Details

sample320.0ms

Algorithm

intervals

Results

47.0ms	97×	body	1280	valid
13.0ms	54×	body	640	valid
4.0ms	24×	body	320	valid
4.0ms	73×	body	80	valid
1.0ms	8×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune4.0ms

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: 14.4b

Counts

2 → 1

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
4.1b	(cos (+ a b))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 84

Calls

3 calls:

9.0ms	(* r (/ (sin b) (cos (+ a b))))
5.0ms	(/ (sin b) (cos (+ a b)))
7.0ms	(cos (+ a b))

series175.0ms

Counts

3 → 9

Calls

3 calls:

109.0ms	(* r (/ (sin b) (cos (+ a b))))
41.0ms	(/ (sin b) (cos (+ a b)))
25.0ms	(cos (+ a b))

simplify43.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	278	596
1	1172	540
2	5001	540

prune184.0ms

Filtered

93 candidates to 69 candidates (74.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	84	9	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	9	94

Merged error: 0.2b

Counts

94 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

280×	`add-sqr-sqrt`
188×	`*-un-lft-identity`
144×	`prod-diff`
119×	`associate-r`
117×	`associate-l`
115×	`add-cube-cbrt`
67×	`times-frac`
64×	`unswap-sqr`
36×	`distribute-lft-out--` `difference-of-squares`
27×	`*-commutative`
22×	`associate-/r*`
17×	`associate-*r/`
13×	`add-exp-log` `add-cbrt-cube`
12×	`fma-neg`
8×	`pow1` `associate-/r/`
7×	`sin-mult` `associate-/l*`
6×	`cos-mult` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `prod-exp` `clear-num` `frac-sub` `flip--` `cbrt-unprod` `sub-div`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `un-div-inv` `div-inv`
1×	`sub-neg` `diff-log`

Counts

4 → 346

Calls

4 calls:

21.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
33.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
5.0ms	(* (sin a) (sin b))
28.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series494.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
235.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
48.0ms	(* (sin a) (sin b))
124.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify128.0ms

Algorithm

egg-herbie

Counts

358 → 358

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	916	6407
1	3339	4942
2	5003	4743

prune577.0ms

Filtered

358 candidates to 159 candidates (44.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	346	12	358
Fresh	8	0	8
Picked	1	0	1
Done	0	0	0
Total	355	12	367

Merged error: 0.0b

Counts

367 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

465×	`add-sqr-sqrt`
341×	`*-un-lft-identity`
276×	`times-frac`
197×	`add-cube-cbrt`
150×	`associate-l`
144×	`prod-diff`
98×	`unswap-sqr`
78×	`associate-r`
72×	`distribute-lft-out--` `difference-of-squares`
43×	`associate-/r*`
26×	`*-commutative`
25×	`associate-/l*`
21×	`associate-/r/`
13×	`add-exp-log` `add-cbrt-cube`
12×	`fma-neg`
8×	`associate-/l/`
7×	`sin-mult`
6×	`pow1` `cos-mult` `div-inv` `add-log-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`flip3--` `frac-2neg` `clear-num` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `diff-log` `div-sub` `pow-prod-down` `prod-exp` `cbrt-unprod`

Counts

4 → 455

Calls

4 calls:

21.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
33.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
26.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
5.0ms	(* (sin a) (sin b))

series517.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
125.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
247.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
54.0ms	(* (sin a) (sin b))

simplify179.0ms

Algorithm

egg-herbie

Counts

467 → 467

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1270	8955
1	4737	7446
2	5001	7446

prune903.0ms

Filtered

467 candidates to 241 candidates (51.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	463	4	467
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	469	10	479

Merged error: 0.0b

Counts

479 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 140

Calls

4 calls:

1.0ms	(fma (* (cos a) 1) (cos b) (- (* (sin b) (sin a))))
4.0ms	(/ (fma (* (cos a) 1) (cos b) (- (* (sin b) (sin a)))) (sin b))
7.0ms	(/ r (/ (fma (* (cos a) 1) (cos b) (- (* (sin b) (sin a)))) (sin b)))
5.0ms	(* (sin b) (sin a))

series524.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(fma (* (cos a) 1) (cos b) (- (* (sin b) (sin a))))
126.0ms	(/ (fma (* (cos a) 1) (cos b) (- (* (sin b) (sin a)))) (sin b))
252.0ms	(/ r (/ (fma (* (cos a) 1) (cos b) (- (* (sin b) (sin a)))) (sin b)))
54.0ms	(* (sin b) (sin a))

simplify68.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	491	2326
1	2215	2140
2	5001	2131

prune430.0ms

Filtered

152 candidates to 125 candidates (82.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	152	10	162

Merged error: 0.0b

Counts

162 → 10

regimes153.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	11
1	26	11
2	26	11

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	2871×	body	1280	valid
472.0ms	1810×	body	640	valid
150.0ms	791×	body	320	valid
120.0ms	2160×	body	80	valid
53.0ms	368×	body	160	valid