Details

sample144.0ms

Algorithm

intervals

Results

70.0ms	58×	body	2560	valid
43.0ms	86×	body	1280	valid
16.0ms	67×	body	640	valid
4.0ms	24×	body	320	valid
2.0ms	12×	body	160	valid
1.0ms	9×	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: 31.4b

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
1.9b	(- 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:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series61.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(- 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

prune379.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma 1/240 (pow x 5) (* 1/2 x))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma 1/240 (pow x 5) (* 1/2 x))

series119.0ms

Counts

1 → 3

Calls

1 calls:

118.0ms

(fma 1/240 (pow x 5) (* 1/2 x))

simplify47.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	59
1	65	52
2	228	52
3	979	52
4	5001	52

prune65.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.4b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.9b	(- 1.0 (cos x))

rewrite29.0ms

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))
6.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
7.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms	(- 1.0 (cos x))

series137.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (- 1.0 (cos x)) (sin x))
40.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
40.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
18.0ms	(- 1.0 (cos x))

simplify42.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (32.0ms)

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

prune351.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- 1.0 (cos x)))
0.3b	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
1.4b	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
1.9b	(- 1.0 (cos x))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

231×	`times-frac`
166×	`add-sqr-sqrt` `*-un-lft-identity`
136×	`exp-prod`
120×	`add-cube-cbrt`
69×	`log-pow`
23×	`distribute-lft-out--` `difference-of-squares`
16×	`associate-/r/`
9×	`prod-diff` `div-inv`
8×	`flip3--` `flip--`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `fma-neg` `associate-/l*`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 227

Calls

4 calls:

7.0ms	(/ (sin x) (- 1.0 (cos x)))
13.0ms	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
15.0ms	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
5.0ms	(- 1.0 (cos x))

series137.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (sin x) (- 1.0 (cos x)))
39.0ms	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
34.0ms	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
24.0ms	(- 1.0 (cos x))

simplify65.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	593	1886
1	2179	1647
2	5002	1502

prune604.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.2b

regimes144.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 31.4b

bsearch81.0ms

Steps

Iters	Range		Point
9	1.2358748968334836e-07	0.22405535791780642	0.026425734950010618
9	-0.11986014733990268	-1.6789357321840064e-10	-0.02028674327720827

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	29
1	39	29

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.2s	1670×	body	2560	valid
1.3s	2817×	body	1280	valid
453.0ms	1829×	body	640	valid
159.0ms	851×	body	320	valid
54.0ms	480×	body	160	valid
24.0ms	352×	body	80	valid
3.0ms	1×	body	5120	valid