Details

sample473.0ms

Algorithm

intervals

Results

114.0ms	59×	body	2560	valid
71.0ms	92×	body	1280	valid
16.0ms	58×	body	640	valid
5.0ms	28×	body	320	valid
1.0ms	10×	body	160	valid
1.0ms	9×	body	80	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: 34.7b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.0b	(- x (tan x))
1.0b	(- x (sin 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:

25.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series177.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(/ (- x (sin x)) (- x (tan x)))
58.0ms	(- x (tan x))
41.0ms	(- x (sin x))

simplify58.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (13.0ms)

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

prune223.0ms

Filtered

119 candidates to 79 candidates (66.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	116	3	119
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	3	120

Merged error: 0b

Counts

120 → 3

localize11.0ms

Local error

Found 2 expressions with local error:

0.4b	(fma 27/2800 (pow x 4) 1/2)
15.3b	(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)))

series131.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(fma 27/2800 (pow x 4) 1/2)
48.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify148.0ms

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

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	26	3	29

Merged error: 0b

Counts

29 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.0b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.0b	(- x (tan x))
1.0b	(- x (tan x))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

713×	`*-un-lft-identity`
703×	`add-sqr-sqrt`
678×	`times-frac`
459×	`prod-diff`
417×	`add-cube-cbrt`
147×	`distribute-lft-out--`
141×	`difference-of-squares`
92×	`associate-/r/`
49×	`flip3--` `flip--`
46×	`div-inv`
27×	`fma-neg`
10×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-/r*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 588

Calls

4 calls:

7.0ms	(/ (sin x) (- x (tan x)))
38.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
4.0ms	(- x (tan x))
4.0ms	(- x (tan x))

series346.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ (sin x) (- x (tan x)))
177.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
51.0ms	(- x (tan x))
56.0ms	(- x (tan x))

simplify217.0ms

Algorithm

egg-herbie

Counts

600 → 600

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	1359	22035
1	3883	15840
2	5001	15776

prune890.0ms

Filtered

600 candidates to 256 candidates (42.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	600	0	600
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	600	3	603

Merged error: 0b

Counts

603 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- x (sin x)) 3)
1.0b	(- x (tan x))
1.0b	(- x (sin x))
19.2b	(cbrt (pow (- x (sin x)) 3))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt` `*-un-lft-identity`
24×	`add-cube-cbrt`
18×	`prod-diff`
16×	`cbrt-prod`
10×	`unpow-prod-down` `cube-prod`
8×	`add-log-exp`
6×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`cube-div` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`pow-unpow`
2×	`cube-mult` `sub-neg` `cbrt-div` `diff-log` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 116

Calls

4 calls:

5.0ms	(pow (- x (sin x)) 3)
4.0ms	(- x (tan x))
4.0ms	(- x (sin x))
5.0ms	(cbrt (pow (- x (sin x)) 3))

series174.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(pow (- x (sin x)) 3)
48.0ms	(- x (tan x))
35.0ms	(- x (sin x))
45.0ms	(cbrt (pow (- x (sin x)) 3))

simplify56.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	451	832
1	1693	631
2	5001	625

prune228.0ms

Filtered

128 candidates to 76 candidates (59.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	128	3	131

Merged error: 0b

Counts

131 → 3

regimes29.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.1b

bsearch86.0ms

Steps

Iters	Range		Point
10	0.0002141056345597589	3206628.0142593775	0.029607457957696412
11	-4.816760182774211e+16	-0.0014803844373699059	-0.029680637313438188

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	13
1	26	13

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.7s	1570×	body	2560	valid
1.7s	2830×	body	1280	valid
494.0ms	1863×	body	640	valid
179.0ms	960×	body	320	valid
60.0ms	449×	body	160	valid
25.0ms	328×	body	80	valid