Details

sample448.0ms

Algorithm

intervals

Results

97.0ms	48×	body	2560	valid
71.0ms	101×	body	1280	valid
18.0ms	51×	body	640	valid
7.0ms	30×	body	320	valid
3.0ms	16×	body	160	valid
1.0ms	10×	body	80	valid

simplify10.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.7b	(- x (tan x))
1.7b	(- x (sin x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

11.0ms	(/ (- x (sin x)) (- x (tan x)))
2.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series176.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(/ (- x (sin x)) (- x (tan x)))
60.0ms	(- x (tan x))
39.0ms	(- x (sin x))

simplify147.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	685
2	4795	685
3	5001	685

prune206.0ms

Filtered

89 candidates to 63 candidates (70.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.0b	(log (exp (/ (- x (sin x)) (- x (tan x)))))
1.7b	(- x (tan x))
1.7b	(- x (sin x))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt` `*-un-lft-identity`
50×	`times-frac`
32×	`log-pow`
31×	`exp-prod`
28×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`associate-/r/`
3×	`log-prod`
2×	`sub-neg` `diff-log` `div-sub` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `log-div` `frac-2neg` `exp-diff` `div-exp` `rem-log-exp` `clear-num`

Counts

4 → 124

Calls

4 calls:

11.0ms	(/ (- x (sin x)) (- x (tan x)))
21.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
2.0ms	(- x (tan x))
3.0ms	(- x (sin x))

series235.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (- x (sin x)) (- x (tan x)))
77.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
48.0ms	(- x (tan x))
34.0ms	(- x (sin x))

simplify41.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	430	1079
1	1247	1027
2	5001	1027

prune312.0ms

Filtered

136 candidates to 95 candidates (69.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.7b	(- x (tan x))
1.7b	(- x (tan x))
1.7b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
33×	`times-frac`
18×	`distribute-lft-out--`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`add-exp-log` `flip3--` `associate-/r/` `add-cbrt-cube` `flip--`
5×	`associate-/r*`
4×	`pow1`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 94

Calls

4 calls:

8.0ms	(/ (sin x) (- x (tan x)))
2.0ms	(- x (tan x))
2.0ms	(- x (tan x))
49.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

series340.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (sin x) (- x (tan x)))
48.0ms	(- x (tan x))
54.0ms	(- x (tan x))
177.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

simplify38.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	376	909
1	1205	872
2	5001	872

prune238.0ms

Filtered

106 candidates to 80 candidates (75.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

1.7b	(- x (tan x))
1.7b	(- x (tan x))
1.7b	(- x (tan x))
1.7b	(- (* (/ x (- x (tan x))) (/ x (- x (tan x)))) (* (/ (sin x) (- x (tan x))) (/ (sin x) (- x (tan x)))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-log-exp`
10×	`add-sqr-sqrt` `-un-lft-identity` `associate-r/` `associate-*l/`
9×	`frac-sub`
8×	`frac-times`
5×	`sub-div`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `difference-of-squares`
3×	`distribute-lft-out--`

Counts

4 → 69

Calls

4 calls:

2.0ms	(- x (tan x))
2.0ms	(- x (tan x))
2.0ms	(- x (tan x))
11.0ms	(- (* (/ x (- x (tan x))) (/ x (- x (tan x)))) (* (/ (sin x) (- x (tan x))) (/ (sin x) (- x (tan x)))))

series349.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- x (tan x))
48.0ms	(- x (tan x))
53.0ms	(- x (tan x))
194.0ms	(- (* (/ x (- x (tan x))) (/ x (- x (tan x)))) (* (/ (sin x) (- x (tan x))) (/ (sin x) (- x (tan x)))))

simplify116.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	335	863
1	1141	768
2	4949	748
3	5001	748

prune200.0ms

Filtered

81 candidates to 58 candidates (71.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes60.0ms

Accuracy

100% (0.0b remaining)

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

bsearch75.0ms

Steps

Iters	Range		Point
9	0.0004320794088804456	4086.0217424804537	0.027107762548292866
7	-0.37949367736095085	-0.007251023403816859	-0.025053611726062623

simplify9.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	61
1	51	61
2	54	61
3	54	61

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.5s	1598×	body	2560	valid
2.0s	2865×	body	1280	valid
636.0ms	1818×	body	640	valid
217.0ms	925×	body	320	valid
75.0ms	452×	body	160	valid
33.0ms	342×	body	80	valid