Details

sample452.0ms

Algorithm

intervals

Results

98.0ms	51×	body	2560	valid
65.0ms	102×	body	1280	valid
18.0ms	52×	body	640	valid
5.0ms	22×	body	320	valid
4.0ms	16×	body	160	valid
1.0ms	13×	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: 31.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.3b	(- x (tan x))
1.3b	(- x (sin x))

rewrite40.0ms

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 (tan x))
7.0ms	(- x (sin x))

series174.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (- x (sin x)) (- x (tan x)))
57.0ms	(- x (tan x))
41.0ms	(- x (sin x))

simplify56.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (12.0ms)

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

prune248.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin x) 2)
0.3b	(pow (cos x) 2)
15.0b	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))
15.0b	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))

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)
2.0ms	(pow (cos x) 2)
7.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))
8.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))

series164.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin x) 2)
16.0ms	(pow (cos x) 2)
57.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))
72.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))

simplify52.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	434	1060
1	1840	950
2	5001	950

prune381.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 27/2800 (pow x 4) 1/2)
18.8b	(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)))

series127.0ms

Counts

2 → 6

Calls

2 calls:

80.0ms	(fma 27/2800 (pow x 4) 1/2)
48.0ms	(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

prune71.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
1.3b	(- (* x x) (* (tan x) (tan x)))
1.3b	(- x (sin x))
17.6b	(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
16×	`times-frac`
11×	`pow1`
10×	`prod-diff`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`difference-of-squares`
5×	`distribute-lft-out`
4×	`tan-quot` `expm1-log1p-u` `fma-neg` `associate-/r` `log1p-expm1-u` `associate-/l`
3×	`flip3--` `swap-sqr` `associate-r` `associate-l` `flip--`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-times` `frac-2neg` `flip3-+` `pow-plus` `div-sub` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 118

Calls

4 calls:

5.0ms	(* (tan x) (tan x))
3.0ms	(- (* x x) (* (tan x) (tan x)))
3.0ms	(- x (sin x))
11.0ms	(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (tan x) (tan x))
89.0ms	(- (* x x) (* (tan x) (tan x)))
30.0ms	(- x (sin x))
145.0ms	(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))

simplify69.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	497	1072
1	2197	909
2	5001	904

prune277.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes41.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.8b

bsearch97.0ms

Steps

Iters	Range		Point
8	0.2287861600326909	251.47950061764826	2.430037265334258
10	-578421416.8415484	-0.03925098124715615	-2.435414209138285

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	28
1	44	28

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.5s	1569×	body	2560	valid
1.9s	2851×	body	1280	valid
616.0ms	1827×	body	640	valid
207.0ms	910×	body	320	valid
71.0ms	458×	body	160	valid
35.0ms	385×	body	80	valid