Details

sample140.0ms

Algorithm

intervals

Results

58.0ms	44×	body	2560	valid
40.0ms	85×	body	1280	valid
22.0ms	62×	body	640	valid
7.0ms	37×	body	320	valid
3.0ms	1×	body	5120	valid
2.0ms	15×	body	160	valid
1.0ms	12×	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: 30.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
1.4b	(- 1.0 (cos x))

rewrite15.0ms

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:

9.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

series60.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(- 1.0 (cos x))

simplify36.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (8.0ms)

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

prune183.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
0.8b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.4b	(- 1.0 (cos x))

rewrite45.0ms

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:

13.0ms	(/ (- 1.0 (cos x)) (sin x))
12.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
12.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms	(- 1.0 (cos x))

series134.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (- 1.0 (cos x)) (sin x))
47.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
35.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
19.0ms	(- 1.0 (cos x))

simplify42.0ms

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

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x)))
0.3b	(pow (cos x) 3)
0.4b	(fma (cos x) (cos x) (* 1.0 (cos x)))
1.2b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

156×	`add-sqr-sqrt`
144×	`prod-diff`
114×	`unpow-prod-down` `*-un-lft-identity` `cube-prod`
84×	`add-cube-cbrt`
50×	`sqr-pow`
48×	`difference-of-squares`
26×	`cube-mult` `unpow3`
25×	`times-frac` `associate-/l*`
15×	`distribute-lft-out--`
12×	`fma-neg`
10×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`difference-cubes` `pow-unpow`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `fma-udef` `div-inv` `rem-cube-cbrt`

Counts

4 → 297

Calls

4 calls:

57.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x)))
2.0ms	(pow (cos x) 3)
0.0ms	(fma (cos x) (cos x) (* 1.0 (cos x)))
25.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series315.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x)))
27.0ms	(pow (cos x) 3)
52.0ms	(fma (cos x) (cos x) (* 1.0 (cos x)))
47.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify134.0ms

Algorithm

egg-herbie

Counts

309 → 309

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	768	3882
1	2922	2862
2	5002	2805

prune447.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
1.4b	(- 1.0 (cos x))

rewrite15.0ms

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:

9.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series56.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ (- 1.0 (cos x)) (sin x))
18.0ms	(- 1.0 (cos x))

simplify35.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (8.0ms)

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

prune136.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.1b

regimes354.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 30.4b

bsearch67.0ms

Steps

Iters	Range		Point
8	0.003211336228265424	0.8894813891870064	0.02225998792679692
8	-1.3862719480695398	-4.2961337728369966e-05	-0.01987492789409989

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	10
1	33	10
2	33	10

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.3s	1646×	body	2560	valid
1.4s	2805×	body	1280	valid
495.0ms	1862×	body	640	valid
156.0ms	873×	body	320	valid
61.0ms	465×	body	160	valid
26.0ms	342×	body	80	valid
24.0ms	7×	body	5120	valid