Details

sample66.0ms

Algorithm

intervals

Results

27.0ms	47×	body	2560	valid
15.0ms	52×	body	1280	valid
9.0ms	46×	body	640	valid
4.0ms	29×	body	320	valid
4.0ms	69×	body	80	valid
2.0ms	13×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	4
1	21	4
2	26	4
3	28	4
4	28	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize6.0ms

Local error

Found 2 expressions with local error:

1.7b	(- 1.0 (cos x))
16.5b	(/ (- 1.0 (cos x)) (* x x))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 58

Calls

2 calls:

3.0ms	(- 1.0 (cos x))
10.0ms	(/ (- 1.0 (cos x)) (* x x))

series63.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(- 1.0 (cos x))
42.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify32.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	279	446
1	1006	326
2	5001	317

prune128.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b	(* 1/24 (pow x 2))
12.1b	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`associate-r`
7×	`add-exp-log`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

2 → 39

Calls

2 calls:

6.0ms	(* 1/24 (pow x 2))
0.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

series68.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(* 1/24 (pow x 2))
44.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

simplify102.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	139	194
1	532	171
2	2601	171
3	5001	170

prune104.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- 1.0 (cos x))) x)
0.1b	(/ (sqrt (- 1.0 (cos x))) x)
1.7b	(- 1.0 (cos x))
1.7b	(- 1.0 (cos x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt` `*-un-lft-identity`
52×	`add-cube-cbrt`
48×	`times-frac`
40×	`sqrt-prod`
18×	`prod-diff`
16×	`associate-/l*`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`fma-neg` `associate-/r*`
4×	`pow1` `expm1-log1p-u` `flip3--` `sqrt-div` `flip--` `log1p-expm1-u` `associate-/l/`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 158

Calls

4 calls:

8.0ms	(/ (sqrt (- 1.0 (cos x))) x)
10.0ms	(/ (sqrt (- 1.0 (cos x))) x)
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

series213.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (sqrt (- 1.0 (cos x))) x)
88.0ms	(/ (sqrt (- 1.0 (cos x))) x)
18.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))

simplify180.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 3 (163.0ms)

Iter	Nodes	Cost
0	301	1368
1	936	1148
2	4953	1118
3	5001	1112

prune349.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sqrt 1) (/ x (sqrt (- 1.0 (cos x))))) (/ (sqrt (- 1.0 (cos x))) x))
0.1b	(/ (sqrt (- 1.0 (cos x))) x)
1.7b	(- 1.0 (cos x))
1.7b	(- 1.0 (cos x))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

437×	`times-frac`
371×	`add-sqr-sqrt`
264×	`*-un-lft-identity`
252×	`sqrt-prod`
201×	`add-cube-cbrt`
185×	`associate-l`
30×	`unswap-sqr`
28×	`associate-r`
27×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
14×	`sqrt-div`
13×	`associate-/r/`
10×	`cbrt-undiv` `div-exp`
9×	`flip3--` `flip--` `div-inv`
8×	`associate-/l*` `add-log-exp`
6×	`pow1` `fma-neg` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r*`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 376

Calls

4 calls:

126.0ms	(* (/ (sqrt 1) (/ x (sqrt (- 1.0 (cos x))))) (/ (sqrt (- 1.0 (cos x))) x))
8.0ms	(/ (sqrt (- 1.0 (cos x))) x)
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

series173.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (/ (sqrt 1) (/ x (sqrt (- 1.0 (cos x))))) (/ (sqrt (- 1.0 (cos x))) x))
89.0ms	(/ (sqrt (- 1.0 (cos x))) x)
18.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))

simplify60.0ms

Algorithm

egg-herbie

Counts

388 → 388

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1200	4980
1	5001	4576

prune863.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

regimes52.0ms

Accuracy

99% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 31.5b

bsearch76.0ms

Steps

Iters	Range		Point
9	0.0012055448239290207	14520.350903362307	0.025388615584991975
9	-1078.7327260164275	-0.0019174381104543623	-0.03385827954078283

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	22
1	35	22

end0.0ms

sample1.9s

Algorithm

intervals

Results

831.0ms	1596×	body	2560	valid
351.0ms	1257×	body	1280	valid
281.0ms	1453×	body	640	valid
140.0ms	954×	body	320	valid
123.0ms	2259×	body	80	valid
48.0ms	481×	body	160	valid