Details

sample535.0ms

Algorithm

intervals

Results

101.0ms	47×	body	2560	valid
54.0ms	86×	body	1280	valid
47.0ms	74×	body	640	valid
4.0ms	21×	body	320	valid
3.0ms	13×	body	160	valid
1.0ms	15×	body	80	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.1b	(- x (sin x))
1.4b	(- x (tan x))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 80

Calls

3 calls:

23.0ms	(/ (- x (sin x)) (- x (tan x)))
6.0ms	(- x (sin x))
8.0ms	(- x (tan x))

series188.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(/ (- x (sin x)) (- x (tan x)))
40.0ms	(- x (sin x))
67.0ms	(- x (tan x))

simplify153.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	685
2	4795	685
3	5001	685

prune206.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (tan x)) (- x (sin x)))
0.0b	(/ 1 (/ (- x (tan x)) (- x (sin x))))
1.1b	(- x (sin x))
1.4b	(- x (tan x))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
200×	`add-sqr-sqrt` `*-un-lft-identity`
92×	`add-cube-cbrt`
54×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`flip3--` `div-exp` `flip--` `associate-/l*` `add-log-exp`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv`
2×	`sub-neg` `rec-exp` `frac-2neg` `diff-log` `1-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `div-sub` `inv-pow`

Counts

4 → 228

Calls

4 calls:

22.0ms	(/ (- x (tan x)) (- x (sin x)))
28.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
6.0ms	(- x (sin x))
5.0ms	(- x (tan x))

series255.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (- x (tan x)) (- x (sin x)))
85.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
33.0ms	(- x (sin x))
54.0ms	(- x (tan x))

simplify86.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	744	2647
1	3445	2441
2	5001	2279

prune352.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (tan x) (- x (sin x)))
1.1b	(- (/ x (- x (sin x))) (/ (tan x) (- x (sin x))))
1.1b	(- x (sin x))
1.1b	(- x (sin x))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
33×	`times-frac`
18×	`distribute-lft-out--`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`add-exp-log` `flip3--` `associate-/r/` `add-cbrt-cube` `flip--`
5×	`associate-/r*`
4×	`pow1`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`tan-quot` `cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `associate-/l/` `sub-div`

Counts

4 → 95

Calls

4 calls:

13.0ms	(/ (tan x) (- x (sin x)))
86.0ms	(- (/ x (- x (sin x))) (/ (tan x) (- x (sin x))))
6.0ms	(- x (sin x))
9.0ms	(- x (sin x))

series274.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (tan x) (- x (sin x)))
148.0ms	(- (/ x (- x (sin x))) (/ (tan x) (- x (sin x))))
34.0ms	(- x (sin x))
38.0ms	(- x (sin x))

simplify116.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	359	902
1	1107	861
2	4262	856
3	5002	856

prune249.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 9/10 (pow x 2)) (+ (* 513/1400 (pow x 4)) 2))
0.0b	(/ 1 (- (+ (* 9/10 (pow x 2)) (+ (* 513/1400 (pow x 4)) 2))))
0.1b	(* 513/1400 (pow x 4))
0.1b	(* 9/10 (pow x 2))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
30×	`times-frac`
18×	`add-exp-log`
15×	`associate-r`
12×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
10×	`associate-/r*` `add-cbrt-cube`
9×	`add-log-exp`
8×	`unpow-prod-down`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
5×	`pow1`
4×	`neg-mul-1` `sqr-pow`
3×	`sum-log` `associate-/l*`
2×	`pow-to-exp` `flip3-+` `div-exp` `pow-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `distribute-neg-frac` `unpow2`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `associate-+r+` `pow-flip` `frac-2neg` `1-exp` `clear-num` `div-inv` `inv-pow`

Counts

4 → 126

Calls

4 calls:

24.0ms	(+ (* 9/10 (pow x 2)) (+ (* 513/1400 (pow x 4)) 2))
76.0ms	(/ 1 (- (+ (* 9/10 (pow x 2)) (+ (* 513/1400 (pow x 4)) 2))))
11.0ms	(* 513/1400 (pow x 4))
12.0ms	(* 9/10 (pow x 2))

series181.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(+ (* 9/10 (pow x 2)) (+ (* 513/1400 (pow x 4)) 2))
63.0ms	(/ 1 (- (+ (* 9/10 (pow x 2)) (+ (* 513/1400 (pow x 4)) 2))))
40.0ms	(* 513/1400 (pow x 4))
28.0ms	(* 9/10 (pow x 2))

simplify66.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	480	1205
1	2108	1113
2	5001	1058

prune232.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes35.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.5b

bsearch82.0ms

Steps

Iters	Range		Point
8	0.002806896206153352	41.96612619086958	0.015291166436094373
7	-0.5149414008252181	-0.002950799818357885	-0.01665811831216181

simplify10.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	36
1	67	36
2	81	36
3	95	36
4	110	36
5	143	36
6	157	36
7	162	36
8	167	36
9	167	36

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.6s	1653×	body	2560	valid
1.9s	2759×	body	1280	valid
590.0ms	1836×	body	640	valid
229.0ms	916×	body	320	valid
72.0ms	478×	body	160	valid
31.0ms	358×	body	80	valid