Details

sample470.0ms

Algorithm

intervals

Results

138.0ms	62×	body	2560	valid
54.0ms	77×	body	1280	valid
15.0ms	55×	body	640	valid
5.0ms	25×	body	320	valid
3.0ms	19×	body	80	valid
3.0ms	18×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 32.5b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.6b	(- x (sin x))
1.6b	(- x (tan x))

rewrite41.0ms

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 (sin x))
7.0ms	(- x (tan x))

series173.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(/ (- x (sin x)) (- x (tan x)))
36.0ms	(- x (sin x))
61.0ms	(- x (tan x))

simplify57.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (13.0ms)

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

prune212.0ms

Filtered

119 candidates to 79 candidates (66.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	115	4	119
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	4	120

Merged error: 0.0b

Counts

120 → 4

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma 27/2800 (pow x 4) 1/2)
14.1b	(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)))

series128.0ms

Counts

2 → 6

Calls

2 calls:

81.0ms	(fma 27/2800 (pow x 4) 1/2)
47.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify145.0ms

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

prune64.0ms

Filtered

26 candidates to 20 candidates (76.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	26	4	30

Merged error: 0.0b

Counts

30 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

1.6b	(- x (sin x))
1.6b	(- x (tan x))
1.6b	(- x (tan x))
1.6b	(- x (tan x))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`add-cube-cbrt`
12×	`fma-neg` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 112

Calls

4 calls:

4.0ms	(- x (sin x))
4.0ms	(- x (tan x))
4.0ms	(- x (tan x))
4.0ms	(- x (tan x))

series185.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- x (sin x))
51.0ms	(- x (tan x))
50.0ms	(- x (tan x))
54.0ms	(- x (tan x))

simplify96.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	258	979
1	749	615
2	3295	579
3	5001	411

prune271.0ms

Filtered

124 candidates to 75 candidates (60.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	124	4	128

Merged error: 0.0b

Counts

128 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
1.6b	(- x (sin x))
1.6b	(- (* x x) (* (tan x) (tan x)))
13.0b	(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
16×	`times-frac`
11×	`pow1`
10×	`prod-diff`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`difference-of-squares`
5×	`distribute-lft-out`
4×	`tan-quot` `expm1-log1p-u` `fma-neg` `associate-/r` `log1p-expm1-u` `associate-/l`
3×	`flip3--` `swap-sqr` `associate-r` `associate-l` `flip--`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-times` `frac-2neg` `flip3-+` `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` `flip-+` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 118

Calls

4 calls:

5.0ms	(* (tan x) (tan x))
4.0ms	(- x (sin x))
4.0ms	(- (* x x) (* (tan x) (tan x)))
10.0ms	(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (tan x) (tan x))
33.0ms	(- x (sin x))
83.0ms	(- (* x x) (* (tan x) (tan x)))
139.0ms	(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))

simplify69.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	497	1072
1	2197	909
2	5001	904

prune234.0ms

Filtered

130 candidates to 89 candidates (68.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	130	4	134

Merged error: 0.0b

Counts

134 → 4

regimes32.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.8b

bsearch81.0ms

Steps

Iters	Range		Point
9	0.006602375602419948	2408.9151023461654	0.03184416870118442
10	-7888799.454350161	-0.0014566459989916651	-0.028761646689302346

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	28
1	32	28

end0.0ms

sample6.6s

Algorithm

intervals

Results

4.1s	1635×	body	2560	valid
1.6s	2712×	body	1280	valid
495.0ms	1897×	body	640	valid
163.0ms	922×	body	320	valid
60.0ms	494×	body	160	valid
25.0ms	340×	body	80	valid