Details

sample152.0ms

Algorithm

intervals

Results

93.0ms	62×	body	2560	valid
32.0ms	78×	body	1280	valid
12.0ms	55×	body	640	valid
4.0ms	26×	body	320	valid
2.0ms	18×	body	160	valid
1.0ms	17×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.9b	(- 1.0 (cos x))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series61.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(/ (- 1.0 (cos x)) (sin x))
18.0ms	(- 1.0 (cos x))

simplify37.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	292	569
1	965	460
2	5002	460

prune187.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
0.6b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
0.9b	(- 1.0 (cos x))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
40×	`add-cube-cbrt`
38×	`exp-prod`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
9×	`prod-diff`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `fma-neg` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 132

Calls

4 calls:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
7.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
8.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
5.0ms	(- 1.0 (cos x))

series138.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
48.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
35.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
19.0ms	(- 1.0 (cos x))

simplify41.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	368	1009
1	1099	873
2	5002	871

prune353.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 3)
0.4b	(+ 1.0 (cos x))
0.6b	(log (exp (/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x))))
0.8b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

491×	`add-sqr-sqrt`
462×	`times-frac`
353×	`*-un-lft-identity`
251×	`add-cube-cbrt`
242×	`log-pow`
241×	`exp-prod`
198×	`unpow-prod-down` `cube-prod`
160×	`difference-of-squares`
144×	`prod-diff`
106×	`sqr-pow`
50×	`distribute-lft-out--`
26×	`cube-mult` `unpow3`
12×	`fma-neg`
10×	`difference-cubes`
8×	`add-log-exp`
6×	`pow1`
5×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`pow-unpow` `log-prod` `fma-def`
2×	`div-sub`
1×	`+-commutative` `pow-to-exp` `sub-neg` `log-div` `flip3--` `pow-pow` `flip3-+` `exp-diff` `diff-log` `rem-log-exp` `pow-exp` `sum-log` `flip--` `flip-+` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 490

Calls

4 calls:

3.0ms	(pow (cos x) 3)
4.0ms	(+ 1.0 (cos x))
59.0ms	(log (exp (/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x))))
17.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series451.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(pow (cos x) 3)
9.0ms	(+ 1.0 (cos x))
153.0ms	(log (exp (/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x))))
257.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify181.0ms

Algorithm

egg-herbie

Counts

502 → 502

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1408	6419
1	4788	5472
2	5001	5472

prune986.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ (pow 1.0 3) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x))
0.4b	(+ 1.0 (cos x))
0.4b	(+ 1.0 (cos x))
0.9b	(- (/ (/ (pow 1.0 3) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x)) (/ (/ (pow (cos x) 3) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x)))

rewrite4.0s

Algorithm

rewrite-expression-head

Rules

57336×	`times-frac`
27010×	`add-sqr-sqrt`
26944×	`*-un-lft-identity`
26842×	`add-cube-cbrt`
15376×	`prod-diff`
6807×	`unpow-prod-down` `cube-prod`
2265×	`sqr-pow`
2253×	`cube-mult` `unpow3`
1009×	`div-inv`
124×	`fma-neg`
49×	`distribute-lft-out--`
40×	`associate-/l*`
36×	`difference-of-squares`
14×	`add-exp-log`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`div-exp`
6×	`fma-def`
4×	`pow1` `expm1-log1p-u` `distribute-rgt-out--` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*`
2×	`+-commutative` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`
1×	`pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `diff-log` `pow-exp` `clear-num` `frac-sub` `flip--` `associate-/l/` `sub-div`

Counts

4 → 15821

Calls

4 calls:

12.0ms	(/ (/ (pow 1.0 3) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x))
4.0ms	(+ 1.0 (cos x))
4.0ms	(+ 1.0 (cos x))
842.0ms	(- (/ (/ (pow 1.0 3) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x)) (/ (/ (pow (cos x) 3) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x)))

series494.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (/ (pow 1.0 3) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x))
9.0ms	(+ 1.0 (cos x))
9.0ms	(+ 1.0 (cos x))
358.0ms	(- (/ (/ (pow 1.0 3) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x)) (/ (/ (pow (cos x) 3) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x)))

simplify11.9s

Algorithm

egg-herbie

Counts

15833 → 15833

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	10447	1584440

prune48.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.0b

regimes193.0ms

Accuracy

98.3% (0.5b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 30.2b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	81
1	68	81
2	68	81

end0.0ms

sample3.9s

Algorithm

intervals

Results

2.0s	1605×	body	2560	valid
1.2s	2781×	body	1280	valid
408.0ms	1894×	body	640	valid
139.0ms	900×	body	320	valid
46.0ms	455×	body	160	valid
35.0ms	7×	body	5120	valid
21.0ms	358×	body	80	valid