Details

sample384.0ms

Algorithm

intervals

Results

53.0ms	51×	body	1280	valid
27.0ms	43×	body	640	valid
22.0ms	157×	body	80	valid
9.0ms	20×	body	320	valid
6.0ms	54×	body	80	nan
3.0ms	11×	body	160	valid

simplify48.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
7.7b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
18.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite42.0ms

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:

2.0ms	(/ 1.0 (tan B))
8.0ms	(* 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)))))
26.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series542.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1.0 (tan B))
112.0ms	(* 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)))))
161.0ms	(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

prune599.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.2b	(/ (* x 1.0) (tan B))
7.7b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
18.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite33.0ms

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))
3.0ms	(/ (* 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))))
24.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series529.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ F (sin B))
107.0ms	(/ (* x 1.0) (tan B))
222.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
147.0ms	(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

prune531.0ms

Pruning

11 alts after pruning (11 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))
0.7b	(/ 1 (fma x 2.0 (fma F F 2.0)))
7.7b	(fma (/ F (sin B)) (pow (/ 1 (fma x 2.0 (fma F F 2.0))) (/ 1.0 2.0)) (- (/ (* x 1.0) (tan B))))
17.8b	(pow (/ 1 (fma x 2.0 (fma F F 2.0))) (/ 1.0 2.0))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

30×	`times-frac`
28×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`add-exp-log`
13×	`unpow-prod-down` `pow-unpow`
11×	`add-cbrt-cube`
7×	`pow1`
6×	`div-exp` `associate-/r*`
4×	`expm1-log1p-u` `pow-exp` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
3×	`cbrt-undiv` `pow-pow`
2×	`rec-exp` `pow-flip` `frac-2neg` `1-exp` `clear-num` `inv-pow`
1×	`tan-quot` `pow-to-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `fma-udef` `sqr-pow`

Counts

4 → 111

Calls

4 calls:

3.0ms	(/ (* x 1.0) (tan B))
2.0ms	(/ 1 (fma x 2.0 (fma F F 2.0)))
0.0ms	(fma (/ F (sin B)) (pow (/ 1 (fma x 2.0 (fma F F 2.0))) (/ 1.0 2.0)) (- (/ (* x 1.0) (tan B))))
5.0ms	(pow (/ 1 (fma x 2.0 (fma F F 2.0))) (/ 1.0 2.0))

series716.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (* x 1.0) (tan B))
86.0ms	(/ 1 (fma x 2.0 (fma F F 2.0)))
221.0ms	(fma (/ F (sin B)) (pow (/ 1 (fma x 2.0 (fma F F 2.0))) (/ 1.0 2.0)) (- (/ (* x 1.0) (tan B))))
300.0ms	(pow (/ 1 (fma x 2.0 (fma F F 2.0))) (/ 1.0 2.0))

simplify59.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	636	964
1	2439	880
2	5001	846

prune452.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

7.7b	(fma (/ F (sin B)) (pow (* (/ 1 (sqrt (fma x 2.0 (fma F F 2.0)))) (/ 1 (sqrt (fma x 2.0 (fma F F 2.0))))) (/ 1.0 2.0)) (- (/ (* x 1.0) (tan B))))
17.8b	(pow (* (/ 1 (sqrt (fma x 2.0 (fma F F 2.0)))) (/ 1 (sqrt (fma x 2.0 (fma F F 2.0))))) (/ 1.0 2.0))
18.6b	(sqrt (fma x 2.0 (fma F F 2.0)))
18.6b	(sqrt (fma x 2.0 (fma F F 2.0)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log`
30×	`pow1`
24×	`pow-flip`
22×	`pow-pow`
17×	`pow-exp`
16×	`div-exp` `prod-exp`
15×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `pow-unpow` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
9×	`times-frac` `pow-prod-up`
8×	`rec-exp` `1-exp` `inv-pow`
6×	`sqrt-prod`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow2` `pow-to-exp` `unpow-prod-down` `pow-plus` `fma-udef` `div-inv` `sqr-pow`

Counts

4 → 104

Calls

4 calls:

0.0ms	(fma (/ F (sin B)) (pow (* (/ 1 (sqrt (fma x 2.0 (fma F F 2.0)))) (/ 1 (sqrt (fma x 2.0 (fma F F 2.0))))) (/ 1.0 2.0)) (- (/ (* x 1.0) (tan B))))
14.0ms	(pow (* (/ 1 (sqrt (fma x 2.0 (fma F F 2.0)))) (/ 1 (sqrt (fma x 2.0 (fma F F 2.0))))) (/ 1.0 2.0))
1.0ms	(sqrt (fma x 2.0 (fma F F 2.0)))
1.0ms	(sqrt (fma x 2.0 (fma F F 2.0)))

series748.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(fma (/ F (sin B)) (pow (* (/ 1 (sqrt (fma x 2.0 (fma F F 2.0)))) (/ 1 (sqrt (fma x 2.0 (fma F F 2.0))))) (/ 1.0 2.0)) (- (/ (* x 1.0) (tan B))))
298.0ms	(pow (* (/ 1 (sqrt (fma x 2.0 (fma F F 2.0)))) (/ 1 (sqrt (fma x 2.0 (fma F F 2.0))))) (/ 1.0 2.0))
108.0ms	(sqrt (fma x 2.0 (fma F F 2.0)))
113.0ms	(sqrt (fma x 2.0 (fma F F 2.0)))

simplify56.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	693	1054
1	1966	985
2	5001	968

prune391.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes244.0ms

Accuracy

98.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 14.1b

bsearch295.0ms

Steps

Iters	Range		Point
8	9.896777056605239e+26	2.3418024522712145e+30	1.0032762422602447e+27
10	-5.276190702543451e+18	-83587.99580701615	-194810752.0873168

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	38
1	51	38
2	51	38

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.7s	1645×	body	1280	valid
866.0ms	1337×	body	640	valid
690.0ms	4855×	body	80	valid
300.0ms	683×	body	320	valid
158.0ms	1499×	body	80	nan
99.0ms	337×	body	160	valid