Details

sample368.0ms

Algorithm

intervals

Results

46.0ms	55×	body	1280	valid
27.0ms	51×	body	640	valid
18.0ms	142×	body	80	valid
7.0ms	20×	body	320	valid
5.0ms	55×	body	80	nan
3.0ms	13×	body	160	valid

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	43	15
1	91	14
2	169	14
3	378	14
4	1100	14
5	5001	14

prune25.0ms

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: 12.0b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))
5.8b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
15.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
37×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
14×	`associate-r`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`add-exp-log`
11×	`add-cbrt-cube`
7×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`unpow-prod-down` `associate-l` `associate-/r` `associate-/l`
2×	`tan-quot` `cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `fma-udef` `pow-sub` `sqr-pow`

Counts

4 → 123

Calls

4 calls:

4.0ms	(/ 1.0 (tan B))
7.0ms	(* x (/ 1.0 (tan B)))
1.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
13.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series528.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ 1.0 (tan B))
107.0ms	(* x (/ 1.0 (tan B)))
224.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
157.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify66.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	628	1028
1	2518	940
2	5001	937

prune582.0ms

Filtered

135 candidates to 112 candidates (83.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	122	13	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	13	136

Merged error: 0.0b

Counts

136 → 13

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.2b	(/ (* x 1.0) (tan B))
5.8b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
15.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity` `times-frac`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`add-exp-log`
11×	`add-cbrt-cube`
6×	`associate-/r*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
3×	`cbrt-undiv` `unpow-prod-down` `div-exp`
2×	`frac-2neg` `clear-num`
1×	`tan-quot` `neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-pow` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `fma-udef` `pow-sub` `sqr-pow`

Counts

4 → 111

Calls

4 calls:

7.0ms	(/ F (sin B))
5.0ms	(/ (* x 1.0) (tan B))
1.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series527.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ F (sin B))
109.0ms	(/ (* x 1.0) (tan B))
228.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
143.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify60.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	616	964
1	2352	876
2	5001	873

prune517.0ms

Filtered

123 candidates to 100 candidates (81.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	116	7	123
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	123	13	136

Merged error: 0.0b

Counts

136 → 13

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.3b	(* F (/ 1 (sin B)))
5.8b	(fma (* F (/ 1 (sin B))) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
15.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
32×	`times-frac`
31×	`*-un-lft-identity`
30×	`add-cube-cbrt` `pow-unpow`
19×	`add-exp-log`
14×	`add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-r`
7×	`pow1`
5×	`prod-exp`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`cbrt-undiv` `unpow-prod-down` `associate-l` `associate-/r*` `cbrt-unprod` `unswap-sqr`
1×	`tan-quot` `neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `rec-exp` `pow-pow` `frac-2neg` `1-exp` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `associate-/r/` `un-div-inv` `-commutative` `fma-udef` `associate-/l*` `pow-sub` `sqr-pow`

Counts

4 → 120

Calls

4 calls:

5.0ms	(/ (* x 1.0) (tan B))
8.0ms	(* F (/ 1 (sin B)))
1.0ms	(fma (* F (/ 1 (sin B))) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series530.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (* x 1.0) (tan B))
52.0ms	(* F (/ 1 (sin B)))
222.0ms	(fma (* F (/ 1 (sin B))) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
149.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify68.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	710	1020
1	2989	910
2	5003	890

prune530.0ms

Filtered

132 candidates to 103 candidates (78.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	128	4	132
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	133	12	145

Merged error: 0.0b

Counts

145 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(* F (/ 1 (sin B)))
0.3b	(/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
5.8b	(fma (* F (/ 1 (sin B))) (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
15.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
41×	`times-frac`
37×	`*-un-lft-identity`
36×	`add-cube-cbrt`
23×	`add-exp-log`
15×	`unpow-prod-down`
13×	`pow-unpow` `associate-r`
11×	`add-cbrt-cube`
8×	`div-exp`
7×	`pow1` `associate-/r*`
5×	`sqr-pow`
4×	`expm1-log1p-u` `pow-to-exp` `rec-exp` `1-exp` `pow-exp` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `div-inv` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `cbrt-unprod`
1×	`pow-flip` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `fma-udef` `inv-pow`

Counts

4 → 132

Calls

4 calls:

7.0ms	(* F (/ 1 (sin B)))
9.0ms	(/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
1.0ms	(fma (* F (/ 1 (sin B))) (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
12.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

47.0ms	(* F (/ 1 (sin B)))
709.0ms	(/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
242.0ms	(fma (* F (/ 1 (sin B))) (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
133.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify69.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	727	1411
1	2871	1264
2	5001	1199

prune459.0ms

Filtered

144 candidates to 93 candidates (64.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	140	4	144
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	144	12	156

Merged error: 0.0b

Counts

156 → 12

regimes227.0ms

Accuracy

95% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 13.9b

bsearch252.0ms

Steps

Iters	Range		Point
10	61404.87568264329	2157434815204663.0	12718342694.297161
7	-4.00406664335678e+129	-1.7063783991581126e+128	-1.2847759360874979e+129

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	40
1	57	40
2	57	40

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.3s	1612×	body	1280	valid
726.0ms	1390×	body	640	valid
584.0ms	4850×	body	80	valid
238.0ms	649×	body	320	valid
138.0ms	1629×	body	80	nan
83.0ms	348×	body	160	valid