Details

sample58.0ms

Algorithm

intervals

Results

27.0ms	61×	body	2560	valid
12.0ms	51×	body	1280	valid
6.0ms	38×	body	640	valid
3.0ms	24×	body	320	valid
2.0ms	61×	body	80	valid
2.0ms	21×	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: 36.5b

localize6.0ms

Local error

Found 2 expressions with local error:

2.4b	(- 1.0 (cos x))
20.4b	(/ (- 1.0 (cos x)) (* x x))

rewrite14.0ms

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))

series65.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(- 1.0 (cos x))
47.0ms	(/ (- 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

prune125.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- 1/2 (* 1/24 (pow x 2)))
0.2b	(* 1/24 (pow x 2))
10.2b	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
8×	`add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
5×	`add-cbrt-cube` `add-log-exp`
4×	`unpow-prod-down` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `fma-neg` `associate-l` `prod-diff` `prod-exp` `log1p-expm1-u`
2×	`unpow2` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef`

Counts

3 → 59

Calls

3 calls:

2.0ms	(- 1/2 (* 1/24 (pow x 2)))
8.0ms	(* 1/24 (pow x 2))
0.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

series119.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(- 1/2 (* 1/24 (pow x 2)))
24.0ms	(* 1/24 (pow x 2))
42.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

simplify184.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (179.0ms)

Iter	Nodes	Cost
0	209	318
1	817	281
2	4271	278
3	5001	273

prune156.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
2.4b	(- 1.0 (cos x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 165

Calls

3 calls:

13.0ms	(/ (/ (- 1.0 (cos x)) x) x)
9.0ms	(/ (- 1.0 (cos x)) x)
3.0ms	(- 1.0 (cos x))

series103.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ (/ (- 1.0 (cos x)) x) x)
41.0ms	(/ (- 1.0 (cos x)) x)
18.0ms	(- 1.0 (cos x))

simplify58.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	592	1453
1	2212	1292
2	5001	1283

prune279.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (log (exp (- 1.0 (cos x)))) x) x)
0.1b	(/ (log (exp (- 1.0 (cos x)))) x)
2.4b	(- 1.0 (cos x))
2.5b	(log (exp (- 1.0 (cos x))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

228×	`times-frac`
169×	`add-sqr-sqrt` `*-un-lft-identity`
133×	`add-cube-cbrt`
102×	`log-pow`
85×	`exp-prod`
40×	`associate-/l*`
21×	`pow1`
18×	`prod-diff` `distribute-lft-out--` `difference-of-squares`
14×	`log-prod`
11×	`add-exp-log` `exp-sum` `add-cbrt-cube`
6×	`associate-/r*` `div-inv` `add-log-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`log-div` `exp-diff` `fma-neg` `div-sub`
2×	`sub-neg` `frac-2neg` `clear-num`
1×	`flip3--` `diff-log` `rem-log-exp` `flip--` `associate-/l/`

Counts

4 → 258

Calls

4 calls:

26.0ms	(/ (/ (log (exp (- 1.0 (cos x)))) x) x)
27.0ms	(/ (log (exp (- 1.0 (cos x)))) x)
3.0ms	(- 1.0 (cos x))
8.0ms	(log (exp (- 1.0 (cos x))))

series126.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ (/ (log (exp (- 1.0 (cos x)))) x) x)
41.0ms	(/ (log (exp (- 1.0 (cos x)))) x)
17.0ms	(- 1.0 (cos x))
21.0ms	(log (exp (- 1.0 (cos x))))

simplify71.0ms

Algorithm

egg-herbie

Counts

270 → 270

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	813	2534
1	2797	2108
2	5001	2093

prune413.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes52.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.5b

bsearch69.0ms

Steps

Iters	Range		Point
10	2.30341956868392e-10	214.50772926448735	0.03032722926070993
8	-0.12347723982223391	-6.246474786567043e-06	-0.03785531443660082

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	27
1	35	27

end0.0ms

sample1.6s

Algorithm

intervals

Results

730.0ms	1595×	body	2560	valid
281.0ms	1196×	body	1280	valid
220.0ms	1471×	body	640	valid
108.0ms	984×	body	320	valid
76.0ms	2249×	body	80	valid
37.0ms	505×	body	160	valid