Details

sample86.0ms

Algorithm

intervals

Results

49.0ms	103×	body	1280	valid
15.0ms	55×	body	640	valid
5.0ms	25×	body	320	valid
3.0ms	56×	body	80	valid
3.0ms	18×	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

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
3.9b	(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×	`times-frac` `associate-r` `associate-l` `associate-/r*` `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 → 47

Calls

3 calls:

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

series158.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* r (sin b))
99.0ms	(/ (* r (sin b)) (cos (+ a b)))
23.0ms	(cos (+ a b))

simplify34.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	198	305
1	861	257
2	5001	256

prune137.0ms

Filtered

56 candidates to 40 candidates (71.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	46	10	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	10	57

Merged error: 0.1b

Counts

57 → 10

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

rewrite27.0ms

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×	`associate-/r/` `cos-mult`
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` `diff-log` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 76

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* r (sin b))
5.0ms	(* (sin a) (sin b))
11.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series377.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
37.0ms	(* r (sin b))
46.0ms	(* (sin a) (sin b))
214.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify46.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	344	771
1	1513	674
2	5002	663

prune261.0ms

Filtered

88 candidates to 64 candidates (72.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	75	13	88
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	85	13	98

Merged error: 0.0b

Counts

98 → 13

localize18.0ms

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
58×	`add-sqr-sqrt`
56×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `div-inv` `associate-/l*` `add-log-exp`
5×	`sin-mult`
4×	`cbrt-undiv` `div-exp` `cos-mult` `associate-/l/`
3×	`associate-r` `associate-l`
2×	`flip3--` `frac-2neg` `clear-num` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `diff-log` `div-sub` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 135

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
5.0ms	(* (sin a) (sin b))
7.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
8.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

series460.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
42.0ms	(* (sin a) (sin b))
224.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
112.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

simplify73.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	570	2145
1	2453	2009
2	5001	1988

prune438.0ms

Filtered

147 candidates to 118 candidates (80.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	143	4	147
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	149	11	160

Merged error: 0.0b

Counts

160 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

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))
0.3b	(/ 1 (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
35×	`times-frac`
28×	`add-cube-cbrt`
24×	`add-exp-log` `associate-r`
18×	`add-cbrt-cube`
9×	`pow1`
8×	`associate-/r*`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`div-exp` `associate-l` `prod-exp`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod` `associate-/l*` `add-log-exp` `unswap-sqr`
3×	`div-inv`
2×	`rec-exp` `flip3--` `frac-2neg` `1-exp` `pow-prod-down` `clear-num` `cos-mult` `*-commutative` `flip--`
1×	`pow-flip` `associate-*r/` `un-div-inv` `associate-/l/` `inv-pow`

Counts

4 → 126

Calls

4 calls:

4.0ms	(* (cos a) (cos b))
14.0ms	(* r (/ 1 (- (/ (* (cos a) (cos b)) (sin b)) (sin a))))
5.0ms	(/ (* (cos a) (cos b)) (sin b))
9.0ms	(/ 1 (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (cos a) (cos b))
189.0ms	(* r (/ 1 (- (/ (* (cos a) (cos b)) (sin b)) (sin a))))
67.0ms	(/ (* (cos a) (cos b)) (sin b))
98.0ms	(/ 1 (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

simplify57.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	472	1352
1	2087	1200
2	5002	1158

prune279.0ms

Filtered

138 candidates to 85 candidates (61.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	138	11	149

Merged error: 0.0b

Counts

149 → 11

regimes158.0ms

Accuracy

0% (0.4b 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	9
1	17	9

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	2952×	body	1280	valid
500.0ms	1816×	body	640	valid
152.0ms	791×	body	320	valid
135.0ms	2099×	body	80	valid
62.0ms	343×	body	160	valid

Details

sample86.0ms

simplify8.0ms

prune2.0ms

localize12.0ms

rewrite17.0ms

series158.0ms

simplify34.0ms

prune137.0ms

localize16.0ms

rewrite27.0ms

series377.0ms

simplify46.0ms

prune261.0ms

localize18.0ms

rewrite30.0ms

series460.0ms

simplify73.0ms

prune438.0ms

localize16.0ms

rewrite40.0ms

series392.0ms

simplify57.0ms

prune279.0ms

regimes158.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.4s

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