Details

sample485.0ms

Algorithm

intervals

Results

146.0ms	59×	body	2560	valid
51.0ms	91×	body	1280	valid
20.0ms	67×	body	640	valid
3.0ms	18×	body	320	valid
3.0ms	12×	body	160	valid
1.0ms	9×	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.9b	(- x (tan x))
0.9b	(- x (sin x))

rewrite22.0ms

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:

8.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series190.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(/ (- x (sin x)) (- x (tan x)))
60.0ms	(- x (tan x))
53.0ms	(- x (sin x))

simplify160.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (9.0ms)

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

prune207.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
16.8b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `sum-log` `flip--` `associate--r+`

Counts

3 → 66

Calls

3 calls:

5.0ms	(* 27/2800 (pow x 4))
5.0ms	(* 9/40 (pow x 2))
7.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series112.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* 27/2800 (pow x 4))
30.0ms	(* 9/40 (pow x 2))
46.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify42.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	273	349
1	1123	318
2	5001	315

prune150.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 9/40 (pow x 2))
0.5b	(+ 81/1600 (+ 27/5600 (* (pow x 4) 729/7840000)))
26.1b	(- (pow (* 9/40 (pow x 2)) 3) (pow (+ (* 27/2800 (pow x 4)) 1/2) 3))
27.8b	(/ (- (pow (* 9/40 (pow x 2)) 3) (pow (+ (* 27/2800 (pow x 4)) 1/2) 3)) (+ (* (pow x 4) (+ 81/1600 (+ 27/5600 (* (pow x 4) 729/7840000)))) (* (+ (* 27/2800 (pow x 4)) 1/2) (+ 1/2 (* 9/40 (pow x 2))))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
40×	`difference-of-squares`
39×	`times-frac`
37×	`*-un-lft-identity`
32×	`sqr-pow`
25×	`add-cube-cbrt`
22×	`flip3-+` `flip-+`
20×	`associate-*r/`
18×	`associate-/r/`
16×	`frac-add`
14×	`unpow-prod-down`
13×	`associate-/l*`
11×	`add-exp-log` `add-log-exp`
10×	`cube-prod`
8×	`frac-times` `associate-r` `add-cbrt-cube`
5×	`difference-cubes` `distribute-lft-out--`
4×	`pow1` `associate-*l/` `unswap-sqr`
3×	`associate-l` `prod-exp` `associate-/r*` `sum-log`
2×	`flip3--` `flip--` `associate-/l/` `unpow2`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `associate-+r+` `frac-2neg` `diff-log` `div-sub` `div-exp` `pow-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out`

Counts

4 → 151

Calls

4 calls:

6.0ms	(* 9/40 (pow x 2))
5.0ms	(+ 81/1600 (+ 27/5600 (* (pow x 4) 729/7840000)))
15.0ms	(- (pow (* 9/40 (pow x 2)) 3) (pow (+ (* 27/2800 (pow x 4)) 1/2) 3))
28.0ms	(/ (- (pow (* 9/40 (pow x 2)) 3) (pow (+ (* 27/2800 (pow x 4)) 1/2) 3)) (+ (* (pow x 4) (+ 81/1600 (+ 27/5600 (* (pow x 4) 729/7840000)))) (* (+ (* 27/2800 (pow x 4)) 1/2) (+ 1/2 (* 9/40 (pow x 2))))))

series378.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* 9/40 (pow x 2))
88.0ms	(+ 81/1600 (+ 27/5600 (* (pow x 4) 729/7840000)))
107.0ms	(- (pow (* 9/40 (pow x 2)) 3) (pow (+ (* 27/2800 (pow x 4)) 1/2) 3))
157.0ms	(/ (- (pow (* 9/40 (pow x 2)) 3) (pow (+ (* 27/2800 (pow x 4)) 1/2) 3)) (+ (* (pow x 4) (+ 81/1600 (+ 27/5600 (* (pow x 4) 729/7840000)))) (* (+ (* 27/2800 (pow x 4)) 1/2) (+ 1/2 (* 9/40 (pow x 2))))))

simplify79.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1050	4219
1	5001	4082

prune703.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
0.9b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.9b	(- x (tan x))
0.9b	(- x (tan x))

rewrite44.0ms

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)))
27.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
3.0ms	(- x (tan x))
3.0ms	(- x (tan x))

series365.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ (sin x) (- x (tan x)))
185.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
58.0ms	(- x (tan x))
57.0ms	(- x (tan x))

simplify40.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (9.0ms)

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

prune236.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes31.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.3b

bsearch106.0ms

Steps

Iters	Range		Point
10	4.9177062248324165e-05	42925490.781275615	0.02588730282387
8	-1.0806682141483241	-0.0004106978961831668	-0.034878409292342524

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	31
1	51	31

end0.0ms

sample6.6s

Algorithm

intervals

Results

4.0s	1588×	body	2560	valid
1.7s	2763×	body	1280	valid
498.0ms	1925×	body	640	valid
164.0ms	903×	body	320	valid
57.0ms	461×	body	160	valid
27.0ms	360×	body	80	valid