Details

sample110.0ms

Algorithm

intervals

Results

55.0ms	103×	body	1280	valid
24.0ms	56×	body	640	valid
6.0ms	23×	body	320	valid
4.0ms	60×	body	80	valid
3.0ms	14×	body	160	valid

simplify6.0ms

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

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 17.5b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.6b	(cos (+ a b))

rewrite13.0ms

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)))
4.0ms	(cos (+ a b))

series35.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(* r (sin b))
23.0ms	(/ (* r (sin b)) (cos (+ a b)))
5.0ms	(cos (+ a b))

simplify28.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (24.0ms)

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

prune96.0ms

Filtered

56 candidates to 40 candidates (28.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	47	9	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	9	57

Merged error: 0.2b

Counts

57 → 9

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

rewrite23.0ms

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

series80.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
7.0ms	(* r (sin b))
9.0ms	(* (sin a) (sin b))
49.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	344	770
1	1513	673
2	5002	663

prune138.0ms

Filtered

88 candidates to 64 candidates (27.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	78	10	88
Fresh	8	0	8
Picked	1	0	1
Done	0	0	0
Total	87	10	97

Merged error: 0.0b

Counts

97 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (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))))

rewrite31.0ms

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)))
11.0ms	(* 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))))

series99.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
46.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
9.0ms	(* (sin a) (sin b))
28.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify53.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (40.0ms)

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

prune173.0ms

Filtered

112 candidates to 84 candidates (25.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	108	4	112
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	111	11	122

Merged error: 0.0b

Counts

122 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* r (/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin a) (sin b)))))))
0.2b	(* (sin a) (sin b))
0.2b	(/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin a) (sin b))))))
1.3b	(log (exp (* (sin a) (sin b))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
18×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`associate-l`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`log-prod` `prod-exp` `associate-/r` `log-pow` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `flip--` `div-inv`
1×	`exp-prod` `exp-to-pow` `frac-2neg` `associate-*r/` `rem-log-exp` `clear-num` `sin-mult`

Counts

4 → 96

Calls

4 calls:

11.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin a) (sin b)))))))
5.0ms	(* (sin a) (sin b))
8.0ms	(/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin a) (sin b))))))
2.0ms	(log (exp (* (sin a) (sin b))))

series106.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin a) (sin b)))))))
9.0ms	(* (sin a) (sin b))
29.0ms	(/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin a) (sin b))))))
9.0ms	(log (exp (* (sin a) (sin b))))

simplify58.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	360	1301
1	1545	1128
2	5002	1121

prune104.0ms

Filtered

108 candidates to 82 candidates (24.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	108	11	119

Merged error: 0.0b

Counts

119 → 11

regimes279.0ms

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	17	12
1	17	12

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.3s	2936×	body	1280	valid
496.0ms	1792×	body	640	valid
144.0ms	749×	body	320	valid
139.0ms	2162×	body	80	valid
54.0ms	361×	body	160	valid

Details

sample110.0ms

simplify6.0ms

prune4.0ms

localize10.0ms

rewrite13.0ms

series35.0ms

simplify28.0ms

prune96.0ms

localize16.0ms

rewrite23.0ms

series80.0ms

simplify43.0ms

prune138.0ms

localize16.0ms

rewrite31.0ms

series99.0ms

simplify53.0ms

prune173.0ms

localize19.0ms

rewrite28.0ms

series106.0ms

simplify58.0ms

prune104.0ms

regimes279.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.5s

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