Details

sample450.0ms

Algorithm

intervals

Results

99.0ms	47×	body	2560	valid
63.0ms	89×	body	1280	valid
24.0ms	66×	body	640	valid
8.0ms	31×	body	320	valid
3.0ms	15×	body	160	valid
1.0ms	8×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.4b	(- x (sin x))
1.4b	(- x (tan 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:

13.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (sin x))
19.0ms	(- x (tan x))

series179.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(/ (- x (sin x)) (- x (tan x)))
38.0ms	(- x (sin x))
63.0ms	(- x (tan x))

simplify55.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (12.0ms)

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

prune240.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (exp (/ (- x (sin x)) (- x (tan x)))))
0.0b	(/ (- x (sin x)) (- x (tan x)))
1.4b	(- x (sin x))
1.4b	(- x (tan x))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt` `*-un-lft-identity`
50×	`times-frac`
42×	`add-cube-cbrt`
32×	`log-pow`
31×	`exp-prod`
24×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`add-log-exp`
6×	`add-exp-log` `fma-neg` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
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 → 156

Calls

4 calls:

24.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
12.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (sin x))
3.0ms	(- x (tan x))

series239.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
77.0ms	(/ (- x (sin x)) (- x (tan x)))
35.0ms	(- x (sin x))
51.0ms	(- x (tan x))

simplify59.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	541	1431
1	1836	1207
2	5001	1207

prune380.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin x) 2)
0.2b	(pow (cos x) 2)
14.5b	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
14.6b	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-exp-log`
42×	`div-exp`
37×	`pow-to-exp` `pow-exp`
36×	`prod-exp`
18×	`unpow-prod-down`
16×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `times-frac` `associate-/l`
14×	`add-cbrt-cube`
6×	`pow1` `pow-unpow` `unpow2` `sqr-pow`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-pow` `frac-2neg` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 144

Calls

4 calls:

1.0ms	(pow (sin x) 2)
1.0ms	(pow (cos x) 2)
7.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
7.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

series172.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (sin x) 2)
17.0ms	(pow (cos x) 2)
75.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
61.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

simplify57.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	434	1060
1	1839	950
2	5002	950

prune381.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.2b	(fma 27/2800 (pow x 4) 1/2)
15.8b	(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)))

series136.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(fma 27/2800 (pow x 4) 1/2)
50.0ms	(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

prune67.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes53.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.3b

bsearch110.0ms

Steps

Iters	Range		Point
10	4.8244160186105205e-08	257763.20554958374	0.029859806300954833
10	-772.3369502403921	-4.163765984402517e-10	-0.026495654945468235

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	12
1	27	12

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.6s	1592×	body	2560	valid
1.9s	2794×	body	1280	valid
690.0ms	1883×	body	640	valid
227.0ms	956×	body	320	valid
78.0ms	440×	body	160	valid
47.0ms	335×	body	80	valid