Details

sample77.0ms

Algorithm

intervals

Results

40.0ms	94×	body	1280	valid
15.0ms	63×	body	640	valid
7.0ms	73×	body	80	valid
3.0ms	18×	body	320	valid
1.0ms	8×	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 (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: 16.8b

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)))
3.3b	(cos (+ a b))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
36×	`times-frac`
30×	`add-cube-cbrt` `*-un-lft-identity`
15×	`associate-r` `associate-l`
12×	`associate-/l*`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `*-commutative` `unswap-sqr`
3×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `cos-sum` `div-exp` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `frac-2neg` `pow-prod-down` `clear-num` `div-inv`

Counts

3 → 98

Calls

3 calls:

4.0ms	(* r (sin b))
8.0ms	(/ (* r (sin b)) (cos (+ a b)))
6.0ms	(cos (+ a b))

series166.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* r (sin b))
104.0ms	(/ (* r (sin b)) (cos (+ a b)))
24.0ms	(cos (+ a b))

simplify47.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	335	803
1	1423	755
2	5001	755

prune205.0ms

Filtered

107 candidates to 81 candidates (24.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	99	8	107
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	8	108

Merged error: 0.2b

Counts

108 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

245×	`add-sqr-sqrt`
163×	`*-un-lft-identity`
132×	`times-frac`
97×	`associate-l`
67×	`unswap-sqr`
59×	`add-cube-cbrt`
52×	`distribute-lft-out--` `difference-of-squares`
45×	`associate-r`
15×	`add-exp-log` `*-commutative` `add-cbrt-cube`
12×	`associate-/l*`
11×	`associate-/r*`
10×	`pow1`
4×	`expm1-log1p-u` `prod-exp` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `cos-mult` `sin-mult`
2×	`cbrt-undiv` `div-exp`
1×	`flip3--` `frac-2neg` `clear-num` `frac-sub` `flip--` `div-inv` `sub-div`

Counts

4 → 237

Calls

4 calls:

4.0ms	(* r (sin b))
4.0ms	(* (cos a) (cos b))
5.0ms	(* (sin a) (sin b))
23.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series357.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* r (sin b))
42.0ms	(* (cos a) (cos b))
47.0ms	(* (sin a) (sin b))
226.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify96.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	714	3499
1	3093	3394
2	5002	3393

prune558.0ms

Filtered

249 candidates to 153 candidates (38.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	235	14	249
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	243	14	257

Merged error: 0b

Counts

257 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.1b	(* (cos a) (cos b))
0.2b	(* (sin a) (sin b))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

134×	`add-sqr-sqrt`
99×	`*-un-lft-identity`
84×	`times-frac`
47×	`add-cube-cbrt`
46×	`associate-l`
33×	`associate-r`
26×	`distribute-lft-out--` `difference-of-squares`
24×	`unswap-sqr`
15×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/l*`
11×	`*-commutative`
10×	`pow1`
7×	`associate-/r*`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`
2×	`cbrt-undiv` `div-exp` `associate-/r/`
1×	`flip3--` `frac-2neg` `clear-num` `cos-mult` `flip--` `div-inv` `sin-mult`

Counts

4 → 183

Calls

4 calls:

4.0ms	(* r (sin b))
4.0ms	(* (cos a) (cos b))
5.0ms	(* (sin a) (sin b))
18.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))))

series409.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* r (sin b))
41.0ms	(* (cos a) (cos b))
50.0ms	(* (sin a) (sin b))
274.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))))

simplify80.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	605	2822
1	2679	2626
2	5001	2587

prune514.0ms

Filtered

195 candidates to 128 candidates (34.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	190	5	195
Fresh	7	6	13
Picked	1	0	1
Done	0	0	0
Total	198	11	209

Merged error: 0b

Counts

209 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

147×	`add-sqr-sqrt`
107×	`*-un-lft-identity`
67×	`times-frac`
47×	`associate-r`
42×	`add-cube-cbrt`
41×	`associate-l`
36×	`unswap-sqr`
32×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r*`
17×	`associate-*r/`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
8×	`associate-/r/`
7×	`associate-/l*`
5×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `clear-num` `*-commutative`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `un-div-inv` `frac-sub` `flip--` `div-inv` `sub-div`

Counts

4 → 187

Calls

4 calls:

4.0ms	(* (cos b) (cos a))
18.0ms	(/ r (- (* (cos b) (cos a)) (* (sin a) (sin b))))
5.0ms	(* (sin a) (sin b))
32.0ms	(* (sin b) (/ r (- (* (cos b) (cos a)) (* (sin a) (sin b)))))

series532.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos b) (cos a))
204.0ms	(/ r (- (* (cos b) (cos a)) (* (sin a) (sin b))))
46.0ms	(* (sin a) (sin b))
240.0ms	(* (sin b) (/ r (- (* (cos b) (cos a)) (* (sin a) (sin b)))))

simplify74.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	564	1979
1	2420	1859
2	5001	1851

prune433.0ms

Filtered

199 candidates to 132 candidates (33.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	196	3	199
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	199	11	210

Merged error: 0b

Counts

210 → 11

regimes167.0ms

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	15	10
1	15	10

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2892×	body	1280	valid
462.0ms	1882×	body	640	valid
130.0ms	774×	body	320	valid
127.0ms	2125×	body	80	valid
41.0ms	330×	body	160	valid