Details

sample55.0ms

Algorithm

intervals

Results

24.0ms	52×	body	2560	valid
10.0ms	45×	body	1280	valid
8.0ms	35×	body	640	valid
3.0ms	32×	body	320	valid
2.0ms	79×	body	80	valid
1.0ms	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: 31.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.9b	(- 1.0 (cos x))
15.2b	(/ (- 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))

series62.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify61.0ms

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

prune106.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- 1.0 (cos x))) x)
0.1b	(/ (sqrt (- 1.0 (cos x))) x)
0.9b	(- 1.0 (cos x))
0.9b	(- 1.0 (cos x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 126

Calls

4 calls:

7.0ms	(/ (sqrt (- 1.0 (cos x))) x)
7.0ms	(/ (sqrt (- 1.0 (cos x))) x)
2.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

series212.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (sqrt (- 1.0 (cos x))) x)
90.0ms	(/ (sqrt (- 1.0 (cos x))) x)
18.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))

simplify97.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	242	1020
1	706	972
2	2968	960
3	5002	960

prune286.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (log (exp (- 1.0 (cos x))))) x)
0.9b	(- 1.0 (cos x))
0.9b	(- 1.0 (cos x))
1.1b	(log (exp (- 1.0 (cos x))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`times-frac` `sqrt-prod`
31×	`add-cube-cbrt`
30×	`log-pow`
25×	`exp-prod`
12×	`associate-/l*`
9×	`pow1`
8×	`add-log-exp`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`add-exp-log` `add-cbrt-cube`
5×	`log-prod`
3×	`sub-neg` `associate-/r*`
2×	`flip3--` `diff-log` `exp-sum` `flip--`
1×	`cbrt-undiv` `log-div` `frac-2neg` `exp-diff` `div-exp` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 111

Calls

4 calls:

18.0ms	(/ (sqrt (log (exp (- 1.0 (cos x))))) x)
2.0ms	(- 1.0 (cos x))
2.0ms	(- 1.0 (cos x))
7.0ms	(log (exp (- 1.0 (cos x))))

series142.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (sqrt (log (exp (- 1.0 (cos x))))) x)
17.0ms	(- 1.0 (cos x))
17.0ms	(- 1.0 (cos x))
18.0ms	(log (exp (- 1.0 (cos x))))

simplify104.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	305	911
1	837	822
2	3341	790
3	5002	789

prune292.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (cos x) 1.0)
0.8b	(- (pow 1.0 3) (pow (cos x) 3))
0.9b	(- 1.0 (cos x))
1.1b	(log (exp (- 1.0 (cos x))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
18×	`difference-of-squares`
12×	`unpow-prod-down` `cube-prod`
10×	`add-log-exp`
8×	`sqr-pow`
7×	`distribute-lft-out--`
6×	`add-cube-cbrt` `log-pow`
5×	`pow1` `log-prod` `exp-prod`
4×	`add-exp-log` `add-cbrt-cube`
3×	`sub-neg`
2×	`flip3--` `diff-log` `exp-sum` `flip--`
1×	`difference-cubes` `+-commutative` `log-div` `flip3-+` `exp-diff` `rem-log-exp` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 80

Calls

4 calls:

3.0ms	(+ (cos x) 1.0)
14.0ms	(- (pow 1.0 3) (pow (cos x) 3))
2.0ms	(- 1.0 (cos x))
7.0ms	(log (exp (- 1.0 (cos x))))

series97.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (cos x) 1.0)
46.0ms	(- (pow 1.0 3) (pow (cos x) 3))
22.0ms	(- 1.0 (cos x))
19.0ms	(log (exp (- 1.0 (cos x))))

simplify105.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	291	533
1	883	504
2	3194	504
3	5002	504

prune303.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes73.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 31.0b

bsearch74.0ms

Steps

Iters	Range		Point
8	0.003342748024832997	13.582308112339199	0.03310073586082224
9	-118.89002763209811	-0.00028315217264546786	-0.036038474483329114

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	40
1	55	40

end0.0ms

sample1.5s

Algorithm

intervals

Results

711.0ms	1589×	body	2560	valid
277.0ms	1263×	body	1280	valid
219.0ms	1472×	body	640	valid
97.0ms	932×	body	320	valid
81.0ms	2283×	body	80	valid
32.0ms	461×	body	160	valid