Details

sample80.0ms

Algorithm

intervals

Results

42.0ms	90×	body	1280	valid
15.0ms	52×	body	640	valid
5.0ms	80×	body	80	valid
4.0ms	22×	body	320	valid
2.0ms	12×	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: 15.3b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.4b	(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:

39.0ms	(* r (sin b))
96.0ms	(/ (* 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

prune131.0ms

Filtered

56 candidates to 40 candidates (71.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	49	7	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	7	57

Merged error: 0.2b

Counts

57 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

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

series372.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
39.0ms	(* r (sin b))
42.0ms	(* (sin a) (sin b))
210.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify47.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (39.0ms)

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

prune275.0ms

Filtered

88 candidates to 64 candidates (72.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	74	14	88
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	80	15	95

Merged error: 0.0b

Counts

95 → 15

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

rewrite32.0ms

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))
11.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
7.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
46.0ms	(* (sin a) (sin b))
110.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
218.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

simplify74.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	570	2145
1	2453	2009
2	5001	1988

prune450.0ms

Filtered

147 candidates to 118 candidates (80.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	143	4	147
Fresh	5	9	14
Picked	1	0	1
Done	0	0	0
Total	149	13	162

Merged error: 0.0b

Counts

162 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-l`
19×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-r` `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-*l/` `clear-num`

Counts

4 → 100

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
6.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
5.0ms	(* (sin a) (sin b))
11.0ms	(* (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (sin b))

series516.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
177.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
43.0ms	(* (sin a) (sin b))
217.0ms	(* (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (sin b))

simplify52.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	404	1241
1	1533	1120
2	5001	1103

prune272.0ms

Filtered

112 candidates to 86 candidates (76.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	113	12	125

Merged error: 0.0b

Counts

125 → 12

regimes160.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	10
1	15	10

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	2913×	body	1280	valid
525.0ms	1861×	body	640	valid
153.0ms	789×	body	320	valid
125.0ms	2079×	body	80	valid
50.0ms	360×	body	160	valid