Details

sample419.0ms

Algorithm

intervals

Results

67.0ms	65×	body	1280	valid
28.0ms	44×	body	640	valid
20.0ms	141×	body	80	valid
12.0ms	26×	body	320	valid
7.0ms	47×	body	80	nan
5.0ms	14×	body	160	valid

simplify46.0ms

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

prune10.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.2b	(* x (/ 1.0 (tan B)))
5.6b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
19.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite45.0ms

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×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`tan-quot` `neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `associate-/r/` `-commutative` `fma-udef` `pow-sub` `sqr-pow`

Counts

4 → 122

Calls

4 calls:

2.0ms	(/ F (sin B))
9.0ms	(* x (/ 1.0 (tan B)))
0.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
27.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series553.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ F (sin B))
110.0ms	(* x (/ 1.0 (tan B)))
234.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
160.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify71.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	666	1019
1	2629	931
2	5001	928

prune592.0ms

Filtered

134 candidates to 110 candidates (82.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.2b	(/ (* x 1.0) (tan B))
5.6b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
19.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite35.0ms

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:

2.0ms	(/ F (sin B))
4.0ms	(/ (* x 1.0) (tan B))
0.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
25.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series535.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ F (sin B))
114.0ms	(/ (* x 1.0) (tan B))
223.0ms	(fma (/ F (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)))

simplify56.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (46.0ms)

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

prune522.0ms

Filtered

123 candidates to 98 candidates (79.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.3b	(* F (/ 1 (sin B)))
5.6b	(fma (* F (/ 1 (sin B))) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
19.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite42.0ms

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:

4.0ms	(/ (* x 1.0) (tan B))
9.0ms	(* F (/ 1 (sin B)))
0.0ms	(fma (* F (/ 1 (sin B))) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
25.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series536.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (* x 1.0) (tan B))
48.0ms	(* F (/ 1 (sin B)))
229.0ms	(fma (* F (/ 1 (sin B))) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
148.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify74.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (58.0ms)

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

prune528.0ms

Filtered

132 candidates to 103 candidates (78.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (- (/ 1.0 2.0))) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (- (/ 1.0 2.0))))
5.6b	(fma (/ F (sin B)) (* (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (- (/ 1.0 2.0))) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (- (/ 1.0 2.0)))) (- (/ (* x 1.0) (tan B))))
19.0b	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))
19.0b	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
44×	`unpow-prod-down`
28×	`sqrt-prod`
18×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log` `unswap-sqr`
12×	`swap-sqr` `sqr-pow`
10×	`associate-r` `associate-l`
9×	`prod-exp`
7×	`pow-neg`
6×	`pow1` `neg-sub0` `pow-to-exp` `pow-exp` `add-cbrt-cube` `pow-sub`
4×	`expm1-log1p-u` `frac-times` `sqrt-div` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `associate-l/` `flip-+`
1×	`pow2` `pow-prod-down` `pow-sqr` `un-div-inv` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef`

Counts

4 → 125

Calls

4 calls:

156.0ms	(* (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (- (/ 1.0 2.0))) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (- (/ 1.0 2.0))))
0.0ms	(fma (/ F (sin B)) (* (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (- (/ 1.0 2.0))) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (- (/ 1.0 2.0)))) (- (/ (* x 1.0) (tan B))))
19.0ms	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))
19.0ms	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))

series572.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(* (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (- (/ 1.0 2.0))) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (- (/ 1.0 2.0))))
244.0ms	(fma (/ F (sin B)) (* (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (- (/ 1.0 2.0))) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (- (/ 1.0 2.0)))) (- (/ (* x 1.0) (tan B))))
57.0ms	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))
57.0ms	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))

simplify63.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	475	2138
1	1774	1932
2	5002	1899

prune456.0ms

Filtered

137 candidates to 83 candidates (60.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes219.0ms

Accuracy

98% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 14.2b

bsearch301.0ms

Steps

Iters	Range		Point
8	8.503002622430935e+53	4.277142149416969e+57	8.686379519706808e+53
10	-1.7728388980308613e+18	-33514344.933988083	-1683736694.5255616

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	43
1	56	43
2	62	43
3	62	43

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.7s	1679×	body	1280	valid
895.0ms	1361×	body	640	valid
708.0ms	4742×	body	80	valid
308.0ms	698×	body	320	valid
181.0ms	1703×	body	80	nan
114.0ms	362×	body	160	valid