Details

sample522.0ms

Algorithm

intervals

Results

125.0ms	53×	body	2560	valid
61.0ms	87×	body	1280	valid
15.0ms	54×	body	640	valid
8.0ms	36×	body	320	valid
2.0ms	17×	body	160	valid
1.0ms	9×	body	80	valid

simplify12.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 30.5b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.3b	(- x (tan x))
1.3b	(- x (sin x))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`fma-neg`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 110

Calls

3 calls:

24.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series169.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(/ (- x (sin x)) (- x (tan x)))
56.0ms	(- x (tan x))
39.0ms	(- x (sin x))

simplify59.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	472	1059
1	1737	854
2	5001	854

prune202.0ms

Filtered

119 candidates to 79 candidates (66.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	117	3	120

Merged error: 0.0b

Counts

120 → 3

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma 27/2800 (pow x 4) 1/2)
17.1b	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

1.0ms	(fma 27/2800 (pow x 4) 1/2)
1.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

series124.0ms

Counts

2 → 6

Calls

2 calls:

81.0ms	(fma 27/2800 (pow x 4) 1/2)
43.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify146.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	51	133
1	162	117
2	626	117
3	3552	117
4	5001	117

prune56.0ms

Filtered

26 candidates to 20 candidates (76.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	26	3	29

Merged error: 0.0b

Counts

29 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
1.3b	(- (* x x) (* (tan x) (tan x)))
1.3b	(- x (sin x))
16.0b	(/ (- x (sin x)) (- (* x x) (* (tan x) (tan x))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
26×	`add-cube-cbrt`
20×	`times-frac`
13×	`difference-of-squares`
11×	`pow1`
10×	`prod-diff`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`distribute-lft-out--`
5×	`associate-/l*`
4×	`tan-quot` `expm1-log1p-u` `flip3--` `fma-neg` `associate-/r*` `flip--` `log1p-expm1-u`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-times` `frac-2neg` `pow-plus` `div-sub` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 123

Calls

4 calls:

5.0ms	(* (tan x) (tan x))
4.0ms	(- (* x x) (* (tan x) (tan x)))
4.0ms	(- x (sin x))
9.0ms	(/ (- x (sin x)) (- (* x x) (* (tan x) (tan x))))

series230.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (tan x) (tan x))
80.0ms	(- (* x x) (* (tan x) (tan x)))
29.0ms	(- x (sin x))
86.0ms	(/ (- x (sin x)) (- (* x x) (* (tan x) (tan x))))

simplify66.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	509	1200
1	2145	1040
2	5003	1031

prune246.0ms

Filtered

135 candidates to 94 candidates (69.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	135	3	138

Merged error: 0.0b

Counts

138 → 3

regimes47.0ms

Accuracy

100% (0.0b remaining)

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

bsearch80.0ms

Steps

Iters	Range		Point
10	0.005370866090842012	4.21737757242384e+15	0.030633531225492793
10	-3.4402871636077537	-5.738045557766166e-18	-0.028549322719814054

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	10
1	25	10

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.8s	1592×	body	2560	valid
1.6s	2767×	body	1280	valid
491.0ms	1847×	body	640	valid
171.0ms	957×	body	320	valid
59.0ms	471×	body	160	valid
27.0ms	366×	body	80	valid