Details

sample131.0ms

Algorithm

intervals

Results

64.0ms	45×	body	2560	valid
37.0ms	90×	body	1280	valid
15.0ms	63×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	16×	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: 27.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.5b	(- 1.0 (cos x))

rewrite13.0ms

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))

series63.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (- 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

prune194.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 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))))
1.5b	(- 1.0 (cos x))

rewrite34.0ms

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

series139.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
48.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
36.0ms	(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 (32.0ms)

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

prune372.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (/ (exp (log (- 1.0 (cos x)))) (sin x)))
0.4b	(log (- 1.0 (cos x)))
1.1b	(log (exp (/ (exp (log (- 1.0 (cos x)))) (sin x))))
1.5b	(- 1.0 (cos x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt` `*-un-lft-identity`
56×	`exp-prod`
48×	`times-frac`
43×	`add-cube-cbrt`
38×	`log-prod`
30×	`exp-sum` `log-pow`
9×	`prod-diff`
8×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`pow1`
5×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg`
2×	`log-div` `flip3--` `rem-log-exp` `flip--` `div-inv`
1×	`sub-neg` `diff-log` `rem-exp-log`

Counts

4 → 126

Calls

4 calls:

8.0ms	(exp (/ (exp (log (- 1.0 (cos x)))) (sin x)))
4.0ms	(log (- 1.0 (cos x)))
9.0ms	(log (exp (/ (exp (log (- 1.0 (cos x)))) (sin x))))
5.0ms	(- 1.0 (cos x))

series176.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(exp (/ (exp (log (- 1.0 (cos x)))) (sin x)))
76.0ms	(log (- 1.0 (cos x)))
35.0ms	(log (exp (/ (exp (log (- 1.0 (cos x)))) (sin x))))
23.0ms	(- 1.0 (cos x))

simplify136.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 3 (121.0ms)

Iter	Nodes	Cost
0	369	1034
1	972	868
2	4108	836
3	5001	833

prune416.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.2b	(exp (log (- 1.0 (cos x))))
0.4b	(log (- 1.0 (cos x)))
1.5b	(- 1.0 (cos x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

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

series153.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
24.0ms	(exp (log (- 1.0 (cos x))))
71.0ms	(log (- 1.0 (cos x)))
23.0ms	(- 1.0 (cos x))

simplify38.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	354	1019
1	1045	861
2	5001	817

prune457.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes135.0ms

Accuracy

97.7% (0.7b remaining)

Error of 0.9b against oracle of 0.2b and baseline of 30.1b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	40
1	32	40

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.2s	1664×	body	2560	valid
1.2s	2668×	body	1280	valid
455.0ms	1899×	body	640	valid
146.0ms	924×	body	320	valid
50.0ms	467×	body	160	valid
24.0ms	377×	body	80	valid
3.0ms	1×	body	5120	valid