Details

sample90.0ms

Algorithm

intervals

Results

52.0ms	112×	body	1280	valid
15.0ms	58×	body	640	valid
5.0ms	24×	body	320	valid
4.0ms	52×	body	80	valid
1.0ms	10×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	16	5
2	19	5
3	20	5
4	20	5

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: 16.2b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
3.0b	(cos (+ a b))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
3×	`times-frac` `associate-r` `associate-l` `associate-/r*` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`cos-sum` `frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 47

Calls

3 calls:

4.0ms	(* r (sin b))
5.0ms	(/ (* r (sin b)) (cos (+ a b)))
6.0ms	(cos (+ a b))

series158.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* r (sin b))
95.0ms	(/ (* r (sin b)) (cos (+ a b)))
23.0ms	(cos (+ a b))

simplify33.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	198	305
1	861	257
2	5001	256

prune136.0ms

Filtered

56 candidates to 40 candidates (71.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	47	9	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	9	57

Merged error: 0.2b

Counts

57 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`sin-mult`
4×	`associate-/r/` `cos-mult`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `diff-log` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 76

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* r (sin b))
8.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
5.0ms	(* (sin a) (sin b))

series373.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
39.0ms	(* r (sin b))
208.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
46.0ms	(* (sin a) (sin b))

simplify49.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	344	770
1	1513	673
2	5002	663

prune282.0ms

Filtered

88 candidates to 64 candidates (72.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	72	16	88
Fresh	8	0	8
Picked	1	0	1
Done	0	0	0
Total	81	16	97

Merged error: 0.0b

Counts

97 → 16

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
0.2b	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
0.2b	(* (sin a) (sin b))
0.3b	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-r`
19×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
3×	`flip3--` `prod-exp` `associate-/r` `frac-sub` `flip--` `cbrt-unprod` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`sub-neg` `frac-2neg` `diff-log` `associate-*r/` `clear-num`

Counts

4 → 100

Calls

4 calls:

5.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
11.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
5.0ms	(* (sin a) (sin b))
8.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

series448.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
211.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
47.0ms	(* (sin a) (sin b))
108.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify55.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	401	1307
1	1733	1182
2	5001	1178

prune334.0ms

Filtered

112 candidates to 84 candidates (75.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	108	4	112
Fresh	5	10	15
Picked	1	0	1
Done	0	0	0
Total	114	14	128

Merged error: 0.0b

Counts

128 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b)))
0.2b	(* r (/ 1 (/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b))))
0.2b	(* (sin a) (sin b))
0.2b	(/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
108×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
92×	`add-cube-cbrt`
47×	`associate-r`
38×	`add-exp-log`
22×	`add-cbrt-cube`
16×	`associate-/r*`
15×	`div-exp`
10×	`div-inv`
9×	`pow1`
8×	`prod-exp`
7×	`cbrt-undiv`
6×	`associate-l` `associate-/l*` `unswap-sqr`
4×	`rec-exp` `1-exp` `cbrt-unprod` `associate-/l/` `add-log-exp`
3×	`sin-mult`
2×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r/` `cos-mult` `*-commutative`
1×	`flip3--` `pow-flip` `div-sub` `associate-*r/` `un-div-inv` `frac-sub` `flip--` `inv-pow` `sub-div`

Counts

4 → 200

Calls

4 calls:

7.0ms	(/ 1 (/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b)))
19.0ms	(* r (/ 1 (/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b))))
5.0ms	(* (sin a) (sin b))
9.0ms	(/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b))

series474.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ 1 (/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b)))
218.0ms	(* r (/ 1 (/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b))))
43.0ms	(* (sin a) (sin b))
105.0ms	(/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b))

simplify94.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	710	3077
1	3595	2767
2	5002	2623

prune472.0ms

Filtered

212 candidates to 136 candidates (64.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	208	4	212
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	214	12	226

Merged error: 0.0b

Counts

226 → 12

regimes160.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	8
1	12	8

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	2867×	body	1280	valid
509.0ms	1829×	body	640	valid
153.0ms	807×	body	320	valid
136.0ms	2133×	body	80	valid
50.0ms	367×	body	160	valid

Details

sample90.0ms

simplify8.0ms

prune2.0ms

localize12.0ms

rewrite17.0ms

series158.0ms

simplify33.0ms

prune136.0ms

localize16.0ms

rewrite24.0ms

series373.0ms

simplify49.0ms

prune282.0ms

localize19.0ms

rewrite32.0ms

series448.0ms

simplify55.0ms

prune334.0ms

localize18.0ms

rewrite48.0ms

series474.0ms

simplify94.0ms

prune472.0ms

regimes160.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.3s

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