Details

sample9.0ms

Algorithm

intervals

Results

4.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	3
1	6	3

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) 1.0)
15.6b	(/ x (+ (* x x) 1.0))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow1` `flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 40

Calls

2 calls:

4.0ms	(+ (* x x) 1.0)
5.0ms	(/ x (+ (* x x) 1.0))

series89.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(+ (* x x) 1.0)
58.0ms	(/ x (+ (* x x) 1.0))

simplify109.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	194	267
1	717	245
2	3053	242
3	5001	242

prune87.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
0.0b	(/ x (sqrt (+ (* x x) 1.0)))
15.6b	(sqrt (+ (* x x) 1.0))
15.6b	(sqrt (+ (* x x) 1.0))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`add-cube-cbrt` `*-un-lft-identity`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`associate-/r*`
11×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 262

Calls

4 calls:

19.0ms	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
6.0ms	(/ x (sqrt (+ (* x x) 1.0)))
4.0ms	(sqrt (+ (* x x) 1.0))
4.0ms	(sqrt (+ (* x x) 1.0))

series263.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
117.0ms	(/ x (sqrt (+ (* x x) 1.0)))
46.0ms	(sqrt (+ (* x x) 1.0))
42.0ms	(sqrt (+ (* x x) 1.0))

simplify84.0ms

Algorithm

egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	774	3878
1	2962	3482
2	5001	3411

prune419.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) 1.0)
0.7b	(/ 1 (+ (* x x) 1.0))
14.8b	(* x (/ 1 (+ (* x x) 1.0)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log`
15×	`associate-r`
10×	`add-cbrt-cube`
6×	`pow1`
5×	`add-log-exp`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`flip3-+` `associate-l` `associate-/r` `flip-+` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

3 → 82

Calls

3 calls:

4.0ms	(+ (* x x) 1.0)
6.0ms	(/ 1 (+ (* x x) 1.0))
10.0ms	(* x (/ 1 (+ (* x x) 1.0)))

series135.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* x x) 1.0)
44.0ms	(/ 1 (+ (* x x) 1.0))
60.0ms	(* x (/ 1 (+ (* x x) 1.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	337	527
1	1491	460
2	5001	424

prune133.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (pow x 5))
0.4b	(/ 1.0 (pow x 3))
21.1b	(- (/ 1.0 (pow x 3)) (* 1.0 (/ 1 (pow x 5))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

57×	`times-frac`
44×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
19×	`associate-/r*`
17×	`add-exp-log`
12×	`cube-prod`
9×	`div-exp`
8×	`sqr-pow`
7×	`add-cbrt-cube`
6×	`associate-/l*`
5×	`add-log-exp`
4×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp`
3×	`pow1` `rec-exp` `1-exp` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `clear-num` `frac-sub`
1×	`sub-neg` `flip3--` `pow-flip` `diff-log` `associate-*r/` `un-div-inv` `flip--` `distribute-lft-out--` `inv-pow`

Counts

3 → 133

Calls

3 calls:

5.0ms	(/ 1 (pow x 5))
5.0ms	(/ 1.0 (pow x 3))
13.0ms	(- (/ 1.0 (pow x 3)) (* 1.0 (/ 1 (pow x 5))))

series214.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(/ 1 (pow x 5))
36.0ms	(/ 1.0 (pow x 3))
131.0ms	(- (/ 1.0 (pow x 3)) (* 1.0 (/ 1 (pow x 5))))

simplify58.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	390	702
1	2042	627
2	5002	627

prune227.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes24.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.9b

bsearch57.0ms

Steps

Iters	Range		Point
10	4.9177062248324165e-05	42925490.781275615	764.6675213818143
8	-1816.595590764893	-1.0806682141483241	-1025.287622873

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	16
1	31	16

end0.0ms

sample219.0ms

Algorithm

intervals

Results

138.0ms

8000×

body

valid