Details

sample450.0ms

Algorithm

intervals

Results

129.0ms	64×	body	2560	valid
47.0ms	91×	body	1280	valid
13.0ms	50×	body	640	valid
5.0ms	26×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	10×	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: 33.5b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

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

23.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
8.0ms	(- x (sin x))

series174.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (- x (sin x)) (- x (tan x)))
58.0ms	(- x (tan x))
40.0ms	(- 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

prune250.0ms

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: 0.1b

Counts

120 → 4

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b	(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)))

series131.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(fma 27/2800 (pow x 4) 1/2)
49.0ms	(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 (4.0ms)

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

prune79.0ms

Filtered

26 candidates to 20 candidates (76.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	24	2	26
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	25	5	30

Merged error: 0.1b

Counts

30 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 27/2800 (pow x 4) 1/2)
0.8b	(exp (log (fma 27/2800 (pow x 4) 1/2)))
16.1b	(fma 9/40 (pow x 2) (- (exp (log (fma 27/2800 (pow x 4) 1/2)))))
20.7b	(log (fma 27/2800 (pow x 4) 1/2))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `log-prod`
5×	`add-exp-log`
4×	`expm1-log1p-u` `exp-prod` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`exp-sum`
2×	`log-pow` `fma-udef`
1×	`rem-log-exp` `rem-exp-log`

Counts

4 → 51

Calls

4 calls:

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

series598.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(fma 27/2800 (pow x 4) 1/2)
80.0ms	(exp (log (fma 27/2800 (pow x 4) 1/2)))
44.0ms	(fma 9/40 (pow x 2) (- (exp (log (fma 27/2800 (pow x 4) 1/2)))))
392.0ms	(log (fma 27/2800 (pow x 4) 1/2))

simplify64.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (58.0ms)

Iter	Nodes	Cost
0	161	336
1	455	292
2	1785	288
3	5001	282

prune197.0ms

Filtered

63 candidates to 47 candidates (74.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	63	5	68

Merged error: 0.1b

Counts

68 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

16.1b	(fma 9/40 (pow x 2) (- (exp (log (fma 27/2800 (pow x 4) 1/2)))))
20.7b	(log (fma 27/2800 (pow x 4) 1/2))
20.7b	(log (fma 27/2800 (pow x 4) 1/2))
20.7b	(log (fma 27/2800 (pow x 4) 1/2))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

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

series1.2s

Counts

4 → 12

Calls

4 calls:

49.0ms	(fma 9/40 (pow x 2) (- (exp (log (fma 27/2800 (pow x 4) 1/2)))))
397.0ms	(log (fma 27/2800 (pow x 4) 1/2))
391.0ms	(log (fma 27/2800 (pow x 4) 1/2))
387.0ms	(log (fma 27/2800 (pow x 4) 1/2))

simplify58.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	133	425
1	380	359
2	1534	358
3	5002	358

prune312.0ms

Filtered

64 candidates to 53 candidates (82.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	64	5	69

Merged error: 0.1b

Counts

69 → 5

regimes82.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.2b

bsearch65.0ms

Steps

Iters	Range		Point
6	0.018000635171863108	0.09117784756913819	0.027293184248221757
10	-1421.6155834850151	-1.485944467815708e-07	-0.026678702825547893

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	12
1	27	12

end0.0ms

sample6.2s

Algorithm

intervals

Results

3.9s	1643×	body	2560	valid
1.5s	2762×	body	1280	valid
457.0ms	1826×	body	640	valid
156.0ms	912×	body	320	valid
55.0ms	483×	body	160	valid
26.0ms	374×	body	80	valid