Details

sample79.0ms

Algorithm

intervals

Results

41.0ms	97×	body	1280	valid
17.0ms	54×	body	640	valid
4.0ms	24×	body	320	valid
4.0ms	73×	body	80	valid
1.0ms	8×	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: 14.4b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
4.1b	(cos (+ a b))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 98

Calls

3 calls:

4.0ms	(* r (sin b))
8.0ms	(/ (* r (sin b)) (cos (+ a b)))
6.0ms	(cos (+ a b))

series169.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* r (sin b))
105.0ms	(/ (* r (sin b)) (cos (+ a b)))
25.0ms	(cos (+ a b))

simplify47.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	335	803
1	1423	755
2	5001	755

prune208.0ms

Filtered

107 candidates to 81 candidates (75.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	99	8	107
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	8	108

Merged error: 0.2b

Counts

108 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
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))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

378×	`add-sqr-sqrt`
244×	`*-un-lft-identity`
173×	`associate-l`
144×	`prod-diff`
132×	`add-cube-cbrt` `times-frac`
117×	`associate-r`
95×	`unswap-sqr`
56×	`distribute-lft-out--` `difference-of-squares`
39×	`*-commutative`
13×	`add-exp-log` `add-cbrt-cube`
12×	`fma-neg` `associate-/l*`
11×	`associate-/r*`
8×	`pow1`
6×	`add-log-exp`
5×	`sin-mult`
4×	`expm1-log1p-u` `associate-/r/` `cos-mult` `log1p-expm1-u`
3×	`prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `frac-2neg` `diff-log` `clear-num` `div-inv`

Counts

4 → 396

Calls

4 calls:

4.0ms	(* r (sin b))
24.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
5.0ms	(* (sin a) (sin b))
24.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series399.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* r (sin b))
85.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
45.0ms	(* (sin a) (sin b))
228.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify148.0ms

Algorithm

egg-herbie

Counts

408 → 408

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1070	7826
1	4074	6379
2	5002	6379

prune696.0ms

Filtered

408 candidates to 188 candidates (46.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	396	12	408
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	404	12	416

Merged error: 0.0b

Counts

416 → 12

localize16.0ms

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))

rewrite117.0ms

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)))
30.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
30.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
5.0ms	(* (sin a) (sin b))

series498.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
125.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
239.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
46.0ms	(* (sin a) (sin b))

simplify177.0ms

Algorithm

egg-herbie

Counts

467 → 467

Iterations

Useful iterations: 1 (30.0ms)

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

prune908.0ms

Filtered

467 candidates to 240 candidates (51.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	460	7	467
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	467	12	479

Merged error: 0.0b

Counts

479 → 12

localize18.0ms

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))

series502.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(fma (* (cos a) 1) (cos b) (- (* (sin b) (sin a))))
120.0ms	(/ (fma (* (cos a) 1) (cos b) (- (* (sin b) (sin a)))) (sin b))
242.0ms	(/ r (/ (fma (* (cos a) 1) (cos b) (- (* (sin b) (sin a)))) (sin b)))
52.0ms	(* (sin b) (sin a))

simplify71.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (52.0ms)

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

prune420.0ms

Filtered

152 candidates to 125 candidates (82.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	148	4	152
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	153	11	164

Merged error: 0.0b

Counts

164 → 11

regimes169.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b 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

sample2.2s

Algorithm

intervals

Results

1.2s	2871×	body	1280	valid
462.0ms	1810×	body	640	valid
145.0ms	791×	body	320	valid
135.0ms	2160×	body	80	valid
48.0ms	368×	body	160	valid