Details

sample87.0ms

Algorithm

intervals

Results

47.0ms	144×	body	1280	valid
14.0ms	17×	body	2560	valid
13.0ms	64×	body	640	valid
2.0ms	18×	body	320	valid
1.0ms	7×	body	160	valid
0.0ms	6×	body	80	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

Filtered

1 candidates to 0 candidates (100.0%)

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: 40.0b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (cos (+ x eps)) (cos x))
2.2b	(cos (+ x eps))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

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

series77.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(- (cos (+ x eps)) (cos x))
24.0ms	(cos (+ x eps))

simplify70.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	193	395
1	504	295
2	2368	285
3	5001	230

prune104.0ms

Filtered

48 candidates to 32 candidates (33.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	36	12	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	12	49

Merged error: 16.2b

Counts

49 → 12

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (sin eps) (sin x) (cos x))
0.1b	(* (cos eps) (cos x))
3.6b	(- (* (cos eps) (cos x)) (fma (sin eps) (sin x) (cos x)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 98

Calls

3 calls:

1.0ms	(fma (sin eps) (sin x) (cos x))
4.0ms	(* (cos eps) (cos x))
11.0ms	(- (* (cos eps) (cos x)) (fma (sin eps) (sin x) (cos x)))

series266.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(fma (sin eps) (sin x) (cos x))
47.0ms	(* (cos eps) (cos x))
150.0ms	(- (* (cos eps) (cos x)) (fma (sin eps) (sin x) (cos x)))

simplify43.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	310	1796
1	911	1138
2	5001	1064

prune236.0ms

Filtered

107 candidates to 59 candidates (44.9%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	90	17	107
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	100	19	119

Merged error: 16.0b

Counts

119 → 19

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos eps) (cos x))
0.2b	(log1p (expm1 (* (cos eps) (cos x))))
0.4b	(expm1 (* (cos eps) (cos x)))
5.5b	(- (log1p (expm1 (* (cos eps) (cos x)))) (fma (sin eps) (sin x) (cos x)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

4.0ms	(* (cos eps) (cos x))
1.0ms	(log1p (expm1 (* (cos eps) (cos x))))
1.0ms	(expm1 (* (cos eps) (cos x)))
4.0ms	(- (log1p (expm1 (* (cos eps) (cos x)))) (fma (sin eps) (sin x) (cos x)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos eps) (cos x))
78.0ms	(log1p (expm1 (* (cos eps) (cos x))))
77.0ms	(expm1 (* (cos eps) (cos x)))
192.0ms	(- (log1p (expm1 (* (cos eps) (cos x)))) (fma (sin eps) (sin x) (cos x)))

simplify148.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	288	926
1	926	658
2	4928	625
3	5001	625

prune237.0ms

Filtered

86 candidates to 53 candidates (38.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	5	13	18
Picked	1	0	1
Done	0	0	0
Total	88	17	105

Merged error: 16.0b

Counts

105 → 17

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(log1p (expm1 (expm1 (log1p (* (cos eps) (cos x))))))
0.4b	(log1p (* (cos eps) (cos x)))
0.4b	(expm1 (expm1 (log1p (* (cos eps) (cos x)))))
23.2b	(- (log1p (expm1 (expm1 (log1p (* (cos eps) (cos x)))))) (fma (sin eps) (sin x) (cos x)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

1.0ms	(log1p (expm1 (expm1 (log1p (* (cos eps) (cos x))))))
1.0ms	(log1p (* (cos eps) (cos x)))
1.0ms	(expm1 (expm1 (log1p (* (cos eps) (cos x)))))
4.0ms	(- (log1p (expm1 (expm1 (log1p (* (cos eps) (cos x)))))) (fma (sin eps) (sin x) (cos x)))

series535.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(log1p (expm1 (expm1 (log1p (* (cos eps) (cos x))))))
75.0ms	(log1p (* (cos eps) (cos x)))
108.0ms	(expm1 (expm1 (log1p (* (cos eps) (cos x)))))
236.0ms	(- (log1p (expm1 (expm1 (log1p (* (cos eps) (cos x)))))) (fma (sin eps) (sin x) (cos x)))

simplify136.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (128.0ms)

Iter	Nodes	Cost
0	257	1010
1	775	726
2	4246	659
3	5001	657

prune193.0ms

Filtered

76 candidates to 50 candidates (34.2%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	72	4	76
Fresh	3	13	16
Picked	0	1	1
Done	0	0	0
Total	75	18	93

Merged error: 16.0b

Counts

93 → 18

regimes199.0ms

Accuracy

80.3% (2.0b remaining)

Error of 16.4b against oracle of 14.4b and baseline of 24.7b

bsearch108.0ms

Steps

Iters	Range		Point
9	8.60615151617276e-12	0.00018057363276660255	3.544639649952985e-07
6	-1.826336704869222e-34	-1.1425473411494959e-35	-1.7962576357457494e-34

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	26
1	33	26

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4435×	body	1280	valid
518.0ms	610×	body	2560	valid
416.0ms	1890×	body	640	valid
101.0ms	688×	body	320	valid
29.0ms	301×	body	160	valid
4.0ms	76×	body	80	valid