Details

sample140.0ms

Algorithm

intervals

Results

67.0ms	53×	body	2560	valid
43.0ms	87×	body	1280	valid
12.0ms	54×	body	640	valid
6.0ms	36×	body	320	valid
2.0ms	17×	body	160	valid
1.0ms	9×	body	80	valid

simplify7.0ms

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: 29.3b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.8b	(- 1.0 (cos x))

rewrite13.0ms

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:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series62.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ (- 1.0 (cos x)) (sin x))
20.0ms	(- 1.0 (cos x))

simplify37.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (9.0ms)

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

prune179.0ms

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: 0.2b

Counts

75 → 13

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)))
0.4b	(pow (cos x) 3)
0.5b	(+ 1.0 (cos x))
1.6b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite66.0ms

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:

23.0ms	(/ (- (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))
14.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series215.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
36.0ms	(pow (cos x) 3)
10.0ms	(+ 1.0 (cos x))
49.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify161.0ms

Algorithm

egg-herbie

Counts

366 → 366

Iterations

Useful iterations: 2 (112.0ms)

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

prune484.0ms

Filtered

366 candidates to 124 candidates (33.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	358	8	366
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	361	18	379

Merged error: 0.2b

Counts

379 → 18

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (pow (cos x) 3) 3)
0.4b	(pow (cos x) 3)
0.5b	(+ 1.0 (cos x))
1.6b	(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

400×	`cbrt-prod`
396×	`prod-diff`
374×	`unpow-prod-down` `cube-prod`
278×	`add-sqr-sqrt`
217×	`*-un-lft-identity`
213×	`add-cube-cbrt`
97×	`sqr-pow`
74×	`cube-mult` `unpow3`
44×	`difference-of-squares`
12×	`fma-neg`
8×	`add-log-exp`
7×	`add-exp-log`
6×	`pow-unpow` `add-cbrt-cube`
5×	`pow1` `pow-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-to-exp` `fma-def`
2×	`pow-pow` `rem-cube-cbrt`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `diff-log` `sum-log` `flip--` `flip-+` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 554

Calls

4 calls:

4.0ms	(pow (pow (cos x) 3) 3)
3.0ms	(pow (cos x) 3)
4.0ms	(+ 1.0 (cos x))
34.0ms	(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

series155.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(pow (pow (cos x) 3) 3)
28.0ms	(pow (cos x) 3)
10.0ms	(+ 1.0 (cos x))
56.0ms	(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

simplify191.0ms

Algorithm

egg-herbie

Counts

566 → 566

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	927	9840
1	2740	5065
2	5001	4777

prune381.0ms

Filtered

566 candidates to 82 candidates (14.5%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	562	4	566
Fresh	2	15	17
Picked	1	0	1
Done	0	0	0
Total	565	19	584

Merged error: 0.2b

Counts

584 → 19

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos x) 3)
0.5b	(+ 1.0 (cos x))
1.1b	(log (- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3))))
1.6b	(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

440×	`cbrt-prod`
396×	`prod-diff`
391×	`unpow-prod-down` `cube-prod`
337×	`add-sqr-sqrt`
213×	`*-un-lft-identity`
207×	`add-cube-cbrt`
117×	`sqr-pow`
88×	`difference-of-squares`
71×	`cube-mult` `unpow3`
48×	`log-prod`
12×	`fma-neg`
8×	`add-log-exp`
6×	`pow1` `add-exp-log`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `fma-def`
2×	`log-div` `flip3--` `flip--` `distribute-lft-out--`
1×	`+-commutative` `pow-to-exp` `sub-neg` `pow-pow` `flip3-+` `diff-log` `rem-log-exp` `pow-exp` `sum-log` `log-pow` `flip-+` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 570

Calls

4 calls:

3.0ms	(pow (cos x) 3)
4.0ms	(+ 1.0 (cos x))
38.0ms	(log (- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3))))
36.0ms	(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(pow (cos x) 3)
10.0ms	(+ 1.0 (cos x))
316.0ms	(log (- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3))))
58.0ms	(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

simplify199.0ms

Algorithm

egg-herbie

Counts

582 → 582

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	963	10615
1	2644	5816
2	5002	5732

prune452.0ms

Filtered

582 candidates to 98 candidates (16.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	580	2	582
Fresh	3	15	18
Picked	1	0	1
Done	0	0	0
Total	584	17	601

Merged error: 0.2b

Counts

601 → 17

regimes180.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.4b

bsearch96.0ms

Steps

Iters	Range		Point
10	0.005370866090842012	4.21737757242384e+15	0.025186331199138896
10	-3.4402871636077537	-5.738045557766166e-18	-0.023141644690732637

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	29
1	39	29

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.1s	1586×	body	2560	valid
1.3s	2776×	body	1280	valid
433.0ms	1838×	body	640	valid
175.0ms	959×	body	320	valid
60.0ms	471×	body	160	valid
25.0ms	368×	body	80	valid
5.0ms	2×	body	5120	valid