Details

sample84.0ms

Algorithm

intervals

Results

42.0ms	85×	body	1280	valid
14.0ms	55×	body	640	valid
5.0ms	31×	body	320	valid
4.0ms	78×	body	80	valid
1.0ms	7×	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: 15.2b

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)))
2.4b	(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))

series179.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(* r (sin b))
110.0ms	(/ (* r (sin b)) (cos (+ a b)))
19.0ms	(cos (+ a b))

simplify30.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (25.0ms)

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

prune309.0ms

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

localize15.0ms

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))))

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

series452.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
44.0ms	(* r (sin b))
55.0ms	(* (sin a) (sin b))
256.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify48.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (38.0ms)

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

prune355.0ms

Filtered

88 candidates to 63 candidates (28.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	76	12	88
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	84	13	97

Merged error: 0.0b

Counts

97 → 13

localize15.0ms

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

rewrite33.0ms

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)))
13.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
8.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
5.0ms	(* (sin a) (sin b))

series534.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
255.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
129.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
51.0ms	(* (sin a) (sin b))

simplify54.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	401	1308
1	1734	1183
2	5002	1178

prune545.0ms

Filtered

112 candidates to 84 candidates (25.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	107	5	112
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	111	14	125

Merged error: 0.0b

Counts

125 → 14

localize21.0ms

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 b) (- (* (cos b) (cos a)) (log (exp (* (sin a) (sin b))))))
0.2b	(* (sin a) (sin b))
3.4b	(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:

10.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin a) (sin b)))))))
8.0ms	(/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin a) (sin b))))))
5.0ms	(* (sin a) (sin b))
2.0ms	(log (exp (* (sin a) (sin b))))

series500.0ms

Counts

4 → 12

Calls

4 calls:

256.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin a) (sin b)))))))
135.0ms	(/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin a) (sin b))))))
52.0ms	(* (sin a) (sin b))
57.0ms	(log (exp (* (sin a) (sin b))))

simplify48.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (38.0ms)

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

prune523.0ms

Filtered

108 candidates to 82 candidates (24.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	108	14	122

Merged error: 0.0b

Counts

122 → 14

regimes350.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b 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

sample2.4s

Algorithm

intervals

Results

1.3s	2898×	body	1280	valid
473.0ms	1812×	body	640	valid
150.0ms	783×	body	320	valid
122.0ms	2147×	body	80	valid
52.0ms	360×	body	160	valid

Details

sample84.0ms

simplify6.0ms

prune4.0ms

localize10.0ms

rewrite13.0ms

series179.0ms

simplify30.0ms

prune309.0ms

localize15.0ms

rewrite23.0ms

series452.0ms

simplify48.0ms

prune355.0ms

localize15.0ms

rewrite33.0ms

series534.0ms

simplify54.0ms

prune545.0ms

localize21.0ms

rewrite28.0ms

series500.0ms

simplify48.0ms

prune523.0ms

regimes350.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.4s

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