Details

sample402.0ms

Algorithm

intervals

Results

59.0ms	60×	body	1280	valid
34.0ms	56×	body	640	valid
19.0ms	128×	body	80	valid
12.0ms	26×	body	320	valid
6.0ms	54×	body	80	nan
2.0ms	6×	body	160	valid

simplify45.0ms

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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
6.5b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
17.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite43.0ms

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)))))
27.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series527.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1.0 (tan B))
107.0ms	(* x (/ 1.0 (tan B)))
225.0ms	(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)))

simplify65.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (54.0ms)

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

prune592.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.2b	(/ (* x 1.0) (tan B))
6.5b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
17.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite34.0ms

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

series512.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ F (sin B))
105.0ms	(/ (* x 1.0) (tan B))
214.0ms	(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)))

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

prune504.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)) (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)))
6.5b	(fma (/ F (sin B)) (* (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)) (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))) (- (/ (* x 1.0) (tan B))))
18.5b	(pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))
18.5b	(pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
188×	`pow-unpow`
178×	`add-sqr-sqrt`
166×	`add-cube-cbrt` `*-un-lft-identity`
78×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
24×	`unpow-prod-down`
18×	`add-exp-log`
14×	`div-inv`
12×	`sqr-pow`
9×	`pow-neg` `distribute-frac-neg` `prod-exp` `unswap-sqr`
8×	`neg-sub0` `pow-to-exp` `div-sub` `pow-exp` `pow-sub`
7×	`swap-sqr` `associate-r` `associate-l`
6×	`pow1` `neg-mul-1` `add-cbrt-cube`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `add-log-exp`
2×	`pow-pow` `associate-r/` `associate-l/`
1×	`pow2` `pow-prod-down` `pow-sqr` `un-div-inv` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef`

Counts

4 → 297

Calls

4 calls:

13.0ms	(* (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)) (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)))
0.0ms	(fma (/ F (sin B)) (* (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)) (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))) (- (/ (* x 1.0) (tan B))))
11.0ms	(pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))
10.0ms	(pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))

series1.7s

Counts

4 → 12

Calls

4 calls:

842.0ms	(* (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)) (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)))
247.0ms	(fma (/ F (sin B)) (* (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)) (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))) (- (/ (* x 1.0) (tan B))))
310.0ms	(pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))
308.0ms	(pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))

simplify118.0ms

Algorithm

egg-herbie

Counts

309 → 309

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	1234	3275
1	4479	3077
2	5002	3052

prune1.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.2b	(* (pow (fma x 2.0 (fma F F 2.0)) (- (/ 1.0 2.0))) F)
0.6b	(/ (* (pow (fma x 2.0 (fma F F 2.0)) (- (/ 1.0 2.0))) F) (sin B))
17.9b	(pow (fma x 2.0 (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 128

Calls

4 calls:

4.0ms	(/ (* x 1.0) (tan B))
6.0ms	(* (pow (fma x 2.0 (fma F F 2.0)) (- (/ 1.0 2.0))) F)
5.0ms	(/ (* (pow (fma x 2.0 (fma F F 2.0)) (- (/ 1.0 2.0))) F) (sin B))
5.0ms	(pow (fma x 2.0 (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.9s

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (* x 1.0) (tan B))
649.0ms	(* (pow (fma x 2.0 (fma F F 2.0)) (- (/ 1.0 2.0))) F)
777.0ms	(/ (* (pow (fma x 2.0 (fma F F 2.0)) (- (/ 1.0 2.0))) F) (sin B))
330.0ms	(pow (fma x 2.0 (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify87.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	821	1215
1	3543	1116
2	5002	1112

prune543.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes221.0ms

Accuracy

98% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.5b

bsearch287.0ms

Steps

Iters	Range		Point
8	88225.78302546946	2686340471.047255	216369780.3554212
9	-4.5377116903385575e+162	-7.864489152983653e+154	-7.999585276668531e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	38
1	52	38
2	52	38

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.7s	1678×	body	1280	valid
912.0ms	1412×	body	640	valid
651.0ms	4736×	body	80	valid
297.0ms	680×	body	320	valid
179.0ms	1728×	body	80	nan
106.0ms	358×	body	160	valid