Details

sample478.0ms

Algorithm

intervals

Results

114.0ms	47×	body	2560	valid
73.0ms	97×	body	1280	valid
21.0ms	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

localize22.0ms

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))

rewrite24.0ms

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:

11.0ms	(/ (- x (sin x)) (- x (tan x)))
2.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series168.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(/ (- x (sin x)) (- x (tan x)))
56.0ms	(- x (tan x))
39.0ms	(- x (sin x))

simplify149.0ms

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

prune201.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
14.8b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite21.0ms

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))
6.0ms	(* 9/40 (pow x 2))
8.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series104.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(* 27/2800 (pow x 4))
23.0ms	(* 9/40 (pow x 2))
47.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify42.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (35.0ms)

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

prune141.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
14.8b	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

rewrite16.0ms

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`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
5×	`add-log-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 64

Calls

3 calls:

5.0ms	(* 27/2800 (pow x 4))
6.0ms	(* 9/40 (pow x 2))
3.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

series160.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(* 27/2800 (pow x 4))
23.0ms	(* 9/40 (pow x 2))
103.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

simplify44.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	249	310
1	1003	281
2	5001	275

prune139.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize13.0ms

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))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt`
8×	`associate-/r/` `add-log-exp`
6×	`flip3--` `flip--`
4×	`frac-times` `times-frac` `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 → 89

Calls

4 calls:

4.0ms	(* (sin x) (sin x))
3.0ms	(- (* x x) (* (sin x) (sin x)))
2.0ms	(- x (tan x))
13.0ms	(/ (- (* x x) (* (sin x) (sin x))) (* (- x (tan x)) (+ x (sin x))))

series277.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (sin x) (sin x))
65.0ms	(- (* x x) (* (sin x) (sin x)))
54.0ms	(- x (tan x))
140.0ms	(/ (- (* x x) (* (sin x) (sin x))) (* (- x (tan x)) (+ x (sin x))))

simplify72.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	565	877
1	2896	760
2	5001	756

prune247.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes48.0ms

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

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	11
1	28	11

end0.0ms

sample6.8s

Algorithm

intervals

Results

3.6s	1602×	body	2560	valid
2.0s	2734×	body	1280	valid
693.0ms	1851×	body	640	valid
240.0ms	954×	body	320	valid
95.0ms	481×	body	160	valid
55.0ms	378×	body	80	valid