Details

sample329.0ms

Algorithm

intervals

Results

38.0ms	89×	body	1280	valid
19.0ms	76×	body	640	valid
5.0ms	57×	body	80	valid
4.0ms	23×	body	320	valid
1.0ms	11×	body	160	valid

simplify12.0ms

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: 16.6b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
4.9b	(cos (+ a b))

rewrite36.0ms

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:

8.0ms	(* r (/ (sin b) (cos (+ a b))))
5.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

series163.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(* r (/ (sin b) (cos (+ a b))))
38.0ms	(/ (sin b) (cos (+ a b)))
25.0ms	(cos (+ a b))

simplify42.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	279	596
1	1182	540
2	5002	540

prune239.0ms

Filtered

93 candidates to 69 candidates (74.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	85	8	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	8	94

Merged error: 0.2b

Counts

94 → 8

localize19.0ms

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))))

rewrite98.0ms

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:

23.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
27.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
5.0ms	(* (sin a) (sin b))
24.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series459.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
214.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
47.0ms	(* (sin a) (sin b))
115.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify124.0ms

Algorithm

egg-herbie

Counts

358 → 358

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	924	6407
1	3400	4942
2	5002	4747

prune715.0ms

Filtered

358 candidates to 159 candidates (44.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	347	11	358
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	355	11	366

Merged error: 0.0b

Counts

366 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite111.0ms

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:

22.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
26.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
5.0ms	(* (sin a) (sin b))
29.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

series479.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
233.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
45.0ms	(* (sin a) (sin b))
121.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

simplify168.0ms

Algorithm

egg-herbie

Counts

467 → 467

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1277	8955
1	4785	7446
2	5001	7446

prune1.1s

Filtered

467 candidates to 241 candidates (51.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	460	7	467
Fresh	7	3	10
Picked	1	0	1
Done	0	0	0
Total	468	10	478

Merged error: 0.0b

Counts

478 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

117×	`times-frac`
109×	`add-sqr-sqrt`
105×	`*-un-lft-identity`
81×	`add-cube-cbrt`
44×	`associate-r`
40×	`fma-def`
36×	`associate-l`
18×	`add-exp-log` `associate-/r*`
16×	`add-cbrt-cube` `unswap-sqr`
15×	`associate-/l*`
12×	`*-commutative`
10×	`distribute-lft-out`
8×	`add-log-exp`
6×	`pow1`
5×	`distribute-rgt-neg-in` `div-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `prod-exp` `log1p-expm1-u`
3×	`cbrt-unprod` `div-inv`
2×	`frac-2neg` `flip3-+` `associate-*r/` `clear-num` `sum-log` `associate-/r/` `cos-mult` `flip-+`
1×	`+-commutative` `neg-sub0` `associate-+r-` `1-exp` `unsub-neg` `pow-prod-down` `neg-log` `associate-/l/`

Counts

4 → 230

Calls

4 calls:

33.0ms	(+ (/ (* (cos a) (cos b)) (sin b)) (- (sin a)))
5.0ms	(* (cos a) (cos b))
33.0ms	(/ r (* 1 (+ (/ (* (cos a) (cos b)) (sin b)) (- (sin a)))))
12.0ms	(/ (* (cos a) (cos b)) (sin b))

series399.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(+ (/ (* (cos a) (cos b)) (sin b)) (- (sin a)))
40.0ms	(* (cos a) (cos b))
194.0ms	(/ r (* 1 (+ (/ (* (cos a) (cos b)) (sin b)) (- (sin a)))))
75.0ms	(/ (* (cos a) (cos b)) (sin b))

simplify77.0ms

Algorithm

egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	717	2196
1	3206	2015
2	5002	1982

prune728.0ms

Filtered

242 candidates to 164 candidates (67.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	240	2	242
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	244	8	252

Merged error: 0b

Counts

252 → 8

regimes128.0ms

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	19	10
1	19	10

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.2s	2763×	body	1280	valid
454.0ms	1820×	body	640	valid
148.0ms	828×	body	320	valid
126.0ms	2251×	body	80	valid
42.0ms	339×	body	160	valid