Details

sample79.0ms

Algorithm

intervals

Results

44.0ms	98×	body	1280	valid
14.0ms	55×	body	640	valid
5.0ms	26×	body	320	valid
3.0ms	64×	body	80	valid
2.0ms	13×	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: 15.7b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
5.0b	(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))

series159.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* r (sin b))
96.0ms	(/ (* 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

prune145.0ms

Filtered

56 candidates to 40 candidates (71.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	45	11	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	11	57

Merged error: 0.2b

Counts

57 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.1b	(- (* (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))))

rewrite24.0ms

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

series378.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* r (sin b))
81.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
46.0ms	(* (sin a) (sin b))
214.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify50.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	344	770
1	1513	673
2	5001	663

prune289.0ms

Filtered

88 candidates to 64 candidates (72.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	74	14	88
Fresh	10	0	10
Picked	1	0	1
Done	0	0	0
Total	85	14	99

Merged error: 0.0b

Counts

99 → 14

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

rewrite34.0ms

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

series450.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
214.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
43.0ms	(* (sin a) (sin b))
111.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify54.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (43.0ms)

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

prune370.0ms

Filtered

112 candidates to 84 candidates (75.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	104	8	112
Fresh	9	4	13
Picked	1	0	1
Done	0	0	0
Total	114	12	126

Merged error: 0.0b

Counts

126 → 12

localize18.0ms

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))
0.3b	(/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin a) (sin b))))))
1.9b	(log (exp (* (sin a) (sin b))))

rewrite31.0ms

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)))))))
7.0ms	(* (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))))

series407.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin a) (sin b)))))))
45.0ms	(* (sin a) (sin b))
109.0ms	(/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin a) (sin b))))))
43.0ms	(log (exp (* (sin a) (sin b))))

simplify53.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (43.0ms)

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

prune357.0ms

Filtered

108 candidates to 82 candidates (75.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	108	12	120

Merged error: 0.0b

Counts

120 → 12

regimes168.0ms

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

sample2.2s

Algorithm

intervals

Results

1.2s	2919×	body	1280	valid
487.0ms	1866×	body	640	valid
135.0ms	765×	body	320	valid
119.0ms	2109×	body	80	valid
44.0ms	344×	body	160	valid