Details

sample473.0ms

Algorithm

intervals

Results

113.0ms	47×	body	2560	valid
71.0ms	97×	body	1280	valid
20.0ms	57×	body	640	valid
7.0ms	29×	body	320	valid
2.0ms	13×	body	160	valid
2.0ms	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: 31.9b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.2b	(- x (tan x))
1.2b	(- x (sin x))

rewrite28.0ms

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)))
4.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series172.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (- x (sin x)) (- x (tan x)))
57.0ms	(- x (tan x))
40.0ms	(- 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

prune234.0ms

Pruning

3 alts after pruning (2 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)
14.8b	(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)))

series131.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(fma 27/2800 (pow x 4) 1/2)
48.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

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

prune70.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2))))
0.0b	(log (exp (fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))))
0.0b	(fma 27/2800 (pow x 4) 1/2)
14.8b	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

1.0ms	(exp (fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2))))
1.0ms	(log (exp (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)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(exp (fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2))))
43.0ms	(log (exp (fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))))
82.0ms	(fma 27/2800 (pow x 4) 1/2)
47.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify43.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (37.0ms)

Iter	Nodes	Cost
0	119	426
1	328	378
2	1289	378
3	5001	376

prune181.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin x))
1.2b	(- (* x x) (* (sin x) (sin x)))
1.2b	(- x (tan x))
14.4b	(/ (- (* x x) (* (sin x) (sin x))) (* (- x (tan x)) (+ x (sin x))))

rewrite27.0ms

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))
13.0ms	(/ (- (* x x) (* (sin x) (sin x))) (* (- x (tan x)) (+ x (sin x))))

series282.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (sin x) (sin x))
64.0ms	(- (* x x) (* (sin x) (sin x)))
53.0ms	(- x (tan x))
146.0ms	(/ (- (* x x) (* (sin x) (sin x))) (* (- x (tan x)) (+ x (sin x))))

simplify81.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (71.0ms)

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

prune282.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes54.0ms

Accuracy

100% (0.0b remaining)

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

bsearch92.0ms

Steps

Iters	Range		Point
9	0.0012055448239290207	14520.350903362307	0.028980233302380854
9	-1078.7327260164275	-0.0019174381104543623	-0.026145755788180215

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	10
1	25	10

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.5s	1602×	body	2560	valid
1.9s	2734×	body	1280	valid
670.0ms	1851×	body	640	valid
236.0ms	954×	body	320	valid
85.0ms	481×	body	160	valid
64.0ms	378×	body	80	valid