Details

sample99.0ms

Algorithm

intervals

Results

45.0ms	136×	body	1280	valid
25.0ms	29×	body	2560	valid
15.0ms	59×	body	640	valid
3.0ms	20×	body	320	valid
1.0ms	9×	body	160	valid
1.0ms	3×	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: 40.4b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.5b	(- (cos (+ x eps)) (cos x))
2.8b	(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))

series71.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify115.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (10.0ms)

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

prune87.0ms

Filtered

30 candidates to 23 candidates (76.7%)

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: 17.6b

Counts

31 → 11

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))
2.3b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite28.0ms

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)))
5.0ms	(* (sin x) (sin eps))
11.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series300.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (cos x) (cos eps))
83.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
49.0ms	(* (sin x) (sin eps))
129.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify117.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	304	632
1	1061	601
2	4487	583
3	5002	583

prune222.0ms

Filtered

82 candidates to 56 candidates (68.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	70	12	82
Fresh	7	3	10
Picked	1	0	1
Done	0	0	0
Total	78	15	93

Merged error: 17.5b

Counts

93 → 15

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))
2.4b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite25.0ms

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))
9.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (cos x) (cos eps))
53.0ms	(+ (* (sin x) (sin eps)) (cos x))
48.0ms	(* (sin x) (sin eps))
125.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify45.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	332	607
1	1284	576
2	5002	567

prune224.0ms

Filtered

77 candidates to 54 candidates (70.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	70	7	77
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	75	17	92

Merged error: 17.4b

Counts

92 → 17

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

rewrite28.0ms

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))
7.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))
9.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series387.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
45.0ms	(* (sin x) (sin eps))
131.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))
129.0ms	(- (- (* (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	826
1	968	768
2	3673	746
3	5002	745

prune191.0ms

Filtered

85 candidates to 57 candidates (67.1%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	83	19	102

Merged error: 17.4b

Counts

102 → 19

regimes195.0ms

Accuracy

79.3% (2.1b remaining)

Error of 16.7b against oracle of 14.7b and baseline of 24.6b

bsearch87.0ms

Steps

Iters	Range		Point
3	2.731921632534707e-06	3.410959855244386e-06	2.774361521454062e-06
9	-7.380054493915698e-30	-9.003243692419012e-36	-7.258807214549238e-30

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	44
1	44	44

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4426×	body	1280	valid
565.0ms	654×	body	2560	valid
410.0ms	1894×	body	640	valid
106.0ms	664×	body	320	valid
32.0ms	274×	body	160	valid
5.0ms	88×	body	80	valid

Details

sample99.0ms

simplify5.0ms

prune2.0ms

localize9.0ms

rewrite11.0ms

series71.0ms

simplify115.0ms

prune87.0ms

localize14.0ms

rewrite28.0ms

series300.0ms

simplify117.0ms

prune222.0ms

localize14.0ms

rewrite25.0ms

series267.0ms

simplify45.0ms

prune224.0ms

localize20.0ms

rewrite28.0ms

series387.0ms

simplify95.0ms

prune191.0ms

regimes195.0ms

bsearch87.0ms

simplify2.0ms

end0.0ms

sample2.8s

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