Details

sample79.0ms

Algorithm

intervals

Results

42.0ms	95×	body	1280	valid
17.0ms	68×	body	640	valid
4.0ms	22×	body	320	valid
3.0ms	58×	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

prune3.0ms

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: 12.6b

Counts

2 → 1

localize12.0ms

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))

rewrite18.0ms

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×	`expm1-log1p-u` `times-frac` `associate-r` `associate-l` `associate-/r*` `log1p-expm1-u` `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 → 53

Calls

3 calls:

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

series161.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* r (sin b))
98.0ms	(/ (* r (sin b)) (cos (+ a b)))
23.0ms	(cos (+ a b))

simplify35.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	207	327
1	884	279
2	5001	279

prune162.0ms

Filtered

62 candidates to 46 candidates (74.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	54	8	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	8	63

Merged error: 0.2b

Counts

63 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
9×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `prod-exp` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `pow-prod-down` `associate-/r` `cos-mult` `-commutative` `sin-mult` `unswap-sqr`
2×	`cbrt-undiv` `div-exp`
1×	`flip3--` `frac-2neg` `clear-num` `frac-sub` `flip--` `div-inv` `associate-/l*` `sub-div`

Counts

4 → 89

Calls

4 calls:

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

series342.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos a) (cos b))
36.0ms	(* r (sin b))
218.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
44.0ms	(* (sin a) (sin b))

simplify51.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	382	724
1	1662	634
2	5001	633

prune321.0ms

Filtered

101 candidates to 73 candidates (72.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	90	11	101
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	97	12	109

Merged error: 0.0b

Counts

109 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
0.2b	(* (sin a) (sin b))
0.3b	(pow (* (sin a) (sin b)) 3)
30.0b	(cbrt (pow (* (sin a) (sin b)) 3))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1`
8×	`cbrt-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `sin-mult` `add-log-exp`
3×	`cube-div` `pow-unpow` `times-frac` `associate-r` `associate-l` `prod-exp` `associate-/r*` `associate-/r/` `cbrt-unprod`
2×	`cbrt-undiv` `cube-mult` `unpow-prod-down` `cbrt-div` `pow-pow` `unpow3` `cube-prod` `div-exp` `pow-prod-down` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `flip3--` `frac-2neg` `pow1/3` `clear-num` `cos-mult` `-commutative` `frac-sub` `flip--` `rem-cbrt-cube` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

11.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
5.0ms	(* (sin a) (sin b))
5.0ms	(pow (* (sin a) (sin b)) 3)
3.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

series373.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
48.0ms	(* (sin a) (sin b))
68.0ms	(pow (* (sin a) (sin b)) 3)
46.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

simplify56.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	402	840
1	1873	732
2	5001	723

prune343.0ms

Filtered

104 candidates to 73 candidates (70.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	103	13	116

Merged error: 0.0b

Counts

116 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos b) (cos a))
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))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
23×	`associate-r`
19×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`associate-l`
8×	`associate-/r/`
5×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `frac-sub` `flip--` `div-inv` `sub-div`
1×	`frac-2neg` `associate-*r/` `clear-num`

Counts

4 → 113

Calls

4 calls:

5.0ms	(* (cos b) (cos a))
12.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
5.0ms	(* (sin a) (sin b))
9.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

series419.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (cos b) (cos a))
221.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
44.0ms	(* (sin a) (sin b))
115.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify58.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	444	1273
1	1890	1154
2	5002	1152

prune346.0ms

Filtered

125 candidates to 94 candidates (75.2%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	3	8	11
Picked	0	1	1
Done	0	1	1
Total	125	13	138

Merged error: 0b

Counts

138 → 13

regimes184.0ms

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	18	12
1	18	12

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2843×	body	1280	valid
500.0ms	1872×	body	640	valid
132.0ms	734×	body	320	valid
131.0ms	2212×	body	80	valid
43.0ms	339×	body	160	valid