Details

sample88.0ms

Algorithm

intervals

Results

51.0ms	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

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: 15.5b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.3b	(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×	`expm1-log1p-u` `times-frac` `associate-r` `associate-l` `associate-/r*` `log1p-expm1-u` `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 → 53

Calls

3 calls:

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

series159.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* r (sin b))
96.0ms	(/ (* r (sin b)) (cos (+ a b)))
23.0ms	(cos (+ a b))

simplify35.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	207	327
1	884	279
2	5001	279

prune151.0ms

Filtered

62 candidates to 46 candidates (74.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	52	10	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	10	63

Merged error: 0.2b

Counts

63 → 10

localize19.0ms

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))))

series377.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
37.0ms	(* r (sin b))
46.0ms	(* (sin a) (sin b))
211.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify53.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (44.0ms)

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

prune295.0ms

Filtered

98 candidates to 74 candidates (75.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	86	12	98
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	96	12	108

Merged error: 0.0b

Counts

108 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

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

series450.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
47.0ms	(* (sin a) (sin b))
211.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
112.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify60.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	427	1384
1	1819	1255
2	5001	1254

prune348.0ms

Filtered

122 candidates to 94 candidates (77.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	122	12	134

Merged error: 0.0b

Counts

134 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.2b	(* (sin a) (sin b))
0.3b	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (* r (sin b)))
0.3b	(/ 1 (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (* r (sin b))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
34×	`add-exp-log`
30×	`add-sqr-sqrt`
26×	`add-cube-cbrt` `*-un-lft-identity`
22×	`add-cbrt-cube`
14×	`div-exp`
9×	`pow1`
8×	`associate-/r*`
7×	`cbrt-undiv`
6×	`associate-r` `associate-l` `prod-exp` `div-inv` `associate-/l*`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`rec-exp` `1-exp` `sin-mult`
2×	`frac-2neg` `pow-prod-down` `clear-num` `cos-mult` `*-commutative` `unswap-sqr`
1×	`flip3--` `pow-flip` `div-sub` `associate-/r/` `frac-sub` `flip--` `inv-pow` `sub-div`

Counts

4 → 127

Calls

4 calls:

6.0ms	(* r (sin b))
5.0ms	(* (sin a) (sin b))
9.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (* r (sin b)))
8.0ms	(/ 1 (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (* r (sin b))))

series498.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* r (sin b))
42.0ms	(* (sin a) (sin b))
170.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (* r (sin b)))
250.0ms	(/ 1 (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (* r (sin b))))

simplify74.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	508	1609
1	2464	1401
2	5001	1347

prune276.0ms

Filtered

139 candidates to 86 candidates (61.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	136	3	139
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	138	13	151

Merged error: 0.0b

Counts

151 → 13

regimes170.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	12
1	20	12

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	2912×	body	1280	valid
502.0ms	1882×	body	640	valid
138.0ms	727×	body	320	valid
129.0ms	2130×	body	80	valid
46.0ms	350×	body	160	valid