Details

sample456.0ms

Algorithm

intervals

Results

113.0ms	51×	body	2560	valid
55.0ms	84×	body	1280	valid
20.0ms	60×	body	640	valid
6.0ms	29×	body	320	valid
3.0ms	21×	body	160	valid
1.0ms	11×	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: 30.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.0b	(- x (tan x))
2.0b	(- x (sin x))

rewrite36.0ms

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))
6.0ms	(- x (sin x))

series183.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(/ (- x (sin x)) (- x (tan x)))
61.0ms	(- x (tan x))
42.0ms	(- x (sin x))

simplify153.0ms

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

prune208.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.6b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
2.0b	(- x (tan x))
2.0b	(- x (tan x))

rewrite65.0ms

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)))
50.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
2.0ms	(- x (tan x))
3.0ms	(- x (tan x))

series355.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (sin x) (- x (tan x)))
183.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
54.0ms	(- x (tan x))
55.0ms	(- 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

prune247.0ms

Pruning

3 alts after pruning (2 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))
2.0b	(- x (/ (sin x) (cos x)))
2.0b	(- x (sin x))

rewrite38.0ms

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:

19.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
3.0ms	(/ (sin x) (cos x))
6.0ms	(- x (/ (sin x) (cos x)))
3.0ms	(- x (sin x))

series188.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
19.0ms	(/ (sin x) (cos x))
55.0ms	(- x (/ (sin x) (cos x)))
33.0ms	(- x (sin x))

simplify46.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (35.0ms)

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

prune271.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
15.3b	(- (* 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))

series113.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* 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

prune141.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes25.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.8b

bsearch82.0ms

Steps

Iters	Range		Point
9	0.004380743253548005	488.5072251079851	0.031971504814548905
9	-3.9934486818618	-6.3299436832828755e-06	-0.030514642582300338

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	21
1	31	21

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.5s	1558×	body	2560	valid
1.8s	2693×	body	1280	valid
637.0ms	1933×	body	640	valid
208.0ms	948×	body	320	valid
87.0ms	513×	body	160	valid
32.0ms	355×	body	80	valid