Details

sample486.0ms

Algorithm

intervals

Results

127.0ms	53×	body	2560	valid
62.0ms	76×	body	1280	valid
28.0ms	68×	body	640	valid
9.0ms	31×	body	320	valid
3.0ms	16×	body	160	valid
1.0ms	12×	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: 34.1b

localize24.0ms

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))

rewrite27.0ms

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:

12.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series172.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (- x (sin x)) (- x (tan x)))
58.0ms	(- x (tan x))
39.0ms	(- 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

prune242.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma 27/2800 (pow x 4) 1/2)
15.6b	(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)))

series125.0ms

Counts

2 → 6

Calls

2 calls:

78.0ms	(fma 27/2800 (pow x 4) 1/2)
47.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify144.0ms

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

prune72.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

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

rewrite26.0ms

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)))))
15.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (tan x))
3.0ms	(- x (sin x))

series273.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(expm1 (log1p (/ (- x (sin x)) (- x (tan x)))))
73.0ms	(/ (- x (sin x)) (- x (tan x)))
50.0ms	(- x (tan x))
30.0ms	(- x (sin x))

simplify52.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 1 (11.0ms)

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

prune309.0ms

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	(* (sin x) (sin x))
1.7b	(- (* x x) (* (sin x) (sin x)))
1.7b	(- x (tan x))
15.1b	(/ (- (* x x) (* (sin x) (sin x))) (* (- x (tan x)) (+ x (sin x))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

4.0ms	(* (sin x) (sin x))
3.0ms	(- (* x x) (* (sin x) (sin x)))
3.0ms	(- x (tan x))
16.0ms	(/ (- (* x x) (* (sin x) (sin x))) (* (- x (tan x)) (+ x (sin x))))

series275.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (sin x) (sin x))
65.0ms	(- (* x x) (* (sin x) (sin x)))
48.0ms	(- x (tan x))
144.0ms	(/ (- (* x x) (* (sin x) (sin x))) (* (- x (tan x)) (+ x (sin x))))

simplify80.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	638	1099
1	3208	889
2	5001	883

prune290.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes53.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.1b

bsearch89.0ms

Steps

Iters	Range		Point
10	2.1112891761060846e-05	363928.4733812492	0.02907288472896622
8	-0.10438916540540782	-0.00034188071245303247	-0.027819204802016273

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	12
1	27	12

end0.0ms

sample7.1s

Algorithm

intervals

Results

3.7s	1602×	body	2560	valid
2.1s	2770×	body	1280	valid
764.0ms	1859×	body	640	valid
261.0ms	919×	body	320	valid
112.0ms	495×	body	160	valid
40.0ms	355×	body	80	valid