Details

sample100.0ms

Algorithm

intervals

Results

47.0ms	110×	body	1280	valid
26.0ms	25×	body	2560	valid
11.0ms	44×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	42×	body	80	valid
1.0ms	10×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize12.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (sin (+ x eps)) (sin x))
3.7b	(sin (+ x eps))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `sin-sum` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

7.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

series61.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(- (sin (+ x eps)) (sin x))
18.0ms	(sin (+ x eps))

simplify73.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	192	386
1	538	285
2	2616	275
3	5002	220

prune110.0ms

Filtered

46 candidates to 31 candidates (67.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (sin eps)) (sin x))
0.1b	(* (sin x) (cos eps))
0.1b	(* (cos x) (sin eps))
3.1b	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`add-log-exp`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l` `prod-diff`
5×	`associate-+r+`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sin-cos-mult`
2×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `frac-add` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `fma-def` `flip3-+` `fma-neg` `flip-+`

Counts

4 → 82

Calls

4 calls:

5.0ms	(- (* (cos x) (sin eps)) (sin x))
5.0ms	(* (sin x) (cos eps))
4.0ms	(* (cos x) (sin eps))
9.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (* (cos x) (sin eps)) (sin x))
41.0ms	(* (sin x) (cos eps))
47.0ms	(* (cos x) (sin eps))
109.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	414	729
1	1617	662
2	5002	648

prune275.0ms

Filtered

94 candidates to 69 candidates (73.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
0.1b	(* (cos x) (sin eps))
2.0b	(- (cos eps) 1)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
12×	`add-cube-cbrt`
9×	`prod-diff`
6×	`add-exp-log`
5×	`pow1` `add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `fma-neg` `associate-r` `associate-l` `log1p-expm1-u`
2×	`difference-of-squares`
1×	`sub-neg` `expm1-def` `flip3--` `diff-log` `difference-of-sqr-1` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `distribute-lft-out--` `unswap-sqr`

Counts

3 → 61

Calls

3 calls:

1.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
4.0ms	(* (cos x) (sin eps))
5.0ms	(- (cos eps) 1)

series175.0ms

Counts

3 → 9

Calls

3 calls:

109.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
46.0ms	(* (cos x) (sin eps))
19.0ms	(- (cos eps) 1)

simplify97.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	276	442
1	932	347
2	3460	325
3	5001	303

prune208.0ms

Filtered

70 candidates to 45 candidates (64.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps))))
2.0b	(- (cos eps) 1)
2.0b	(- (cos eps) 1)
2.0b	(- (cos eps) 1)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
27×	`prod-diff`
26×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`fma-neg`
7×	`add-exp-log`
6×	`difference-of-squares`
4×	`pow1` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-prod` `sub-neg` `expm1-def` `flip3--` `diff-log` `difference-of-sqr-1` `flip--` `distribute-lft-out--`
1×	`pow1/3`

Counts

4 → 106

Calls

4 calls:

1.0ms	(cbrt (fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps))))
5.0ms	(- (cos eps) 1)
5.0ms	(- (cos eps) 1)
5.0ms	(- (cos eps) 1)

series260.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(cbrt (fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps))))
23.0ms	(- (cos eps) 1)
18.0ms	(- (cos eps) 1)
18.0ms	(- (cos eps) 1)

simplify79.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	225	805
1	727	595
2	2423	536
3	5002	470

prune333.0ms

Filtered

118 candidates to 69 candidates (58.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes126.0ms

Accuracy

95% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 3.4b

bsearch123.0ms

Steps

Iters	Range		Point
9	2.7581197155588776e-09	0.16151685480387348	0.031224219371673023
7	-2.8826286267759595	-0.10280128843953673	-0.10397230740886179

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	45
1	44	45

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	3298×	body	1280	valid
610.0ms	672×	body	2560	valid
449.0ms	1826×	body	640	valid
138.0ms	762×	body	320	valid
55.0ms	1100×	body	80	valid
37.0ms	342×	body	160	valid