Details

sample400.0ms

Algorithm

intervals

Results

60.0ms	59×	body	1280	valid
26.0ms	41×	body	640	valid
22.0ms	143×	body	80	valid
12.0ms	27×	body	320	valid
6.0ms	19×	body	160	valid
4.0ms	40×	body	80	nan

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: 13.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.2b	(* x (/ 1.0 (tan B)))
6.3b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
18.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite130.0ms

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×	`frac-times` `*-commutative`
1×	`tan-quot` `neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `clear-num` `associate-/r/` `un-div-inv`

Counts

4 → 154

Calls

4 calls:

2.0ms	(/ F (sin B))
9.0ms	(* x (/ 1.0 (tan B)))
85.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
27.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series604.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ F (sin B))
112.0ms	(* x (/ 1.0 (tan B)))
287.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
157.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify85.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	765	1418
1	3213	1329
2	5001	1328

prune628.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
0.2b	(* x (/ 1.0 (tan B)))
0.3b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
18.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite183.0ms

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:

81.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
8.0ms	(* x (/ 1.0 (tan B)))
58.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
27.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series925.0ms

Counts

4 → 12

Calls

4 calls:

351.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
109.0ms	(* x (/ 1.0 (tan B)))
320.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
144.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify93.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	848	2078
1	3742	1960
2	5001	1960

prune705.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

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)) (- (/ 1.0 2.0))) (sin B)))
0.3b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
18.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite175.0ms

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:

4.0ms	(/ (* x 1.0) (tan B))
80.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
58.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
27.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series908.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (* x 1.0) (tan B))
345.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
314.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
144.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify87.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	801	2023
1	3500	1905
2	5002	1905

prune669.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* F (/ 1 (/ (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))))
0.3b	(/ 1 (/ (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))))
0.3b	(/ (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
18.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

362×	`times-frac`
217×	`add-sqr-sqrt`
195×	`*-un-lft-identity`
191×	`add-cube-cbrt`
86×	`associate-r`
80×	`unpow-prod-down`
68×	`add-exp-log`
37×	`div-exp`
34×	`associate-/r*`
30×	`pow-unpow`
28×	`sqr-pow`
20×	`add-cbrt-cube`
18×	`associate-/r/`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `prod-exp`
12×	`div-inv`
9×	`neg-sub0` `pow-neg` `pow-sub` `unswap-sqr`
8×	`pow1` `pow-to-exp` `rec-exp` `1-exp` `pow-exp`
7×	`cbrt-undiv`
6×	`associate-/l*`
4×	`add-log-exp`
3×	`associate-l` `cbrt-unprod`
2×	`frac-2neg` `clear-num`
1×	`neg-mul-1` `pow-flip` `pow-pow` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 356

Calls

4 calls:

103.0ms	(* F (/ 1 (/ (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))))
41.0ms	(/ 1 (/ (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))))
38.0ms	(/ (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)))

series1.4s

Counts

4 → 12

Calls

4 calls:

289.0ms	(* F (/ 1 (/ (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))))
722.0ms	(/ 1 (/ (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))))
223.0ms	(/ (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
150.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify78.0ms

Algorithm

egg-herbie

Counts

368 → 368

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1344	5507
1	5001	5146

prune1.2s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes206.0ms

Accuracy

98.3% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.6b

bsearch343.0ms

Steps

Iters	Range		Point
11	0.2287861600326909	4.253017872043058e+35	880497.3495401609
9	-3.634948470477859e+45	-3.596465999237397e+36	-3.6741442446631564e+36

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	39
1	48	39

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.8s	1712×	body	1280	valid
889.0ms	1355×	body	640	valid
695.0ms	4802×	body	80	valid
295.0ms	669×	body	320	valid
176.0ms	1663×	body	80	nan
104.0ms	335×	body	160	valid