Details

sample392.0ms

Algorithm

intervals

Results

55.0ms	55×	body	1280	valid
27.0ms	42×	body	640	valid
23.0ms	154×	body	80	valid
8.0ms	18×	body	320	valid
5.0ms	49×	body	80	nan
3.0ms	9×	body	160	valid

simplify45.0ms

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))
6.0b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
16.8b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite132.0ms

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:

2.0ms	(/ 1.0 (tan B))
9.0ms	(* x (/ 1.0 (tan B)))
86.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
28.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series613.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ 1.0 (tan B))
114.0ms	(* x (/ 1.0 (tan B)))
300.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
158.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify84.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	767	1428
1	3183	1338
2	5001	1337

prune692.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt F)
0.6b	(cbrt F)
2.0b	(* (/ (cbrt F) (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
16.8b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
42×	`times-frac`
37×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
22×	`associate-l`
18×	`add-exp-log` `cbrt-prod`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
9×	`unpow-prod-down` `unswap-sqr`
8×	`add-cbrt-cube`
7×	`associate-r`
6×	`prod-exp`
5×	`pow1` `sqr-pow`
4×	`pow-neg` `add-log-exp`
3×	`neg-sub0` `pow-to-exp` `div-exp` `pow-exp` `div-inv` `pow-sub`
2×	`frac-times` `pow1/3` `associate-*r/` `cbrt-unprod`
1×	`cbrt-undiv` `neg-mul-1` `pow-pow` `associate-l/` `un-div-inv` `-commutative`

Counts

4 → 128

Calls

4 calls:

1.0ms	(cbrt F)
1.0ms	(cbrt F)
88.0ms	(* (/ (cbrt F) (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
24.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series873.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(cbrt F)
183.0ms	(cbrt F)
356.0ms	(* (/ (cbrt F) (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
147.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify71.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	656	1441
1	2463	1372
2	5002	1365

prune694.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt F)
2.0b	(* (/ (cbrt F) (sin B)) (cbrt (pow (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) 3)))
16.8b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))
23.1b	(cbrt (pow (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) 3))

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-sqr-sqrt`
85×	`cbrt-prod`
54×	`times-frac`
45×	`add-cube-cbrt` `*-un-lft-identity`
44×	`unpow-prod-down`
30×	`pow-unpow`
27×	`unswap-sqr`
23×	`cube-prod` `associate-r`
22×	`associate-l`
16×	`sqr-pow`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
10×	`add-exp-log`
7×	`pow1`
6×	`cube-div` `cbrt-div` `add-cbrt-cube`
4×	`neg-sub0` `pow-neg` `pow-sub` `add-log-exp`
3×	`div-inv`
2×	`cube-mult` `frac-times` `pow1/3` `unpow3` `associate-*r/` `prod-exp` `cbrt-unprod`
1×	`cbrt-undiv` `pow-to-exp` `neg-mul-1` `pow-pow` `div-exp` `pow-prod-down` `associate-l/` `pow-exp` `-commutative` `rem-cbrt-cube`

Counts

4 → 178

Calls

4 calls:

1.0ms	(cbrt F)
163.0ms	(* (/ (cbrt F) (sin B)) (cbrt (pow (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) 3)))
24.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))
35.0ms	(cbrt (pow (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) 3))

series825.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(cbrt F)
349.0ms	(* (/ (cbrt F) (sin B)) (cbrt (pow (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) 3)))
142.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))
149.0ms	(cbrt (pow (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) 3))

simplify91.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	809	2500
1	3369	2454
2	5001	2443

prune882.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))
6.0b	(/ (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
16.8b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

191×	`times-frac`
117×	`add-sqr-sqrt`
112×	`add-cube-cbrt` `*-un-lft-identity`
45×	`unpow-prod-down`
25×	`add-exp-log`
16×	`add-cbrt-cube` `associate-/l*`
15×	`sqr-pow`
14×	`associate-r`
13×	`pow-unpow`
12×	`div-inv`
11×	`div-exp`
10×	`associate-/r*`
7×	`pow1`
5×	`cbrt-undiv`
4×	`add-log-exp`
3×	`pow-to-exp` `associate-l` `pow-exp`
2×	`tan-quot` `frac-2neg` `prod-exp` `clear-num` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`pow-pow` `associate-r/` `pow-prod-down` `-commutative` `associate-/l/`

Counts

4 → 218

Calls

4 calls:

2.0ms	(/ 1.0 (tan B))
8.0ms	(* x (/ 1.0 (tan B)))
40.0ms	(/ (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
25.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series601.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1.0 (tan B))
119.0ms	(* x (/ 1.0 (tan B)))
307.0ms	(/ (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
139.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify109.0ms

Algorithm

egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1011	3107
1	4477	3017
2	5002	3017

prune871.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes181.0ms

Accuracy

98.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 11.3b

bsearch172.0ms

Steps

Iters	Range		Point
3	134.08440984297408	194.8494816658418	191.05166467691257
8	-1.2579556351517705e+22	-2.891063626338147e+17	-3.322533047566384e+17

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	37
1	46	37

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.8s	1718×	body	1280	valid
882.0ms	1331×	body	640	valid
688.0ms	4811×	body	80	valid
316.0ms	689×	body	320	valid
177.0ms	1654×	body	80	nan
107.0ms	361×	body	160	valid