Details

sample437.0ms

Algorithm

intervals

Results

89.0ms	42×	body	2560	valid
63.0ms	88×	body	1280	valid
21.0ms	58×	body	640	valid
10.0ms	38×	body	320	valid
3.0ms	19×	body	160	valid
1.0ms	11×	body	80	valid

simplify11.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.6b	(- x (tan x))
1.6b	(- x (sin x))

rewrite59.0ms

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:

26.0ms	(/ (- x (sin x)) (- x (tan x)))
18.0ms	(- x (tan x))
10.0ms	(- x (sin x))

series164.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(/ (- x (sin x)) (- x (tan x)))
54.0ms	(- x (tan x))
38.0ms	(- x (sin x))

simplify54.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (11.0ms)

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

prune377.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (/ (- x (sin x)) (- x (tan x)))))
0.0b	(/ (- x (sin x)) (- x (tan x)))
1.6b	(- x (tan x))
1.6b	(- x (sin x))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `fma-neg` `add-cbrt-cube`
5×	`associate-/r` `associate-/l`
4×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `expm1-log1p` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv` `expm1-udef`

Counts

4 → 121

Calls

4 calls:

0.0ms	(expm1 (log1p (/ (- x (sin x)) (- x (tan x)))))
26.0ms	(/ (- x (sin x)) (- x (tan x)))
6.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series273.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(expm1 (log1p (/ (- x (sin x)) (- x (tan x)))))
74.0ms	(/ (- x (sin x)) (- x (tan x)))
46.0ms	(- x (tan x))
32.0ms	(- x (sin x))

simplify53.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	484	1189
1	1751	973
2	5001	973

prune461.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2))))
0.0b	(expm1 (log1p (fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))))
0.3b	(fma 27/2800 (pow x 4) 1/2)
15.1b	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`expm1-log1p-u`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `expm1-udef`

Counts

4 → 42

Calls

4 calls:

0.0ms	(log1p (fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2))))
0.0ms	(expm1 (log1p (fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))))
0.0ms	(fma 27/2800 (pow x 4) 1/2)
0.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

series336.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(log1p (fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2))))
130.0ms	(expm1 (log1p (fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))))
78.0ms	(fma 27/2800 (pow x 4) 1/2)
40.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify73.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	204	388
1	642	343
2	2489	321
3	5002	320

prune205.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.3b	(fma 27/2800 (pow x 4) 1/2)
15.1b	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

rewrite1.0ms

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:

0.0ms	(fma 27/2800 (pow x 4) 1/2)
0.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

series121.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(fma 27/2800 (pow x 4) 1/2)
43.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify141.0ms

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

prune98.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes49.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.4b

bsearch100.0ms

Steps

Iters	Range		Point
9	0.007285382865895221	15234496.061427226	0.02670032604590421
10	-569.2304264003914	-7.772245281701499e-10	-0.027558206962883136

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	14
1	29	14

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.5s	1568×	body	2560	valid
2.0s	2848×	body	1280	valid
681.0ms	1862×	body	640	valid
226.0ms	928×	body	320	valid
82.0ms	459×	body	160	valid
32.0ms	335×	body	80	valid