Details

sample370.0ms

Algorithm

intervals

Results

50.0ms	57×	body	1280	valid
24.0ms	41×	body	640	valid
20.0ms	149×	body	80	valid
10.0ms	26×	body	320	valid
5.0ms	55×	body	80	nan
3.0ms	11×	body	160	valid

simplify49.0ms

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

prune28.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 13.7b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (+ (* F F) 2.0) (* 2.0 x))
0.2b	(* x (/ 1.0 (tan B)))
6.0b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
20.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
40×	`times-frac`
37×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
23×	`add-exp-log`
21×	`associate-r`
16×	`associate-l`
14×	`add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
9×	`add-log-exp`
8×	`unpow-prod-down` `prod-exp` `unswap-sqr`
7×	`pow1`
4×	`pow-neg` `div-exp` `cbrt-unprod` `div-inv` `sqr-pow`
3×	`neg-sub0` `pow-to-exp` `associate-*r/` `pow-exp` `sum-log` `pow-sub`
2×	`cbrt-undiv` `frac-times` `*-commutative`
1×	`tan-quot` `+-commutative` `neg-mul-1` `associate-+l+` `pow-pow` `flip3-+` `pow-prod-down` `associate-*l/` `associate-/r/` `un-div-inv` `flip-+`

Counts

4 → 140

Calls

4 calls:

6.0ms	(+ (+ (* F F) 2.0) (* 2.0 x))
7.0ms	(* x (/ 1.0 (tan B)))
14.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
13.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series643.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (+ (* F F) 2.0) (* 2.0 x))
121.0ms	(* x (/ 1.0 (tan B)))
317.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
176.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify91.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	813	1382
1	3495	1293
2	5001	1292

prune598.0ms

Filtered

152 candidates to 115 candidates (75.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	139	13	152
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	140	13	153

Merged error: 0.0b

Counts

153 → 13

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)))
0.4b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
20.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite48.0ms

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:

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

series1.0s

Counts

4 → 12

Calls

4 calls:

117.0ms	(* x (/ 1.0 (tan B)))
384.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
345.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
161.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify96.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	848	2078
1	3740	1960
2	5002	1960

prune675.0ms

Filtered

186 candidates to 143 candidates (76.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	182	4	186
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	186	13	199

Merged error: 0.0b

Counts

199 → 13

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (+ (* F F) 2.0) (* 2.0 x))
0.2b	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
0.4b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
20.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

63×	`times-frac`
61×	`add-sqr-sqrt`
51×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
25×	`unpow-prod-down` `associate-r`
20×	`add-exp-log`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
11×	`add-cbrt-cube`
9×	`add-log-exp` `sqr-pow`
7×	`pow1` `associate-/l*`
6×	`div-exp`
4×	`prod-exp` `div-inv` `unswap-sqr`
3×	`pow-to-exp` `associate-l` `pow-exp` `associate-/r*` `sum-log`
2×	`cbrt-undiv` `neg-sub0` `pow-neg` `cbrt-unprod` `associate-/l/` `pow-sub`
1×	`+-commutative` `neg-mul-1` `associate-+l+` `pow-pow` `frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip-+`

Counts

4 → 154

Calls

4 calls:

6.0ms	(+ (+ (* F F) 2.0) (* 2.0 x))
13.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
10.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series928.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (+ (* F F) 2.0) (* 2.0 x))
392.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
344.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
163.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify88.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	757	2000
1	3313	1894
2	5001	1894

prune614.0ms

Filtered

166 candidates to 129 candidates (77.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	166	13	179

Merged error: 0.0b

Counts

179 → 13

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1.0 (tan B)))
0.3b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.3b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
20.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
25×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
22×	`times-frac`
21×	`associate-r`
16×	`add-cbrt-cube`
13×	`pow-unpow`
8×	`prod-exp`
7×	`pow1` `unpow-prod-down`
6×	`associate-l`
5×	`div-exp` `unswap-sqr`
4×	`cbrt-unprod` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `pow-exp` `div-inv` `associate-/l*` `sqr-pow`
2×	`*-commutative`
1×	`tan-quot` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `associate-/r/`

Counts

4 → 108

Calls

4 calls:

7.0ms	(* x (/ 1.0 (tan B)))
10.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
10.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
9.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series858.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* x (/ 1.0 (tan B)))
270.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
326.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
145.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify71.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	654	1088
1	2850	977
2	5002	977

prune378.0ms

Filtered

120 candidates to 89 candidates (74.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	116	4	120
Fresh	5	6	11
Picked	1	0	1
Done	0	1	1
Total	122	11	133

Merged error: 0.0b

Counts

133 → 11

regimes185.0ms

Accuracy

98.1% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.8b

bsearch304.0ms

Steps

Iters	Range		Point
10	0.000608309806168642	2529654550.545884	170093912.0872669
9	-4.9334811240918525e+148	-5.335099083904646e+143	-2.310238641427746e+145

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	38
1	50	38

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	1624×	body	1280	valid
783.0ms	1435×	body	640	valid
564.0ms	4792×	body	80	valid
260.0ms	694×	body	320	valid
136.0ms	1609×	body	80	nan
94.0ms	368×	body	160	valid