Details

sample450.0ms

Algorithm

intervals

Results

105.0ms	51×	body	2560	valid
56.0ms	85×	body	1280	valid
22.0ms	62×	body	640	valid
8.0ms	36×	body	320	valid
2.0ms	16×	body	160	valid
1.0ms	6×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize11.0ms

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))

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:

38.0ms	(/ (- x (sin x)) (- x (tan x)))
6.0ms	(- x (tan x))
10.0ms	(- x (sin x))

series167.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(/ (- x (sin x)) (- x (tan x)))
55.0ms	(- x (tan x))
40.0ms	(- 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

prune236.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (expm1 (/ (- x (sin x)) (- x (tan x)))))
0.5b	(expm1 (/ (- x (sin x)) (- x (tan x))))
1.7b	(- x (tan x))
1.7b	(- x (sin x))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt` `prod-diff`
8×	`add-log-exp`
6×	`fma-neg`
5×	`log1p-expm1-u`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `expm1-udef`

Counts

4 → 78

Calls

4 calls:

0.0ms	(log1p (expm1 (/ (- x (sin x)) (- x (tan x)))))
0.0ms	(expm1 (/ (- x (sin x)) (- x (tan x))))
6.0ms	(- x (tan x))
8.0ms	(- x (sin x))

series337.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(log1p (expm1 (/ (- x (sin x)) (- x (tan x)))))
101.0ms	(expm1 (/ (- x (sin x)) (- x (tan x))))
47.0ms	(- x (tan x))
34.0ms	(- x (sin x))

simplify48.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	443	803
1	1635	588
2	5002	580

prune203.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (exp -1/2) (+ (* 9/40 (pow x 2)) (* (pow x 4) 351/22400)))
0.2b	(* 9/40 (pow x 2))
0.5b	(* (pow x 4) 351/22400)
23.3b	(log1p (+ (* (exp -1/2) (+ (* 9/40 (pow x 2)) (* (pow x 4) 351/22400))) (expm1 -1/2)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
15×	`add-exp-log`
14×	`associate-r`
13×	`associate-l`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-cbrt-cube`
8×	`unpow-prod-down` `unswap-sqr`
7×	`prod-exp`
6×	`pow1`
5×	`expm1-log1p-u`
4×	`log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`*-commutative` `cbrt-unprod`
2×	`pow-to-exp` `associate-*r/` `pow-exp` `unpow2`
1×	`distribute-rgt-in` `log1p-udef` `distribute-lft-in` `flip3-+` `log1p-expm1` `pow-prod-down` `flip-+`

Counts

4 → 91

Calls

4 calls:

33.0ms	(* (exp -1/2) (+ (* 9/40 (pow x 2)) (* (pow x 4) 351/22400)))
11.0ms	(* 9/40 (pow x 2))
11.0ms	(* (pow x 4) 351/22400)
1.0ms	(log1p (+ (* (exp -1/2) (+ (* 9/40 (pow x 2)) (* (pow x 4) 351/22400))) (expm1 -1/2)))

series501.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(* (exp -1/2) (+ (* 9/40 (pow x 2)) (* (pow x 4) 351/22400)))
24.0ms	(* 9/40 (pow x 2))
39.0ms	(* (pow x 4) 351/22400)
233.0ms	(log1p (+ (* (exp -1/2) (+ (* 9/40 (pow x 2)) (* (pow x 4) 351/22400))) (expm1 -1/2)))

simplify63.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	425	611
1	1865	542
2	5002	541

prune308.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes47.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.5b

bsearch93.0ms

Steps

Iters	Range		Point
10	8.950540206577903e-05	66689094922.78456	0.038612806086461615
10	-1500.694570789724	-6.177030851099824e-09	-0.03745543377887085

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	22
1	34	22

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.5s	1601×	body	2560	valid
1.9s	2790×	body	1280	valid
632.0ms	1874×	body	640	valid
203.0ms	930×	body	320	valid
86.0ms	474×	body	160	valid
30.0ms	331×	body	80	valid