Details

sample122.0ms

Algorithm

intervals

Results

53.0ms	42×	body	2560	valid
39.0ms	88×	body	1280	valid
13.0ms	57×	body	640	valid
6.0ms	40×	body	320	valid
2.0ms	19×	body	160	valid
1.0ms	10×	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: 29.2b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite32.0ms

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:

23.0ms	(/ (- 1.0 (cos x)) (sin x))
7.0ms	(- 1.0 (cos x))

series48.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(/ (- 1.0 (cos x)) (sin x))
16.0ms	(- 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

prune266.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b	(/ (sin x) (- 1.0 (cos x)))
2.0b	(- 1.0 (cos x))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
112×	`add-sqr-sqrt` `*-un-lft-identity`
78×	`add-cube-cbrt`
26×	`associate-/r*`
17×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
9×	`prod-diff`
8×	`div-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `fma-neg` `log1p-expm1-u`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `inv-pow`

Counts

3 → 177

Calls

3 calls:

21.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
16.0ms	(/ (sin x) (- 1.0 (cos x)))
7.0ms	(- 1.0 (cos x))

series91.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
33.0ms	(/ (sin x) (- 1.0 (cos x)))
17.0ms	(- 1.0 (cos x))

simplify68.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	572	1779
1	2636	1549
2	5001	1441

prune444.0ms

Pruning

14 alts after pruning (14 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))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.2b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.0b	(- 1.0 (cos x))

rewrite73.0ms

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:

18.0ms	(/ (- 1.0 (cos x)) (sin x))
22.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
21.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
7.0ms	(- 1.0 (cos x))

series128.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (- 1.0 (cos x)) (sin x))
39.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
36.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
16.0ms	(- 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

prune531.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

1.3b	(log (sqrt (exp (/ (- 1.0 (cos x)) (sin x)))))
1.3b	(log (sqrt (exp (/ (- 1.0 (cos x)) (sin x)))))
2.0b	(- 1.0 (cos x))
2.0b	(- 1.0 (cos x))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt` `*-un-lft-identity`
44×	`log-pow`
40×	`add-cube-cbrt` `sqrt-pow1`
38×	`exp-prod`
30×	`times-frac`
18×	`prod-diff`
12×	`log-prod`
8×	`pow1` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
6×	`add-exp-log` `fma-neg` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `log-div` `flip3--` `pow1/2` `exp-diff` `sqrt-div` `diff-log` `div-sub` `rem-log-exp` `flip--` `div-inv`

Counts

4 → 134

Calls

4 calls:

24.0ms	(log (sqrt (exp (/ (- 1.0 (cos x)) (sin x)))))
27.0ms	(log (sqrt (exp (/ (- 1.0 (cos x)) (sin x)))))
7.0ms	(- 1.0 (cos x))
7.0ms	(- 1.0 (cos x))

series312.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(log (sqrt (exp (/ (- 1.0 (cos x)) (sin x)))))
139.0ms	(log (sqrt (exp (/ (- 1.0 (cos x)) (sin x)))))
16.0ms	(- 1.0 (cos x))
16.0ms	(- 1.0 (cos x))

simplify126.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 3 (115.0ms)

Iter	Nodes	Cost
0	283	1162
1	754	934
2	3469	912
3	5001	906

prune747.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

regimes275.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.3b

bsearch105.0ms

Steps

Iters	Range		Point
9	0.007285382865895221	15234496.061427226	0.02292212347773066
10	-569.2304264003914	-7.772245281701499e-10	-0.023345271957993404

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	19
1	39	19

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.1s	1559×	body	2560	valid
1.3s	2849×	body	1280	valid
437.0ms	1870×	body	640	valid
148.0ms	929×	body	320	valid
51.0ms	457×	body	160	valid
22.0ms	332×	body	80	valid
18.0ms	4×	body	5120	valid