Details

sample129.0ms

Algorithm

intervals

Results

62.0ms	51×	body	2560	valid
36.0ms	85×	body	1280	valid
14.0ms	62×	body	640	valid
5.0ms	35×	body	320	valid
2.0ms	17×	body	160	valid
0.0ms	6×	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: 29.8b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite33.0ms

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:

18.0ms	(/ (- 1.0 (cos x)) (sin x))
7.0ms	(- 1.0 (cos x))

series50.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(/ (- 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

prune176.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

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)))
1.4b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.0b	(- 1.0 (cos x))

rewrite77.0ms

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:

19.0ms	(/ (- 1.0 (cos x)) (sin x))
20.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
22.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
10.0ms	(- 1.0 (cos x))

series123.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (- 1.0 (cos x)) (sin x))
43.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
31.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
17.0ms	(- 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

prune336.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

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)))
2.0b	(- 1.0 (cos x))
29.7b	(log (expm1 (log1p (exp (/ (- 1.0 (cos x)) (sin x))))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

21.0ms	(/ (- 1.0 (cos x)) (sin x))
20.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
7.0ms	(- 1.0 (cos x))
1.0ms	(log (expm1 (log1p (exp (/ (- 1.0 (cos x)) (sin x))))))

series338.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (- 1.0 (cos x)) (sin x))
37.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
16.0ms	(- 1.0 (cos x))
248.0ms	(log (expm1 (log1p (exp (/ (- 1.0 (cos x)) (sin x))))))

simplify39.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	355	909
1	1086	769
2	5002	767

prune353.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- 1.0 (cos x)))
0.2b	(/ (log (exp (- 1.0 (cos x)))) (sin x))
2.0b	(- 1.0 (cos x))
2.1b	(log (exp (- 1.0 (cos x))))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 141

Calls

4 calls:

16.0ms	(exp (- 1.0 (cos x)))
50.0ms	(/ (log (exp (- 1.0 (cos x)))) (sin x))
7.0ms	(- 1.0 (cos x))
19.0ms	(log (exp (- 1.0 (cos x))))

series104.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(exp (- 1.0 (cos x)))
36.0ms	(/ (log (exp (- 1.0 (cos x)))) (sin x))
16.0ms	(- 1.0 (cos x))
17.0ms	(log (exp (- 1.0 (cos x))))

simplify41.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	385	1279
1	1183	956
2	5001	809

prune267.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.1b

regimes143.0ms

Accuracy

98.3% (0.5b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 30.4b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	27
1	30	27

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.1s	1593×	body	2560	valid
1.3s	2803×	body	1280	valid
427.0ms	1876×	body	640	valid
139.0ms	915×	body	320	valid
54.0ms	482×	body	160	valid
21.0ms	327×	body	80	valid
13.0ms	4×	body	5120	valid