Details

sample331.0ms

Algorithm

intervals

Results

206.0ms	152×	body	80	valid
49.0ms	52×	body	1280	valid
34.0ms	57×	body	640	valid
10.0ms	23×	body	320	valid
5.0ms	49×	body	80	nan
2.0ms	6×	body	160	valid

simplify43.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	42	15
1	83	14
2	151	14
3	356	14
4	1063	14
5	5002	14

prune14.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 12.8b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))
5.8b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
17.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
49×	`times-frac`
45×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
25×	`add-exp-log`
21×	`associate-r`
16×	`associate-l` `add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
8×	`unpow-prod-down` `prod-exp` `unswap-sqr`
7×	`pow1`
5×	`div-exp` `div-inv`
4×	`pow-neg` `cbrt-unprod` `add-log-exp` `sqr-pow`
3×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `associate-r/` `pow-exp` `associate-/r` `associate-/l*` `pow-sub`
2×	`tan-quot` `frac-times` `associate-/r/` `*-commutative`
1×	`neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `clear-num` `un-div-inv`

Counts

4 → 155

Calls

4 calls:

4.0ms	(/ 1.0 (tan B))
7.0ms	(* x (/ 1.0 (tan B)))
14.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
20.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series136.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ 1.0 (tan B))
25.0ms	(* x (/ 1.0 (tan B)))
66.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
33.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify84.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	817	1480
1	3336	1390
2	5001	1389

prune385.0ms

Filtered

128 candidates to 167 candidates (-30.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	154	13	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	155	13	168

Merged error: 1.0b

Counts

168 → 13

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B)))
0.2b	(* x (/ 1.0 (tan B)))
0.3b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B))
17.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
73×	`times-frac`
59×	`add-cube-cbrt` `*-un-lft-identity`
39×	`associate-r`
30×	`pow-unpow`
25×	`add-exp-log` `unpow-prod-down`
16×	`add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
9×	`pow1` `sqr-pow`
7×	`div-exp` `associate-/l*`
6×	`associate-l` `prod-exp` `unswap-sqr`
5×	`div-inv`
4×	`cbrt-unprod` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `pow-exp` `associate-/r*`
2×	`neg-sub0` `pow-neg` `associate-r/` `pow-prod-down` `-commutative` `associate-/l/` `pow-sub`
1×	`tan-quot` `neg-mul-1` `pow-pow` `frac-2neg` `clear-num` `associate-/r/`

Counts

4 → 174

Calls

4 calls:

14.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B)))
7.0ms	(* x (/ 1.0 (tan B)))
10.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B))
12.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series160.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B)))
24.0ms	(* x (/ 1.0 (tan B)))
54.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B))
23.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify97.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	892	2150
1	3830	2033
2	5001	2033

prune442.0ms

Filtered

142 candidates to 186 candidates (-31.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	182	4	186
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	187	12	199

Merged error: 1.0b

Counts

199 → 12

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.2b	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B)))
0.3b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B))
17.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
63×	`add-sqr-sqrt`
53×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
25×	`add-exp-log` `unpow-prod-down` `associate-r`
16×	`add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
9×	`sqr-pow`
8×	`div-exp` `associate-/l*`
7×	`pow1`
6×	`associate-/r*`
5×	`prod-exp` `div-inv`
4×	`cbrt-undiv` `add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `associate-l` `pow-exp` `cbrt-unprod`
2×	`neg-sub0` `pow-neg` `frac-2neg` `clear-num` `associate-/l/` `pow-sub`
1×	`tan-quot` `neg-mul-1` `pow-pow` `associate-r/` `pow-prod-down` `associate-/r/` `-commutative`

Counts

4 → 163

Calls

4 calls:

5.0ms	(/ (* x 1.0) (tan B))
16.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B)))
10.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series155.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (* x 1.0) (tan B))
59.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B)))
50.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B))
23.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify91.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	845	2095
1	3589	1978
2	5002	1978

prune413.0ms

Filtered

136 candidates to 175 candidates (-28.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	173	2	175
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	176	11	187

Merged error: 1.0b

Counts

187 → 11

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B)))
0.3b	(/ 1 (/ (tan B) (* x 1.0)))
0.3b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B))
17.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

96×	`times-frac`
77×	`add-sqr-sqrt`
67×	`add-cube-cbrt` `*-un-lft-identity`
41×	`add-exp-log`
30×	`pow-unpow`
25×	`unpow-prod-down` `associate-r`
20×	`add-cbrt-cube`
18×	`div-exp`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
10×	`associate-/r` `associate-/l`
9×	`div-inv` `sqr-pow`
8×	`pow1`
7×	`cbrt-undiv` `prod-exp`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `rec-exp` `1-exp` `associate-l` `pow-exp` `cbrt-unprod`
2×	`neg-sub0` `pow-neg` `frac-2neg` `clear-num` `associate-/l/` `pow-sub`
1×	`neg-mul-1` `pow-flip` `pow-pow` `associate-r/` `pow-prod-down` `associate-/r/` `-commutative` `inv-pow`

Counts

4 → 197

Calls

4 calls:

14.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B)))
6.0ms	(/ 1 (/ (tan B) (* x 1.0)))
10.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series154.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B)))
19.0ms	(/ 1 (/ (tan B) (* x 1.0)))
53.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B))
23.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify105.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	987	2376
1	4489	2222
2	5001	2183

prune396.0ms

Filtered

143 candidates to 209 candidates (-46.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	209	0	209
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	209	11	220

Merged error: 1.0b

Counts

220 → 11

regimes298.0ms

Accuracy

95.6% (0.4b remaining)

Error of 1.5b against oracle of 1.1b and baseline of 10.6b

bsearch157.0ms

Steps

Iters	Range		Point
8	8.814840369262004e+132	3.631543391359148e+136	3.5769895011461384e+136
8	-8.223900071640638e+161	-7.327808308686989e+158	-7.414991998393748e+158

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	66
1	78	66

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.5s	1677×	body	1280	valid
891.0ms	1475×	body	640	valid
635.0ms	4691×	body	80	valid
282.0ms	676×	body	320	valid
162.0ms	1660×	body	80	nan
98.0ms	341×	body	160	valid

Details

sample331.0ms

simplify43.0ms

prune14.0ms

localize26.0ms

rewrite51.0ms

series136.0ms

simplify84.0ms

prune385.0ms

localize23.0ms

rewrite50.0ms

series160.0ms

simplify97.0ms

prune442.0ms

localize23.0ms

rewrite48.0ms

series155.0ms

simplify91.0ms

prune413.0ms

localize26.0ms

rewrite48.0ms

series154.0ms

simplify105.0ms

prune396.0ms

regimes298.0ms

bsearch157.0ms

simplify2.0ms

end0.0ms

sample4.0s

Profiling