Details

sample61.0ms

Algorithm

intervals

Results

27.0ms	61×	body	2560	valid
15.0ms	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

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: 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))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

2.0ms	(- 1.0 (cos x))
8.0ms	(/ (- 1.0 (cos x)) (* x x))

series66.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
48.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify60.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	221	271
1	735	239
2	2396	239
3	5002	239

prune107.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 1/720 (pow x 4))
0.2b	(* 1/24 (pow x 2))
10.2b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

3 → 66

Calls

3 calls:

5.0ms	(* 1/720 (pow x 4))
5.0ms	(* 1/24 (pow x 2))
23.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series114.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(* 1/720 (pow x 4))
26.0ms	(* 1/24 (pow x 2))
47.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify38.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	268	347
1	1132	316
2	5001	310

prune152.0ms

Pruning

10 alts after pruning (9 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))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 147

Calls

3 calls:

11.0ms	(/ (/ (- 1.0 (cos x)) x) x)
7.0ms	(/ (- 1.0 (cos x)) x)
3.0ms	(- 1.0 (cos x))

series110.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ (/ (- 1.0 (cos x)) x) x)
48.0ms	(/ (- 1.0 (cos x)) x)
19.0ms	(- 1.0 (cos x))

simplify54.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	531	1270
1	1899	1197
2	5001	1186

prune260.0ms

Pruning

10 alts after pruning (9 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))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 229

Calls

4 calls:

26.0ms	(/ (/ (log (exp (- 1.0 (cos x)))) x) x)
25.0ms	(/ (log (exp (- 1.0 (cos x)))) x)
2.0ms	(- 1.0 (cos x))
8.0ms	(log (exp (- 1.0 (cos x))))

series133.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ (/ (log (exp (- 1.0 (cos x)))) x) x)
44.0ms	(/ (log (exp (- 1.0 (cos x)))) x)
23.0ms	(- 1.0 (cos x))
18.0ms	(log (exp (- 1.0 (cos x))))

simplify62.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	725	2184
1	2499	1931
2	5001	1910

prune379.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes56.0ms

Accuracy

99.1% (0.3b remaining)

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

bsearch67.0ms

Steps

Iters	Range		Point
10	2.30341956868392e-10	214.50772926448735	0.03303884749464856
8	-0.12347723982223391	-6.246474786567043e-06	-0.03785531443660082

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	19
1	35	19

end0.0ms

sample1.6s

Algorithm

intervals

Results

746.0ms	1595×	body	2560	valid
279.0ms	1196×	body	1280	valid
224.0ms	1471×	body	640	valid
103.0ms	984×	body	320	valid
72.0ms	2249×	body	80	valid
45.0ms	505×	body	160	valid