Details

sample106.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

52.0ms	132×	body	1280	valid
21.0ms	23×	body	2560	valid
14.0ms	61×	body	640	valid
4.0ms	26×	body	320	valid
1.0ms	13×	body	160	valid
0.0ms	1×	body	80	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

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: 42.5b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
3.4b	(cos (+ x eps))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `cos-sum` `add-cbrt-cube`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

6.0ms	(- (cos (+ x eps)) (cos x))
4.0ms	(cos (+ x eps))

series14.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(- (cos (+ x eps)) (cos x))
5.0ms	(cos (+ x eps))

simplify115.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	134	176
1	281	167
2	840	164
3	2958	164
4	5002	164

prune70.0ms

Filtered

23 candidates to 30 candidates (-30.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	19	11	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	20	11	31

Merged error: 15.3b

Counts

31 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
2.7b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

4.0ms	(* (cos x) (cos eps))
5.0ms	(+ (* (sin x) (sin eps)) (cos x))
5.0ms	(* (sin x) (sin eps))
8.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series54.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos x) (cos eps))
14.0ms	(+ (* (sin x) (sin eps)) (cos x))
9.0ms	(* (sin x) (sin eps))
23.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	332	607
1	1284	574
2	5002	565

prune138.0ms

Filtered

53 candidates to 77 candidates (-45.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	63	14	77
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	70	18	88

Merged error: 15.1b

Counts

88 → 18

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
0.4b	(pow (+ (* (sin x) (sin eps)) (cos x)) 3)
0.6b	(pow (* (cos x) (cos eps)) 3)
2.6b	(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
20×	`add-exp-log` `add-cbrt-cube`
18×	`add-sqr-sqrt` `pow-prod-down`
10×	`*-un-lft-identity`
9×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `difference-of-squares` `sqr-pow`
7×	`cube-div` `cos-mult`
6×	`unpow-prod-down` `pow-unpow` `cube-prod` `add-log-exp`
4×	`pow-sqr` `pow-prod-up`
3×	`pow-pow` `pow-exp` `rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `flip3-+` `pow-plus` `unpow3` `frac-sub` `flip-+`
1×	`difference-cubes` `pow2` `frac-times` `sub-neg` `flip3--` `diff-log` `associate-r/` `swap-sqr` `associate-r` `associate-l` `associate-l/` `*-commutative` `flip--` `distribute-lft-out--`

Counts

4 → 109

Calls

4 calls:

8.0ms	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
7.0ms	(pow (+ (* (sin x) (sin eps)) (cos x)) 3)
4.0ms	(pow (* (cos x) (cos eps)) 3)
16.0ms	(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

series148.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
18.0ms	(pow (+ (* (sin x) (sin eps)) (cos x)) 3)
14.0ms	(pow (* (cos x) (cos eps)) 3)
102.0ms	(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

simplify97.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	538	1125
1	2679	1049
2	5001	1037

prune241.0ms

Filtered

65 candidates to 121 candidates (-86.2%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	108	13	121
Fresh	8	9	17
Picked	1	0	1
Done	0	0	0
Total	117	22	139

Merged error: 15.1b

Counts

139 → 22

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
2.7b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))
2.7b	(log (exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

5.0ms	(+ (* (sin x) (sin eps)) (cos x))
4.0ms	(* (sin x) (sin eps))
8.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))
7.0ms	(log (exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))))

series69.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (* (sin x) (sin eps)) (cos x))
9.0ms	(* (sin x) (sin eps))
23.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))
27.0ms	(log (exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))))

simplify130.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	318	771
1	1131	712
2	4817	698
3	5002	698

prune77.0ms

Filtered

54 candidates to 76 candidates (-40.7%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	2	19	21
Picked	1	0	1
Done	0	0	0
Total	77	21	98

Merged error: 15.1b

Counts

98 → 21

regimes315.0ms

Accuracy

80.8% (1.9b remaining)

Error of 16.5b against oracle of 14.6b and baseline of 24.5b

bsearch123.0ms

Steps

Iters	Range		Point
10	1.1473974335323604e-05	233655.5123930368	1.1601672568020436e-05
8	-9.69771118835226e-21	-2.356842946276999e-24	-9.538806412147545e-21

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	45
1	47	45

end0.0ms

sample3.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

1.7s	4452×	body	1280	valid
650.0ms	1836×	body	640	valid
601.0ms	657×	body	2560	valid
111.0ms	685×	body	320	valid
31.0ms	274×	body	160	valid
6.0ms	96×	body	80	valid

Details

sample106.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite11.0ms

series14.0ms

simplify115.0ms

prune70.0ms

localize14.0ms

rewrite23.0ms

series54.0ms

simplify44.0ms

prune138.0ms

localize24.0ms

rewrite38.0ms

series148.0ms

simplify97.0ms

prune241.0ms

localize18.0ms

rewrite26.0ms

series69.0ms

simplify130.0ms

prune77.0ms

regimes315.0ms

bsearch123.0ms

simplify2.0ms

end0.0ms

sample3.3s

Profiling