Details

sample88.0ms

Algorithm

intervals

Results

47.0ms	146×	body	1280	valid
15.0ms	18×	body	2560	valid
12.0ms	59×	body	640	valid
4.0ms	21×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	4×	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: 39.0b

Counts

2 → 1

localize13.0ms

Local error

Found 2 expressions with local error:

0.6b	(- (cos (+ x eps)) (cos x))
3.5b	(cos (+ x eps))

rewrite13.0ms

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))
5.0ms	(cos (+ x eps))

series63.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(- (cos (+ x eps)) (cos x))
14.0ms	(cos (+ x eps))

simplify79.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (70.0ms)

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

prune122.0ms

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: 14.7b

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:

4.0ms	(* (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))

series292.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (cos x) (cos eps))
82.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
48.0ms	(* (sin x) (sin eps))
123.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify50.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (40.0ms)

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

prune327.0ms

Filtered

105 candidates to 73 candidates (69.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	90	15	105
Fresh	10	2	12
Picked	1	0	1
Done	0	0	0
Total	101	17	118

Merged error: 14.5b

Counts

118 → 17

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.5b	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.5b	(+ (- (* (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))))

series376.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin x) (sin eps))
97.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
97.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
138.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify87.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (79.0ms)

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

prune412.0ms

Filtered

87 candidates to 70 candidates (80.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	81	6	87
Fresh	5	11	16
Picked	1	0	1
Done	0	0	0
Total	87	17	104

Merged error: 14.5b

Counts

104 → 17

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.5b	(+ (- (* (cos x) (cos eps)) (expm1 (log1p (* (sin x) (sin eps))))) (cos x))
0.5b	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
2.8b	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

5.0ms	(* (sin x) (sin eps))
9.0ms	(+ (- (* (cos x) (cos eps)) (expm1 (log1p (* (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))))

series416.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (sin x) (sin eps))
130.0ms	(+ (- (* (cos x) (cos eps)) (expm1 (log1p (* (sin x) (sin eps))))) (cos x))
97.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
139.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify132.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 3 (123.0ms)

Iter	Nodes	Cost
0	336	848
1	957	701
2	4426	673
3	5001	671

prune405.0ms

Filtered

90 candidates to 72 candidates (80.0%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	88	2	90
Fresh	2	14	16
Picked	0	1	1
Done	0	0	0
Total	90	17	107

Merged error: 14.5b

Counts

107 → 17

regimes210.0ms

Accuracy

82.5% (1.7b remaining)

Error of 16.1b against oracle of 14.4b and baseline of 24.2b

bsearch159.0ms

Steps

Iters	Range		Point
8	3.88064682879673e-06	0.018000635171863108	4.6943453837178825e-06
9	-2.981750332052767e-33	-1.3727521311823731e-39	-2.9500525747086803e-33

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	69
1	47	69

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4480×	body	1280	valid
547.0ms	635×	body	2560	valid
392.0ms	1845×	body	640	valid
106.0ms	673×	body	320	valid
28.0ms	289×	body	160	valid
4.0ms	78×	body	80	valid