Details

sample101.0ms

Algorithm

intervals

Results

50.0ms	143×	body	1280	valid
24.0ms	22×	body	2560	valid
13.0ms	63×	body	640	valid
3.0ms	20×	body	320	valid
1.0ms	6×	body	160	valid
0.0ms	2×	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: 40.3b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (cos (+ x eps)) (cos x))
3.0b	(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))

series69.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify113.0ms

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

prune86.0ms

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: 14.7b

Counts

31 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.2b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.3b	(* (sin x) (sin eps))
2.4b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite24.0ms

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

series306.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos x) (cos eps))
83.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
45.0ms	(* (sin x) (sin eps))
134.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify114.0ms

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 57 candidates (69.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	70	12	82
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	78	16	94

Merged error: 14.5b

Counts

94 → 16

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.3b	(* (sin x) (sin eps))
2.4b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
2.5b	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

rewrite32.0ms

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:

6.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
5.0ms	(* (sin x) (sin eps))
12.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
6.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

series390.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
44.0ms	(* (sin x) (sin eps))
133.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
129.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

simplify96.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	300	826
1	970	768
2	3675	746
3	5002	745

prune245.0ms

Filtered

85 candidates to 58 candidates (68.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	0	15	15
Picked	1	0	1
Done	0	0	0
Total	84	17	101

Merged error: 14.5b

Counts

101 → 17

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
0.3b	(/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
0.4b	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
3.7b	(- (/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (cos x))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

82×	`pow1`
34×	`pow-prod-down`
30×	`add-exp-log` `add-cbrt-cube`
23×	`cos-mult` `sin-mult`
18×	`add-sqr-sqrt`
16×	`prod-exp` `cbrt-unprod` `associate-/l/`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt` `times-frac`
12×	`associate-r/` `associate-l/`
10×	`frac-times`
9×	`frac-sub`
8×	`pow-sqr` `pow-prod-up`
6×	`add-log-exp` `difference-of-squares`
5×	`sub-div`
4×	`pow-plus` `associate-/l*`
3×	`associate-/r*` `associate-/r/`
2×	`pow2` `flip3--` `div-sub` `swap-sqr` `associate-r` `associate-l` `*-commutative` `flip--`
1×	`cbrt-undiv` `associate--l-` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `frac-add` `clear-num` `flip-+` `div-inv` `distribute-lft-out--`

Counts

4 → 141

Calls

4 calls:

9.0ms	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
20.0ms	(/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
8.0ms	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
18.0ms	(- (/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (cos x))

series697.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
208.0ms	(/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
53.0ms	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
380.0ms	(- (/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (cos x))

simplify96.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	620	2413
1	3209	2128
2	5001	2122

prune398.0ms

Filtered

153 candidates to 95 candidates (62.1%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	140	13	153
Fresh	8	8	16
Picked	1	0	1
Done	0	0	0
Total	149	21	170

Merged error: 14.5b

Counts

170 → 21

regimes273.0ms

Accuracy

83.2% (1.6b remaining)

Error of 16.1b against oracle of 14.4b and baseline of 24.1b

bsearch155.0ms

Steps

Iters	Range		Point
11	5.860352841659277e-39	1.3971991050448233e-15	5.959656621595075e-16
9	-1.3867281281148419e-07	-2.4492797358270376e-13	-4.0043015660238715e-09

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	50
1	48	50
2	48	50

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	4441×	body	1280	valid
545.0ms	622×	body	2560	valid
443.0ms	1861×	body	640	valid
111.0ms	729×	body	320	valid
30.0ms	279×	body	160	valid
4.0ms	68×	body	80	valid

Details

sample101.0ms

simplify5.0ms

prune2.0ms

localize8.0ms

rewrite11.0ms

series69.0ms

simplify113.0ms

prune86.0ms

localize14.0ms

rewrite24.0ms

series306.0ms

simplify114.0ms

prune223.0ms

localize17.0ms

rewrite32.0ms

series390.0ms

simplify96.0ms

prune245.0ms

localize19.0ms

rewrite63.0ms

series697.0ms

simplify96.0ms

prune398.0ms

regimes273.0ms

bsearch155.0ms

simplify2.0ms

end0.0ms

sample2.9s

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