Details

sample133.0ms

Algorithm

intervals

Results

58.0ms	46×	body	2560	valid
40.0ms	90×	body	1280	valid
19.0ms	66×	body	640	valid
5.0ms	31×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	8×	body	80	valid

simplify7.0ms

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: 29.7b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 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:

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

series60.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ (- 1.0 (cos x)) (sin x))
18.0ms	(- 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

prune182.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.1b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.9b	(- 1.0 (cos x))

rewrite44.0ms

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:

12.0ms	(/ (- 1.0 (cos x)) (sin x))
11.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
12.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms	(- 1.0 (cos x))

series136.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (- 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

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sin x))
0.2b	(/ (cos x) (sin x))
2.0b	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

271×	`times-frac`
222×	`add-sqr-sqrt`
218×	`*-un-lft-identity`
210×	`add-cube-cbrt`
169×	`prod-diff`
31×	`div-inv`
13×	`fma-neg`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
5×	`add-log-exp`
4×	`distribute-lft-out--` `difference-of-squares`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `diff-log` `frac-sub` `flip--` `sub-div`

Counts

3 → 265

Calls

3 calls:

5.0ms	(/ 1.0 (sin x))
3.0ms	(/ (cos x) (sin x))
26.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

series124.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(/ 1.0 (sin x))
18.0ms	(/ (cos x) (sin x))
87.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

simplify92.0ms

Algorithm

egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	810	7180
1	2234	5060
2	5001	4434

prune380.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 3)
0.4b	(fma (cos x) (cos x) (* 1.0 (cos x)))
1.1b	(log (exp (/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x)))))
1.7b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

144×	`prod-diff`
133×	`add-sqr-sqrt`
105×	`*-un-lft-identity`
102×	`unpow-prod-down` `cube-prod`
85×	`add-cube-cbrt`
42×	`sqr-pow`
32×	`difference-of-squares`
30×	`log-pow`
29×	`exp-prod`
26×	`cube-mult` `unpow3`
25×	`times-frac`
12×	`fma-neg`
10×	`distribute-lft-out--`
6×	`pow1` `add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `log-prod`
2×	`difference-cubes`
1×	`pow-to-exp` `sub-neg` `log-div` `flip3--` `pow-pow` `exp-diff` `diff-log` `div-sub` `rem-log-exp` `pow-exp` `flip--` `fma-udef` `div-inv` `rem-cube-cbrt`

Counts

4 → 271

Calls

4 calls:

1.0ms	(pow (cos x) 3)
0.0ms	(fma (cos x) (cos x) (* 1.0 (cos x)))
60.0ms	(log (exp (/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x)))))
21.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series324.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow (cos x) 3)
52.0ms	(fma (cos x) (cos x) (* 1.0 (cos x)))
195.0ms	(log (exp (/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x)))))
48.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify115.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	678	3335
1	2244	2379
2	5001	2337

prune413.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

regimes90.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.2b

bsearch110.0ms

Steps

Iters	Range		Point
10	4.8244160186105205e-08	257763.20554958374	0.02404422484670463
10	-772.3369502403921	-4.163765984402517e-10	-0.019039573390386873

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	36
1	46	36
2	46	36

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.1s	1584×	body	2560	valid
1.5s	2805×	body	1280	valid
455.0ms	1880×	body	640	valid
164.0ms	961×	body	320	valid
52.0ms	434×	body	160	valid
38.0ms	332×	body	80	valid
11.0ms	4×	body	5120	valid