Details

sample429.0ms

Algorithm

intervals

Results

84.0ms	41×	body	2560	valid
64.0ms	99×	body	1280	valid
18.0ms	52×	body	640	valid
7.0ms	30×	body	320	valid
3.0ms	17×	body	160	valid
2.0ms	17×	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: 29.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.2b	(- x (tan x))
2.2b	(- x (sin x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

20.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series177.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(/ (- x (sin x)) (- x (tan x)))
59.0ms	(- x (tan x))
41.0ms	(- x (sin x))

simplify147.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	685
2	4795	685
3	5001	685

prune207.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
0.0b	(pow (/ (- x (sin x)) (- x (tan x))) 3)
2.2b	(- x (tan x))
2.2b	(- x (sin x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

134×	`add-sqr-sqrt` `*-un-lft-identity`
100×	`times-frac`
68×	`cbrt-prod`
62×	`unpow-prod-down` `cube-prod`
50×	`add-cube-cbrt`
42×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-/r/` `add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
6×	`flip3--` `flip--`
5×	`pow1`
4×	`div-inv`
3×	`pow-unpow`
2×	`cube-div` `cube-mult` `sub-neg` `diff-log` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `div-exp` `rem-cbrt-cube`

Counts

4 → 188

Calls

4 calls:

12.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
10.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
3.0ms	(- x (tan x))
4.0ms	(- x (sin x))

series254.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
91.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
49.0ms	(- x (tan x))
36.0ms	(- x (sin x))

simplify79.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	736	2195
1	3051	2083
2	5001	2069

prune303.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (pow (/ (- x (sin x)) (- x (tan x))) 3) 3)
0.0b	(pow (/ (- x (sin x)) (- x (tan x))) 3)
2.2b	(- x (tan x))
2.2b	(- x (sin x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

198×	`add-sqr-sqrt` `*-un-lft-identity`
161×	`unpow-prod-down` `cube-prod`
150×	`times-frac`
74×	`add-cube-cbrt`
62×	`distribute-lft-out--` `difference-of-squares`
12×	`associate-/r/`
11×	`add-exp-log`
8×	`flip3--` `pow-exp` `add-cbrt-cube` `flip--` `add-log-exp`
6×	`pow-unpow` `div-inv`
5×	`pow1`
4×	`cube-mult` `unpow3` `sqr-pow`
3×	`cube-div` `pow-to-exp` `rem-cube-cbrt`
2×	`sub-neg` `pow-pow` `diff-log` `div-exp`
1×	`cbrt-undiv`

Counts

4 → 267

Calls

4 calls:

19.0ms	(pow (pow (/ (- x (sin x)) (- x (tan x))) 3) 3)
11.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
3.0ms	(- x (tan x))
4.0ms	(- x (sin x))

series291.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(pow (pow (/ (- x (sin x)) (- x (tan x))) 3) 3)
92.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
50.0ms	(- x (tan x))
36.0ms	(- x (sin x))

simplify54.0ms

Algorithm

egg-herbie

Counts

279 → 279

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1015	3577
1	5002	3343

prune415.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
2.1b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
2.2b	(- x (tan x))
2.2b	(- x (tan x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
33×	`times-frac`
18×	`distribute-lft-out--`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`add-exp-log` `flip3--` `associate-/r/` `add-cbrt-cube` `flip--`
5×	`associate-/r*`
4×	`pow1`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 94

Calls

4 calls:

6.0ms	(/ (sin x) (- x (tan x)))
25.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
3.0ms	(- x (tan x))
3.0ms	(- x (tan x))

series350.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (sin x) (- x (tan x)))
179.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
55.0ms	(- x (tan x))
53.0ms	(- x (tan x))

simplify39.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	376	909
1	1205	872
2	5001	872

prune240.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.1b

regimes83.0ms

Accuracy

100% (0.0b remaining)

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

bsearch69.0ms

Steps

Iters	Range		Point
10	9.558161037350472e-13	0.8818080259852756	0.027208711435501284
5	-0.041603525395973645	-0.015510049556855336	-0.028868508597387585

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	23
1	34	23

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.5s	1588×	body	2560	valid
1.9s	2762×	body	1280	valid
639.0ms	1826×	body	640	valid
219.0ms	945×	body	320	valid
88.0ms	509×	body	160	valid
34.0ms	370×	body	80	valid