Details

sample454.0ms

Algorithm

intervals

Results

116.0ms	58×	body	2560	valid
53.0ms	86×	body	1280	valid
16.0ms	67×	body	640	valid
4.0ms	24×	body	320	valid
1.0ms	12×	body	160	valid
1.0ms	9×	body	80	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 32.5b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.4b	(- x (tan x))
1.4b	(- x (sin x))

rewrite21.0ms

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))

series184.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(/ (- x (sin x)) (- x (tan x)))
53.0ms	(- x (tan x))
52.0ms	(- x (sin x))

simplify149.0ms

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

prune213.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.3b	(* 9/40 (pow x 2))
17.1b	(- (* 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))

series109.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* 27/2800 (pow x 4))
29.0ms	(* 9/40 (pow x 2))
45.0ms	(- (* 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

prune152.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
0.2b	(/ (sin x) (cos x))
1.4b	(- x (/ (sin x) (cos x)))
1.4b	(- x (sin x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
46×	`times-frac`
25×	`add-cube-cbrt`
22×	`difference-of-squares`
15×	`distribute-lft-out--`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
4×	`pow1` `flip3--` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `associate-/r/` `div-inv` `associate-/l/`
1×	`quot-tan` `div-sub`

Counts

4 → 115

Calls

4 calls:

11.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
4.0ms	(/ (sin x) (cos x))
6.0ms	(- x (/ (sin x) (cos x)))
4.0ms	(- x (sin x))

series177.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
18.0ms	(/ (sin x) (cos x))
49.0ms	(- x (/ (sin x) (cos x)))
34.0ms	(- x (sin x))

simplify50.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	458	1225
1	1565	1175
2	5001	1173

prune276.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (cos x))
0.2b	(* (sin x) (/ 1 (cos x)))
1.4b	(- x (* (sin x) (/ 1 (cos x))))
1.4b	(- x (sin x))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
4×	`div-exp` `prod-exp`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `sub-neg` `rec-exp` `flip3--` `diff-log` `1-exp` `flip--` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 93

Calls

4 calls:

3.0ms	(/ 1 (cos x))
8.0ms	(* (sin x) (/ 1 (cos x)))
3.0ms	(- x (* (sin x) (/ 1 (cos x))))
4.0ms	(- x (sin x))

series117.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ 1 (cos x))
20.0ms	(* (sin x) (/ 1 (cos x)))
51.0ms	(- x (* (sin x) (/ 1 (cos x))))
34.0ms	(- x (sin x))

simplify44.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	346	567
1	1397	505
2	5001	475

prune188.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes38.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.6b

bsearch78.0ms

Steps

Iters	Range		Point
9	1.2358748968334836e-07	0.22405535791780642	0.027692563310526046
9	-0.11986014733990268	-1.6789357321840064e-10	-0.024784357953886005

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	14
1	35	14

end0.0ms

sample6.6s

Algorithm

intervals

Results

4.1s	1677×	body	2560	valid
1.6s	2811×	body	1280	valid
447.0ms	1827×	body	640	valid
139.0ms	856×	body	320	valid
53.0ms	478×	body	160	valid
24.0ms	351×	body	80	valid