Details

sample473.0ms

Algorithm

intervals

Results

128.0ms	48×	body	2560	valid
51.0ms	86×	body	1280	valid
17.0ms	64×	body	640	valid
6.0ms	36×	body	320	valid
3.0ms	14×	body	80	valid
1.0ms	8×	body	160	valid

simplify12.0ms

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 (100.0%)

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: 34.6b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.9b	(- x (sin x))
1.1b	(- x (tan x))

rewrite43.0ms

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:

27.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (sin x))
6.0ms	(- x (tan x))

series181.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(/ (- x (sin x)) (- x (tan x)))
38.0ms	(- x (sin x))
64.0ms	(- x (tan x))

simplify57.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	469	1059
1	1694	854
2	5003	854

prune189.0ms

Filtered

119 candidates to 79 candidates (33.6%)

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:

0.0b	(fma 27/2800 (pow x 4) 1/2)
14.8b	(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)))

series138.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(fma 27/2800 (pow x 4) 1/2)
51.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify147.0ms

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

prune65.0ms

Filtered

26 candidates to 20 candidates (23.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	25	1	26
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	25	5	30

Merged error: 0.0b

Counts

30 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (fma 27/2800 (pow x 4) 1/2) 3)
0.0b	(fma 27/2800 (pow x 4) 1/2)
3.6b	(cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3))
14.8b	(fma 9/40 (pow x 2) (- (cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
8×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt`
6×	`unpow-prod-down`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u` `add-log-exp`
2×	`unpow3` `rem-cbrt-cube` `fma-udef` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cube-cbrt`

Counts

4 → 61

Calls

4 calls:

2.0ms	(pow (fma 27/2800 (pow x 4) 1/2) 3)
1.0ms	(fma 27/2800 (pow x 4) 1/2)
2.0ms	(cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3))
1.0ms	(fma 9/40 (pow x 2) (- (cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3))))

series337.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(pow (fma 27/2800 (pow x 4) 1/2) 3)
92.0ms	(fma 27/2800 (pow x 4) 1/2)
88.0ms	(cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3))
48.0ms	(fma 9/40 (pow x 2) (- (cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3))))

simplify147.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	165	351
1	582	318
2	3437	313
3	5003	313

prune153.0ms

Filtered

73 candidates to 47 candidates (35.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	73	5	78

Merged error: 0.0b

Counts

78 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

14.8b	(fma 9/40 (pow x 2) (- (cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3))))
14.9b	(cbrt (fma 9/40 (pow x 2) (- (cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3)))))
14.9b	(cbrt (fma 9/40 (pow x 2) (- (cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3)))))
14.9b	(cbrt (fma 9/40 (pow x 2) (- (cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3)))))

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	(fma 9/40 (pow x 2) (- (cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3))))
1.0ms	(cbrt (fma 9/40 (pow x 2) (- (cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3)))))
1.0ms	(cbrt (fma 9/40 (pow x 2) (- (cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3)))))
1.0ms	(cbrt (fma 9/40 (pow x 2) (- (cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3)))))

series508.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(fma 9/40 (pow x 2) (- (cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3))))
153.0ms	(cbrt (fma 9/40 (pow x 2) (- (cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3)))))
152.0ms	(cbrt (fma 9/40 (pow x 2) (- (cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3)))))
156.0ms	(cbrt (fma 9/40 (pow x 2) (- (cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	163	806
1	472	737
2	1907	724
3	5002	715

prune239.0ms

Filtered

61 candidates to 58 candidates (4.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	0	3	3
Picked	1	0	1
Done	1	0	1
Total	62	4	66

Merged error: 0.0b

Counts

66 → 4

regimes36.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.0b

bsearch91.0ms

Steps

Iters	Range		Point
9	0.0004381094517774334	96283.49646244562	2.5070089716143773
6	-0.04448272872103196	-0.010589856477353462	-0.030040886285671604

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	55
1	57	55

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.9s	1602×	body	2560	valid
1.5s	2716×	body	1280	valid
496.0ms	1933×	body	640	valid
156.0ms	918×	body	320	valid
57.0ms	489×	body	160	valid
29.0ms	342×	body	80	valid