Details

analyze2.0ms

Algorithm

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 100%

sample103.0ms

Algorithm

intervals

Results

58.0ms	145×	body	1280	valid
19.0ms	22×	body	2560	valid
14.0ms	63×	body	640	valid
3.0ms	17×	body	320	valid
1.0ms	9×	body	160	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: 40.2b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (cos (+ x eps)) (cos x))
2.6b	(cos (+ x eps))

rewrite10.0ms

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))

series13.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(- (cos (+ x eps)) (cos x))
4.0ms	(cos (+ x eps))

simplify110.0ms

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

prune80.0ms

Filtered

23 candidates to 30 candidates (-30.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	18	12	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	19	12	31

Merged error: 13.2b

Counts

31 → 12

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))
2.2b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

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

series57.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos x) (cos eps))
18.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
9.0ms	(* (sin x) (sin eps))
23.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify114.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	304	632
1	1061	600
2	4487	582
3	5002	582

prune139.0ms

Filtered

56 candidates to 82 candidates (-46.4%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	69	13	82
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	76	18	94

Merged error: 13.1b

Counts

94 → 18

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps)))))
0.2b	(* (sin x) (sin eps))
2.2b	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
2.9b	(log (exp (* (sin x) (sin eps))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1`
6×	`add-exp-log` `log-prod` `add-cbrt-cube`
4×	`diff-log`
3×	`sub-neg` `associate-r` `associate-l` `log-pow` `associate--r+`
2×	`flip3--` `associate--l+` `flip--`
1×	`associate--l-` `exp-prod` `exp-to-pow` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

8.0ms	(- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps)))))
5.0ms	(* (sin x) (sin eps))
9.0ms	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
2.0ms	(log (exp (* (sin x) (sin eps))))

series56.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps)))))
9.0ms	(* (sin x) (sin eps))
23.0ms	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
9.0ms	(log (exp (* (sin x) (sin eps))))

simplify82.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	266	688
1	792	625
2	3018	609
3	5001	609

prune130.0ms

Filtered

54 candidates to 78 candidates (-44.4%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	1	16	17
Picked	0	1	1
Done	0	0	0
Total	77	19	96

Merged error: 13.1b

Counts

96 → 19

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
2.2b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
2.3b	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

5.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
5.0ms	(* (sin x) (sin eps))
9.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
6.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

series72.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
9.0ms	(* (sin x) (sin eps))
22.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
23.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

simplify95.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	300	825
1	970	767
2	3675	746
3	5002	745

prune83.0ms

Filtered

57 candidates to 85 candidates (-49.1%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	81	4	85
Fresh	2	15	17
Picked	1	0	1
Done	0	1	1
Total	84	20	104

Merged error: 13.1b

Counts

104 → 20

Details

analyze2.0ms

sample103.0ms

simplify4.0ms

prune3.0ms

localize9.0ms

rewrite10.0ms

series13.0ms

simplify110.0ms

prune80.0ms

localize14.0ms

rewrite23.0ms

series57.0ms

simplify114.0ms

prune139.0ms

localize17.0ms

rewrite25.0ms

series56.0ms

simplify82.0ms

prune130.0ms

localize20.0ms

rewrite26.0ms

series72.0ms

simplify95.0ms

prune83.0ms

regimes273.0ms

bsearch1.0ms

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