Details

sample86.0ms

Algorithm

intervals

Results

46.0ms	101×	body	1280	valid
19.0ms	59×	body	640	valid
4.0ms	63×	body	80	valid
4.0ms	19×	body	320	valid
2.0ms	14×	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: 19.4b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
4.9b	(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))

series160.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* r (sin b))
97.0ms	(/ (* r (sin b)) (cos (+ a b)))
23.0ms	(cos (+ a b))

simplify33.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (27.0ms)

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

prune136.0ms

Filtered

56 candidates to 40 candidates (71.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	46	10	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	10	57

Merged error: 0.2b

Counts

57 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

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

4.0ms	(* r (sin b))
5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
5.0ms	(* (sin a) (sin b))
9.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series380.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* r (sin b))
82.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
45.0ms	(* (sin a) (sin b))
214.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify47.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	344	770
1	1513	673
2	5001	663

prune280.0ms

Filtered

88 candidates to 64 candidates (72.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	74	14	88
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	82	16	98

Merged error: 0.0b

Counts

98 → 16

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
0.2b	(* (sin a) (sin b))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
3.8b	(log (exp (* (sin a) (sin b))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`log-prod` `add-log-exp`
3×	`times-frac` `associate-r` `associate-l` `associate-/r*` `log-pow` `associate--r+`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod`
1×	`sub-neg` `exp-prod` `exp-to-pow` `frac-2neg` `diff-log` `rem-log-exp` `pow-prod-down` `clear-num` `-commutative` `div-inv` `sin-mult` `associate-/l` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

6.0ms	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
5.0ms	(* (sin a) (sin b))
8.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
2.0ms	(log (exp (* (sin a) (sin b))))

series383.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
43.0ms	(* (sin a) (sin b))
214.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
44.0ms	(log (exp (* (sin a) (sin b))))

simplify39.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	322	847
1	1257	710
2	5002	703

prune259.0ms

Filtered

83 candidates to 59 candidates (71.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	5	10	15
Picked	0	1	1
Done	0	0	0
Total	85	14	99

Merged error: 0.0b

Counts

99 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 135

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
5.0ms	(* (sin a) (sin b))
7.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
8.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

series461.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
47.0ms	(* (sin a) (sin b))
218.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
115.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

simplify74.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	570	2147
1	2453	2011
2	5001	1990

prune419.0ms

Filtered

147 candidates to 119 candidates (81.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	144	3	147
Fresh	3	9	12
Picked	0	1	1
Done	1	0	1
Total	148	13	161

Merged error: 0.0b

Counts

161 → 13

regimes176.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	10
1	14	10

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	2938×	body	1280	valid
488.0ms	1776×	body	640	valid
150.0ms	782×	body	320	valid
131.0ms	2171×	body	80	valid
46.0ms	335×	body	160	valid