Details

sample77.0ms

Algorithm

intervals

Results

40.0ms	91×	body	1280	valid
16.0ms	56×	body	640	valid
5.0ms	29×	body	320	valid
4.0ms	70×	body	80	valid
1.0ms	10×	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: 14.5b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.2b	(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))

series162.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* r (sin b))
102.0ms	(/ (* r (sin b)) (cos (+ a b)))
23.0ms	(cos (+ a b))

simplify33.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (28.0ms)

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

prune125.0ms

Filtered

56 candidates to 40 candidates (71.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	48	8	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	8	57

Merged error: 0.2b

Counts

57 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

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

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

series382.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* r (sin b))
83.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
44.0ms	(* (sin a) (sin b))
213.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify50.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	344	771
1	1513	674
2	5001	663

prune259.0ms

Filtered

88 candidates to 64 candidates (72.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	77	11	88
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	85	11	96

Merged error: 0.0b

Counts

96 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

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`
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` `diff-log` `associate-*r/` `clear-num`

Counts

4 → 100

Calls

4 calls:

5.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
15.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
5.0ms	(* (sin a) (sin b))
8.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

series461.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
220.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
43.0ms	(* (sin a) (sin b))
114.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify55.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	401	1307
1	1733	1182
2	5001	1178

prune309.0ms

Filtered

112 candidates to 84 candidates (75.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	110	13	123

Merged error: 0.0b

Counts

123 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sin b) (- (* (* (cos b) (cos a)) (* (cos b) (cos a))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (+ (* (cos b) (cos a)) (* (sin a) (sin b))))
0.2b	(/ (sin b) (- (* (* (cos b) (cos a)) (* (cos b) (cos a))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
0.2b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.4b	(* (* (cos b) (cos a)) (* (cos b) (cos a)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

84×	`pow1`
42×	`cos-mult` `sin-mult`
35×	`add-exp-log` `pow-prod-down` `add-cbrt-cube`
34×	`associate-l`
32×	`associate-/r/`
27×	`add-sqr-sqrt`
25×	`times-frac` `associate-*r/`
23×	`associate-*l/`
22×	`add-cube-cbrt` `*-un-lft-identity`
21×	`frac-times`
18×	`prod-exp` `frac-sub` `cbrt-unprod`
10×	`sub-div`
8×	`pow-sqr` `pow-prod-up`
7×	`difference-of-squares`
5×	`associate-r`
4×	`pow-plus` `associate-/r*` `add-log-exp`
3×	`-commutative` `associate-/l`
2×	`cbrt-undiv` `pow2` `flip3--` `flip3-+` `swap-sqr` `div-exp` `frac-add` `flip--` `flip-+` `div-inv` `unswap-sqr`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`

Counts

4 → 180

Calls

4 calls:

24.0ms	(* (/ (sin b) (- (* (* (cos b) (cos a)) (* (cos b) (cos a))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (+ (* (cos b) (cos a)) (* (sin a) (sin b))))
14.0ms	(/ (sin b) (- (* (* (cos b) (cos a)) (* (cos b) (cos a))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
9.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
9.0ms	(* (* (cos b) (cos a)) (* (cos b) (cos a)))

series499.0ms

Counts

4 → 12

Calls

4 calls:

250.0ms	(* (/ (sin b) (- (* (* (cos b) (cos a)) (* (cos b) (cos a))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (+ (* (cos b) (cos a)) (* (sin a) (sin b))))
142.0ms	(/ (sin b) (- (* (* (cos b) (cos a)) (* (cos b) (cos a))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
54.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
52.0ms	(* (* (cos b) (cos a)) (* (cos b) (cos a)))

simplify143.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	940	3187
1	4929	2746
2	5001	2746

prune564.0ms

Filtered

192 candidates to 122 candidates (63.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	189	3	192
Fresh	3	8	11
Picked	1	0	1
Done	0	1	1
Total	193	12	205

Merged error: 0.0b

Counts

205 → 12

regimes184.0ms

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

sample2.3s

Algorithm

intervals

Results

1.3s	2928×	body	1280	valid
487.0ms	1817×	body	640	valid
156.0ms	804×	body	320	valid
132.0ms	2126×	body	80	valid
48.0ms	327×	body	160	valid

Details

sample77.0ms

simplify8.0ms

prune2.0ms

localize11.0ms

rewrite17.0ms

series162.0ms

simplify33.0ms

prune125.0ms

localize15.0ms

rewrite27.0ms

series382.0ms

simplify50.0ms

prune259.0ms

localize16.0ms

rewrite36.0ms

series461.0ms

simplify55.0ms

prune309.0ms

localize20.0ms

rewrite68.0ms

series499.0ms

simplify143.0ms

prune564.0ms

regimes184.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.3s

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