Details

sample70.0ms

Algorithm

intervals

Results

32.0ms	53×	body	2560	valid
12.0ms	40×	body	1280	valid
9.0ms	44×	body	640	valid
4.0ms	30×	body	320	valid
4.0ms	74×	body	80	valid
2.0ms	15×	body	160	valid

simplify7.0ms

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: 33.7b

localize6.0ms

Local error

Found 2 expressions with local error:

1.9b	(- 1.0 (cos x))
15.0b	(/ (- 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))

series63.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(- 1.0 (cos x))
46.0ms	(/ (- 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

prune132.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.2b	(* 1/24 (pow x 2))
12.4b	(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))))

series64.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(* 1/24 (pow x 2))
40.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

simplify105.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 3 (97.0ms)

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

prune103.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
33×	`add-cube-cbrt`
28×	`cbrt-prod`
27×	`prod-diff`
12×	`cbrt-div`
11×	`pow1`
10×	`swap-sqr` `add-log-exp`
9×	`flip3--` `fma-neg` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l`
7×	`difference-of-squares`
6×	`add-exp-log` `pow1/3`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `diff-log`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 142

Calls

4 calls:

19.0ms	(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

series185.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
17.0ms	(- 1.0 (cos x))
21.0ms	(- 1.0 (cos x))
17.0ms	(- 1.0 (cos x))

simplify165.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 3 (150.0ms)

Iter	Nodes	Cost
0	283	1323
1	928	1020
2	4905	923
3	5001	914

prune313.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.9b	(- 1.0 (cos x))
15.0b	(/ (exp (log (- 1.0 (cos x)))) (* x x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

4.0ms	(exp (log (- 1.0 (cos x))))
3.0ms	(log (- 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))
11.0ms	(/ (exp (log (- 1.0 (cos x)))) (* x x))

series154.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(exp (log (- 1.0 (cos x))))
73.0ms	(log (- 1.0 (cos x)))
18.0ms	(- 1.0 (cos x))
45.0ms	(/ (exp (log (- 1.0 (cos x)))) (* x x))

simplify36.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	335	787
1	1119	595
2	5001	586

prune223.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes48.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.8b

bsearch66.0ms

Steps

Iters	Range		Point
10	2.1112891761060846e-05	363928.4733812492	0.0331222017964037
8	-0.10438916540540782	-0.00034188071245303247	-0.03145496023122399

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	10
1	31	10

end0.0ms

sample2.0s

Algorithm

intervals

Results

883.0ms	1594×	body	2560	valid
372.0ms	1255×	body	1280	valid
311.0ms	1447×	body	640	valid
138.0ms	927×	body	320	valid
117.0ms	2293×	body	80	valid
51.0ms	484×	body	160	valid