	1280	valid
768.0ms	2630×	body	640	valid
536.0ms	8494×	body	80	valid
307.0ms	1489×	body	320	valid
106.0ms	770×	body	160	valid