Details

sample140.0ms

Algorithm

intervals

Results

78.0ms	57×	body	2560	valid
31.0ms	75×	body	1280	valid
16.0ms	71×	body	640	valid
4.0ms	27×	body	320	valid
1.0ms	12×	body	160	valid
1.0ms	14×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	4

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: 30.0b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
1.3b	(- 1.0 (cos x))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

12.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series54.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(- 1.0 (cos x))

simplify36.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	292	569
1	965	460
2	5002	460

prune178.0ms

Filtered

74 candidates to 51 candidates (68.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	61	13	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	13	75

Merged error: 0.0b

Counts

75 → 13

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
0.9b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.3b	(- 1.0 (cos x))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
40×	`add-cube-cbrt`
38×	`exp-prod`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
9×	`prod-diff`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `fma-neg` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 132

Calls

4 calls:

11.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
7.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms	(- 1.0 (cos x))

series137.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
48.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
35.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
19.0ms	(- 1.0 (cos x))

simplify43.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	368	1009
1	1099	873
2	5002	871

prune315.0ms

Filtered

144 candidates to 103 candidates (71.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	140	4	144
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	142	15	157

Merged error: 0.0b

Counts

157 → 15

localize8.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1 (sin x))
0.2b	(* (- 1.0 (cos x)) (/ 1 (sin x)))
1.3b	(- 1.0 (cos x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
26×	`add-cube-cbrt`
20×	`times-frac`
16×	`add-exp-log`
13×	`associate-r`
10×	`add-cbrt-cube`
9×	`prod-diff`
6×	`pow1`
5×	`associate-l` `add-log-exp`
4×	`div-exp` `prod-exp`
3×	`expm1-log1p-u` `flip3--` `fma-neg` `associate-/r` `flip--` `log1p-expm1-u` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

3 → 105

Calls

3 calls:

4.0ms	(/ 1 (sin x))
10.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
4.0ms	(- 1.0 (cos x))

series74.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(/ 1 (sin x))
42.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
19.0ms	(- 1.0 (cos x))

simplify50.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	381	728
1	1613	574
2	5002	548

prune183.0ms

Filtered

114 candidates to 68 candidates (59.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	114	15	129

Merged error: 0.0b

Counts

129 → 15

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
0.3b	(pow (cos x) 3)
0.5b	(+ 1.0 (cos x))
1.3b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

233×	`add-sqr-sqrt`
165×	`*-un-lft-identity`
144×	`prod-diff`
138×	`unpow-prod-down` `cube-prod`
113×	`add-cube-cbrt`
80×	`difference-of-squares`
75×	`times-frac`
66×	`sqr-pow`
26×	`cube-mult` `unpow3`
25×	`associate-/l*` `distribute-lft-out--`
12×	`fma-neg`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `difference-cubes`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `fma-def` `associate-/r*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `flip-+` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 354

Calls

4 calls:

28.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
2.0ms	(pow (cos x) 3)
4.0ms	(+ 1.0 (cos x))
15.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series215.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
29.0ms	(pow (cos x) 3)
17.0ms	(+ 1.0 (cos x))
49.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify156.0ms

Algorithm

egg-herbie

Counts

366 → 366

Iterations

Useful iterations: 2 (104.0ms)

Iter	Nodes	Cost
0	828	4951
1	3244	4033
2	5002	3940

prune430.0ms

Filtered

366 candidates to 124 candidates (33.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	363	3	366
Fresh	2	11	13
Picked	1	0	1
Done	1	0	1
Total	367	14	381

Merged error: 0.0b

Counts

381 → 14

regimes131.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.5b

bsearch60.0ms

Steps

Iters	Range		Point
6	0.011261476250181132	0.06406876111163662	0.02361334001762777
9	-3.7752751361666412	-2.6386627092684764e-08	-0.023427378097045405

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	25
1	36	25

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.1s	1597×	body	2560	valid
1.2s	2707×	body	1280	valid
438.0ms	1924×	body	640	valid
140.0ms	913×	body	320	valid
51.0ms	489×	body	160	valid
29.0ms	6×	body	5120	valid
23.0ms	364×	body	80	valid