Details

sample330.0ms

Algorithm

intervals

Results

50.0ms	100×	body	1280	valid
18.0ms	67×	body	640	valid
4.0ms	19×	body	320	valid
3.0ms	56×	body	80	valid
2.0ms	14×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	5
1	16	5
2	20	5
3	21	5
4	21	5

prune5.0ms

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: 15.6b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.3b	(/ (sin b) (cos (+ a b)))
3.3b	(cos (+ a b))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`expm1-log1p-u` `associate-l` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

3 → 73

Calls

3 calls:

21.0ms	(* r (/ (sin b) (cos (+ a b))))
4.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

series156.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(* r (/ (sin b) (cos (+ a b))))
37.0ms	(/ (sin b) (cos (+ a b)))
23.0ms	(cos (+ a b))

simplify43.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	263	560
1	1093	504
2	5002	504

prune220.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	71	11	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	11	83

Merged error: 0.2b

Counts

83 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u`
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` `fma-neg` `diff-log` `associate-*r/` `prod-diff` `clear-num`

Counts

4 → 110

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
5.0ms	(* (sin a) (sin b))
12.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series439.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
43.0ms	(* (sin a) (sin b))
207.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
111.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify61.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	432	1384
1	1847	1255
2	5002	1249

prune388.0ms

Filtered

122 candidates to 96 candidates (78.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	110	12	122
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	120	13	133

Merged error: 0.0b

Counts

133 → 13

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

rewrite25.0ms

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×	`expm1-log1p-u` `associate-/r/` `cos-mult` `log1p-expm1-u`
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` `fma-neg` `diff-log` `prod-diff` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 86

Calls

4 calls:

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

series368.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
38.0ms	(* r (sin b))
43.0ms	(* (sin a) (sin b))
210.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify53.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	369	835
1	1591	735
2	5002	730

prune280.0ms

Filtered

98 candidates to 72 candidates (73.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	97	14	111

Merged error: 0.0b

Counts

111 → 14

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.2b	(/ (* r (sin b)) (expm1 (log1p (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
0.3b	(expm1 (log1p (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.4b	(log1p (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
5×	`expm1-log1p-u`
4×	`log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`log1p-udef` `expm1-log1p` `frac-2neg` `log1p-expm1` `pow-prod-down` `clear-num` `-commutative` `div-inv` `sin-mult` `associate-/l` `expm1-udef` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

5.0ms	(* (sin a) (sin b))
5.0ms	(/ (* r (sin b)) (expm1 (log1p (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
1.0ms	(expm1 (log1p (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
1.0ms	(log1p (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series519.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin a) (sin b))
251.0ms	(/ (* r (sin b)) (expm1 (log1p (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
114.0ms	(expm1 (log1p (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
112.0ms	(log1p (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify129.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	286	820
1	1061	689
2	4958	680
3	5001	680

prune204.0ms

Filtered

78 candidates to 56 candidates (71.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	1	11	12
Picked	0	1	1
Done	1	0	1
Total	79	13	92

Merged error: 0.0b

Counts

92 → 13

regimes179.0ms

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	17	12
1	17	12

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	2912×	body	1280	valid
515.0ms	1882×	body	640	valid
143.0ms	727×	body	320	valid
133.0ms	2130×	body	80	valid
48.0ms	350×	body	160	valid