Details

sample92.0ms

Algorithm

intervals

Results

47.0ms	140×	body	1280	valid
20.0ms	23×	body	2560	valid
12.0ms	58×	body	640	valid
2.0ms	17×	body	320	valid
2.0ms	16×	body	160	valid
0.0ms	2×	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 (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: 41.4b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (cos (+ x eps)) (cos x))
3.8b	(cos (+ 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` `cos-sum` `add-cbrt-cube` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

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

series71.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(- (cos (+ x eps)) (cos x))
23.0ms	(cos (+ x eps))

simplify74.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	192	385
1	523	285
2	2519	275
3	5001	220

prune113.0ms

Filtered

46 candidates to 31 candidates (67.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	33	13	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	34	13	47

Merged error: 16.8b

Counts

47 → 13

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
2.8b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

5.0ms	(* (cos x) (cos eps))
5.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
5.0ms	(* (sin x) (sin eps))
10.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series293.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos x) (cos eps))
79.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
44.0ms	(* (sin x) (sin eps))
128.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify49.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	381	988
1	1342	837
2	5002	822

prune283.0ms

Filtered

105 candidates to 72 candidates (68.6%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	91	14	105
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	99	19	118

Merged error: 16.7b

Counts

118 → 19

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.3b	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
2.8b	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

5.0ms	(* (sin x) (sin eps))
9.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
9.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
1.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

series382.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin x) (sin eps))
106.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
97.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
134.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify85.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (77.0ms)

Iter	Nodes	Cost
0	238	768
1	735	681
2	3112	663
3	5002	661

prune342.0ms

Filtered

87 candidates to 70 candidates (80.5%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	81	6	87
Fresh	5	13	18
Picked	1	0	1
Done	0	0	0
Total	87	19	106

Merged error: 16.6b

Counts

106 → 19

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(+ (* (cos x) (cos eps)) (fma (- (sin x)) (sin eps) (cos x)))
0.3b	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
2.8b	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

5.0ms	(* (sin x) (sin eps))
5.0ms	(+ (* (cos x) (cos eps)) (fma (- (sin x)) (sin eps) (cos x)))
9.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
1.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

series376.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin x) (sin eps))
98.0ms	(+ (* (cos x) (cos eps)) (fma (- (sin x)) (sin eps) (cos x)))
96.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
138.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify125.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	318	723
1	1136	642
2	4956	634
3	5001	634

prune272.0ms

Filtered

80 candidates to 64 candidates (80.0%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	2	16	18
Picked	1	0	1
Done	0	0	0
Total	81	18	99

Merged error: 16.6b

Counts

99 → 18

regimes195.0ms

Accuracy

87.2% (1.3b remaining)

Error of 15.1b against oracle of 13.8b and baseline of 24.0b

bsearch124.0ms

Steps

Iters	Range		Point
9	0.0002141056345597589	30542.545607798078	0.00021733742411115183
7	-3.110173650790201e-07	-6.09662256770312e-09	-2.7905907270542693e-08

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	48
1	42	48

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	4531×	body	1280	valid
542.0ms	608×	body	2560	valid
417.0ms	1873×	body	640	valid
98.0ms	616×	body	320	valid
35.0ms	291×	body	160	valid
4.0ms	81×	body	80	valid