Details

sample105.0ms

Algorithm

intervals

Results

43.0ms	92×	body	1280	valid
23.0ms	23×	body	2560	valid
22.0ms	73×	body	640	valid
5.0ms	20×	body	320	valid
3.0ms	36×	body	80	valid
2.0ms	12×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.2b

localize8.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (sin (+ x eps)) (sin x))
3.3b	(sin (+ x eps))

rewrite36.0ms

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:

31.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

series57.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

simplify75.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (71.0ms)

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

prune113.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin x) (cos eps))
0.2b	(* (cos x) (sin eps))
0.2b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
4.1b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
11×	`add-log-exp`
9×	`prod-diff`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg`
2×	`diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `sub-neg` `flip3--` `fma-def` `flip3-+` `associate--l+` `sin-cos-mult` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 85

Calls

4 calls:

4.0ms	(* (sin x) (cos eps))
4.0ms	(* (cos x) (sin eps))
4.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
25.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series292.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sin x) (cos eps))
43.0ms	(* (cos x) (sin eps))
91.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
110.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify50.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	373	918
1	1424	763
2	5002	741

prune282.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
0.2b	(* (cos x) (sin eps))
1.4b	(- (cos eps) 1)

rewrite10.0ms

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:

0.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
4.0ms	(* (cos x) (sin eps))
4.0ms	(- (cos eps) 1)

series173.0ms

Counts

3 → 9

Calls

3 calls:

108.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
47.0ms	(* (cos x) (sin eps))
18.0ms	(- (cos eps) 1)

simplify98.0ms

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

prune236.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (cos x) (sin eps)))
0.6b	(cbrt (* (cos x) (sin eps)))
0.6b	(cbrt (* (cos x) (sin eps)))
1.4b	(- (cos eps) 1)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

2.0ms	(cbrt (* (cos x) (sin eps)))
2.0ms	(cbrt (* (cos x) (sin eps)))
2.0ms	(cbrt (* (cos x) (sin eps)))
4.0ms	(- (cos eps) 1)

series275.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(cbrt (* (cos x) (sin eps)))
84.0ms	(cbrt (* (cos x) (sin eps)))
85.0ms	(cbrt (* (cos x) (sin eps)))
20.0ms	(- (cos eps) 1)

simplify73.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	205	462
1	668	361
2	2118	337
3	5001	315

prune248.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.0b

regimes160.0ms

Accuracy

85.8% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 1.5b

bsearch126.0ms

Steps

Iters	Range		Point
6	3.9715340067303715	22.710463948410766	4.01911916950482
9	-3.92976936792683	-5.033370145566524e-07	-0.03286941482849303

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	31
1	44	31
2	44	31

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.8s	3263×	body	1280	valid
656.0ms	660×	body	2560	valid
536.0ms	1800×	body	640	valid
165.0ms	793×	body	320	valid
98.0ms	1128×	body	80	valid
53.0ms	356×	body	160	valid