Details

sample495.0ms

Algorithm

intervals

Results

166.0ms	57×	body	2560	valid
43.0ms	75×	body	1280	valid
19.0ms	72×	body	640	valid
4.0ms	26×	body	320	valid
1.0ms	12×	body	160	valid
1.0ms	14×	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: 31.3b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.2b	(- x (tan x))
1.2b	(- 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:

9.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series178.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(/ (- x (sin x)) (- x (tan x)))
58.0ms	(- x (tan x))
41.0ms	(- x (sin x))

simplify57.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (12.0ms)

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

prune212.0ms

Filtered

119 candidates to 79 candidates (66.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	116	3	119
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	116	4	120

Merged error: 0.0b

Counts

120 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- x (tan x)))
0.1b	(* (- x (sin x)) (/ 1 (- x (tan x))))
1.2b	(- x (tan x))
1.2b	(- x (sin x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
38×	`add-cube-cbrt`
32×	`times-frac`
21×	`associate-r`
18×	`prod-diff`
17×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
7×	`pow1`
6×	`flip3--` `fma-neg` `flip--`
5×	`associate-l` `associate-/r*`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `associate-/r/` `log1p-expm1-u`
3×	`associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `diff-log` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 151

Calls

4 calls:

5.0ms	(/ 1 (- x (tan x)))
14.0ms	(* (- x (sin x)) (/ 1 (- x (tan x))))
4.0ms	(- x (tan x))
4.0ms	(- x (sin x))

series214.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ 1 (- x (tan x)))
77.0ms	(* (- x (sin x)) (/ 1 (- x (tan x))))
50.0ms	(- x (tan x))
35.0ms	(- x (sin x))

simplify74.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	573	1256
1	2566	990
2	5001	948

prune247.0ms

Filtered

163 candidates to 99 candidates (60.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	163	4	167

Merged error: 0.0b

Counts

167 → 4

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 27/2800 (pow x 4) 1/2)
16.1b	(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)))

series129.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(fma 27/2800 (pow x 4) 1/2)
46.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify143.0ms

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

prune66.0ms

Filtered

26 candidates to 20 candidates (76.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	25	1	26
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	25	5	30

Merged error: 0.0b

Counts

30 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

15.4b	(cbrt (fma 27/2800 (pow x 4) 1/2))
15.4b	(cbrt (fma 27/2800 (pow x 4) 1/2))
15.4b	(cbrt (fma 27/2800 (pow x 4) 1/2))
16.1b	(fma 9/40 (pow x 2) (- (* (* (cbrt (fma 27/2800 (pow x 4) 1/2)) (cbrt (fma 27/2800 (pow x 4) 1/2))) (cbrt (fma 27/2800 (pow x 4) 1/2)))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

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

series1.7s

Counts

4 → 12

Calls

4 calls:

546.0ms	(cbrt (fma 27/2800 (pow x 4) 1/2))
554.0ms	(cbrt (fma 27/2800 (pow x 4) 1/2))
536.0ms	(cbrt (fma 27/2800 (pow x 4) 1/2))
48.0ms	(fma 9/40 (pow x 2) (- (* (* (cbrt (fma 27/2800 (pow x 4) 1/2)) (cbrt (fma 27/2800 (pow x 4) 1/2))) (cbrt (fma 27/2800 (pow x 4) 1/2)))))

simplify66.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (58.0ms)

Iter	Nodes	Cost
0	163	620
1	464	567
2	2007	528
3	5001	483

prune212.0ms

Filtered

61 candidates to 55 candidates (90.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	0	1	1
Picked	1	0	1
Done	0	3	3
Total	61	5	66

Merged error: 0.0b

Counts

66 → 5

regimes67.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.7b

bsearch58.0ms

Steps

Iters	Range		Point
6	0.011261476250181132	0.06406876111163662	0.028659494739821132
9	-3.7752751361666412	-2.6386627092684764e-08	-0.02756508271726965

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	10
1	25	10

end0.0ms

sample6.2s

Algorithm

intervals

Results

3.8s	1609×	body	2560	valid
1.6s	2707×	body	1280	valid
471.0ms	1922×	body	640	valid
153.0ms	912×	body	320	valid
65.0ms	490×	body	160	valid
25.0ms	360×	body	80	valid