Details

sample37.0ms

Algorithm

intervals

Results

17.0ms	86×	body	1280	valid
5.0ms	47×	body	640	valid
4.0ms	169×	body	80	valid
2.0ms	23×	body	320	valid
1.0ms	15×	body	160	valid

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	3
1	18	3
2	27	3
3	50	3
4	115	3
5	329	3
6	1642	3
7	5001	3

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 29.7b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.9b	(- (exp (* a x)) 1.0)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
6×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `exp-prod` `flip3--` `exp-to-pow` `diff-log` `flip--` `rem-exp-log` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

2.0ms	(exp (* a x))
7.0ms	(- (exp (* a x)) 1.0)

series47.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
35.0ms	(- (exp (* a x)) 1.0)

simplify83.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	173	292
1	562	211
2	2710	200
3	5002	164

prune71.0ms

Filtered

46 candidates to 28 candidates (60.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	43	3	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	3	47

Merged error: 8.6b

Counts

47 → 3

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.0b	(pow (- (exp (* a x)) 1.0) 3)
0.1b	(cbrt (pow (- (exp (* a x)) 1.0) 3))
3.9b	(- (exp (* a x)) 1.0)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`cbrt-prod`
10×	`unpow-prod-down` `cube-prod`
9×	`prod-diff`
8×	`add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `flip3--` `fma-neg` `flip--`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `exp-prod` `exp-to-pow` `pow-pow` `pow1/3` `diff-log` `pow-exp` `rem-cbrt-cube` `rem-exp-log` `rem-cube-cbrt`

Counts

4 → 100

Calls

4 calls:

2.0ms	(exp (* a x))
8.0ms	(pow (- (exp (* a x)) 1.0) 3)
5.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
5.0ms	(- (exp (* a x)) 1.0)

series130.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(exp (* a x))
52.0ms	(pow (- (exp (* a x)) 1.0) 3)
33.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
33.0ms	(- (exp (* a x)) 1.0)

simplify49.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	333	721
1	1342	623
2	5001	613

prune160.0ms

Filtered

112 candidates to 62 candidates (55.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	112	3	115

Merged error: 8.6b

Counts

115 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
12.1b	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
15.4b	(* (pow a 2) (pow x 2))
17.7b	(* (pow a 3) (pow x 3))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
32×	`unswap-sqr`
28×	`add-exp-log` `unpow-prod-down`
20×	`associate-r` `associate-l` `sqr-pow`
18×	`prod-exp`
14×	`add-cube-cbrt` `*-un-lft-identity` `cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
8×	`add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cube-mult` `unpow3` `pow-prod-down` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 134

Calls

4 calls:

1.0ms	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
1.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
7.0ms	(* (pow a 2) (pow x 2))
9.0ms	(* (pow a 3) (pow x 3))

series312.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
102.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
32.0ms	(* (pow a 2) (pow x 2))
64.0ms	(* (pow a 3) (pow x 3))

simplify78.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	369	802
1	1845	699
2	5001	656

prune306.0ms

Filtered

146 candidates to 81 candidates (55.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	145	4	149

Merged error: 5.2b

Counts

149 → 4

localize9.0ms

Local error

Found 2 expressions with local error:

4.8b	(fma 1/2 (* (pow a 2) (pow x 2)) (* a x))
15.4b	(* (pow a 2) (pow x 2))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
16×	`unswap-sqr`
14×	`add-exp-log` `unpow-prod-down`
10×	`unpow2` `sqr-pow`
9×	`prod-exp`
8×	`associate-r` `associate-l`
6×	`pow-to-exp` `add-cube-cbrt` `*-un-lft-identity` `pow-exp`
4×	`add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`pow-prod-down` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

2 → 63

Calls

2 calls:

1.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (* a x))
7.0ms	(* (pow a 2) (pow x 2))

series94.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (* a x))
31.0ms	(* (pow a 2) (pow x 2))

simplify181.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	188	337
1	727	280
2	4608	269
3	5001	269

prune96.0ms

Filtered

69 candidates to 39 candidates (56.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	70	3	73

Merged error: 0b

Counts

73 → 3

regimes138.0ms

Accuracy

97.6% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 21.9b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	10

end0.0ms

sample1.0s

Algorithm

intervals

Results

476.0ms	2689×	body	1280	valid
156.0ms	1317×	body	640	valid
134.0ms	5512×	body	80	valid
62.0ms	732×	body	320	valid
22.0ms	414×	body	160	valid