Details

sample53.0ms

Algorithm

intervals

Results

24.0ms	52×	body	2560	valid
11.0ms	45×	body	1280	valid
5.0ms	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))

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))

series69.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
50.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify33.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (27.0ms)

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

prune137.0ms

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))

rewrite28.0ms

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)
8.0ms	(/ (sqrt (- 1.0 (cos x))) x)
3.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

series229.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (sqrt (- 1.0 (cos x))) x)
99.0ms	(/ (sqrt (- 1.0 (cos x))) x)
18.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))

simplify182.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 3 (167.0ms)

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

prune359.0ms

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))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt` `*-un-lft-identity`
51×	`add-cube-cbrt`
36×	`times-frac` `sqrt-prod`
30×	`log-pow`
27×	`prod-diff`
25×	`exp-prod`
14×	`log-prod`
12×	`associate-/l*`
11×	`exp-sum`
9×	`pow1`
8×	`add-log-exp`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`add-exp-log` `fma-neg` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `associate-/r*`
2×	`flip3--` `diff-log` `flip--`
1×	`cbrt-undiv` `log-div` `frac-2neg` `exp-diff` `div-exp` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 152

Calls

4 calls:

19.0ms	(/ (sqrt (log (exp (- 1.0 (cos x))))) x)
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))
9.0ms	(log (exp (- 1.0 (cos x))))

series149.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (sqrt (log (exp (- 1.0 (cos x))))) x)
18.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))
19.0ms	(log (exp (- 1.0 (cos x))))

simplify49.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	391	1413
1	1100	1067
2	5001	909

prune375.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

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))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

162×	`prod-diff`
123×	`add-sqr-sqrt`
111×	`*-un-lft-identity`
95×	`add-cube-cbrt`
87×	`unpow-prod-down` `cube-prod`
33×	`sqr-pow`
25×	`cube-mult` `unpow3`
18×	`difference-of-squares`
15×	`fma-neg`
14×	`log-prod`
11×	`exp-sum`
10×	`add-log-exp`
7×	`distribute-lft-out--`
6×	`log-pow`
5×	`pow1` `exp-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `fma-def`
2×	`flip3--` `diff-log` `flip--`
1×	`difference-cubes` `+-commutative` `log-div` `flip3-+` `exp-diff` `rem-log-exp` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 268

Calls

4 calls:

3.0ms	(+ (cos x) 1.0)
24.0ms	(- (pow 1.0 3) (pow (cos x) 3))
3.0ms	(- 1.0 (cos x))
9.0ms	(log (exp (- 1.0 (cos x))))

series102.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (cos x) 1.0)
54.0ms	(- (pow 1.0 3) (pow (cos x) 3))
18.0ms	(- 1.0 (cos x))
19.0ms	(log (exp (- 1.0 (cos x))))

simplify112.0ms

Algorithm

egg-herbie

Counts

280 → 280

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	648	2916
1	2187	1973
2	5001	1892

prune467.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes78.0ms

Accuracy

98.9% (0.3b remaining)

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

bsearch72.0ms

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	50	38
1	50	38

end0.0ms

sample1.6s

Algorithm

intervals

Results

718.0ms	1589×	body	2560	valid
309.0ms	1263×	body	1280	valid
221.0ms	1472×	body	640	valid
96.0ms	932×	body	320	valid
77.0ms	2283×	body	80	valid
35.0ms	461×	body	160	valid