Details

sample89.0ms

Algorithm

intervals

Results

48.0ms	145×	body	1280	valid
17.0ms	20×	body	2560	valid
13.0ms	62×	body	640	valid
3.0ms	18×	body	320	valid
0.0ms	5×	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 (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: 39.8b

Counts

2 → 1

localize15.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ x eps)) (cos x))
2.9b	(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))

series64.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

simplify112.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (9.0ms)

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

prune92.0ms

Filtered

30 candidates to 23 candidates (76.7%)

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: 15.3b

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))
3.5b	(- (- (* (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))

series292.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (cos x) (cos eps))
82.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
43.0ms	(* (sin x) (sin eps))
129.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify121.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (31.0ms)

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

prune223.0ms

Filtered

82 candidates to 56 candidates (68.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	71	11	82
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	78	16	94

Merged error: 15.2b

Counts

94 → 16

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(pow (* (sin x) (sin eps)) 3)
3.5b	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
29.9b	(cbrt (pow (* (sin x) (sin eps)) 3))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
9×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
8×	`cbrt-prod` `add-cube-cbrt`
3×	`pow-unpow` `diff-log` `associate-r` `associate-l` `sin-mult`
2×	`cube-div` `cube-mult` `sub-neg` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `associate--l+` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`associate--l-` `pow-to-exp` `cbrt-div` `flip3--` `pow1/3` `*-commutative` `flip--` `rem-cbrt-cube` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

5.0ms	(* (sin x) (sin eps))
5.0ms	(pow (* (sin x) (sin eps)) 3)
10.0ms	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
3.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

series287.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sin x) (sin eps))
66.0ms	(pow (* (sin x) (sin eps)) 3)
123.0ms	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
48.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

simplify41.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	293	634
1	1142	580
2	5001	565

prune252.0ms

Filtered

90 candidates to 58 candidates (64.4%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	86	4	90
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	86	20	106

Merged error: 15.1b

Counts

106 → 20

localize21.0ms

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))
3.5b	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
4.2b	(log (exp (* (sin x) (sin eps))))

rewrite23.0ms

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:

6.0ms	(- (* (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))))

series303.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps)))))
45.0ms	(* (sin x) (sin eps))
131.0ms	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
44.0ms	(log (exp (* (sin x) (sin eps))))

simplify83.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (23.0ms)

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

prune174.0ms

Filtered

78 candidates to 52 candidates (66.7%)

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	18	18
Picked	0	1	1
Done	0	1	1
Total	77	21	98

Merged error: 15.1b

Counts

98 → 21

Details

sample89.0ms

simplify5.0ms

prune2.0ms

localize15.0ms

rewrite11.0ms

series64.0ms

simplify112.0ms

prune92.0ms

localize14.0ms

rewrite23.0ms

series292.0ms

simplify121.0ms

prune223.0ms

localize17.0ms

rewrite25.0ms

series287.0ms

simplify41.0ms

prune252.0ms

localize21.0ms

rewrite23.0ms

series303.0ms

simplify83.0ms

prune174.0ms

regimes219.0ms

bsearch2.0ms

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