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: 16.2b

localize6.0ms

Local error

Found 1 expressions with local error:

16.2b

(/ x (+ (* x x) 1.0))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 29

Calls

1 calls:

5.0ms

(/ x (+ (* x x) 1.0))

series56.0ms

Counts

1 → 3

Calls

1 calls:

56.0ms

(/ x (+ (* x x) 1.0))

simplify53.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	165	210
1	555	195
2	1839	192
3	5001	192

prune64.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize6.0ms

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)))
16.1b	(sqrt (+ (* x x) 1.0))
16.1b	(sqrt (+ (* x x) 1.0))

rewrite43.0ms

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:

15.0ms	(/ (/ 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))

series276.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
125.0ms	(/ x (sqrt (+ (* x x) 1.0)))
43.0ms	(sqrt (+ (* x x) 1.0))
48.0ms	(sqrt (+ (* x x) 1.0))

simplify79.0ms

Algorithm

egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 2 (48.0ms)

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

prune408.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

7.3b	(* (/ x (fabs (cbrt (+ (* x x) 1.0)))) (/ (/ 1 (sqrt (+ (* x x) 1.0))) (sqrt (cbrt (+ (* x x) 1.0)))))
16.1b	(sqrt (+ (* x x) 1.0))
16.6b	(cbrt (+ (* x x) 1.0))
16.6b	(cbrt (+ (* x x) 1.0))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

457×	`times-frac`
327×	`add-sqr-sqrt`
260×	`sqrt-prod`
222×	`associate-r`
216×	`*-un-lft-identity`
204×	`add-cube-cbrt`
88×	`cbrt-prod`
39×	`add-exp-log`
32×	`unswap-sqr`
25×	`add-cbrt-cube`
22×	`sqrt-div`
20×	`associate-/r/`
17×	`div-exp`
13×	`flip3-+` `associate-l` `flip-+`
11×	`div-inv`
10×	`prod-exp`
9×	`cbrt-undiv`
7×	`pow1`
6×	`cbrt-div` `cbrt-unprod`
4×	`add-log-exp`
2×	`rec-exp` `pow1/3` `1-exp`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 336

Calls

4 calls:

81.0ms	(* (/ x (fabs (cbrt (+ (* x x) 1.0)))) (/ (/ 1 (sqrt (+ (* x x) 1.0))) (sqrt (cbrt (+ (* x x) 1.0)))))
4.0ms	(sqrt (+ (* x x) 1.0))
4.0ms	(cbrt (+ (* x x) 1.0))
4.0ms	(cbrt (+ (* x x) 1.0))

series669.0ms

Counts

4 → 12

Calls

4 calls:

274.0ms	(* (/ x (fabs (cbrt (+ (* x x) 1.0)))) (/ (/ 1 (sqrt (+ (* x x) 1.0))) (sqrt (cbrt (+ (* x x) 1.0)))))
48.0ms	(sqrt (+ (* x x) 1.0))
173.0ms	(cbrt (+ (* x x) 1.0))
174.0ms	(cbrt (+ (* x x) 1.0))

simplify83.0ms

Algorithm

egg-herbie

Counts

348 → 348

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1982	6232
1	5002	5862

prune830.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

2.0b	(/ x (+ (- (* 1.0 1.0)) (pow x 4)))
21.9b	(* (/ x (+ (- (* 1.0 1.0)) (pow x 4))) (- (* x x) 1.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`times-frac`
20×	`add-cube-cbrt`
18×	`associate-l`
9×	`add-exp-log` `add-cbrt-cube`
7×	`distribute-lft-out`
4×	`pow1` `associate-r` `associate-/r*` `associate-/r/`
3×	`associate-/l*`
2×	`cbrt-undiv` `distribute-rgt-in` `frac-times` `sub-neg` `flip3--` `distribute-lft-in` `flip3-+` `associate-*r/` `div-exp` `prod-exp` `flip--` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `difference-of-squares`

Counts

2 → 79

Calls

2 calls:

7.0ms	(/ x (+ (- (* 1.0 1.0)) (pow x 4)))
14.0ms	(* (/ x (+ (- (* 1.0 1.0)) (pow x 4))) (- (* x x) 1.0))

series242.0ms

Counts

2 → 6

Calls

2 calls:

130.0ms	(/ x (+ (- (* 1.0 1.0)) (pow x 4)))
112.0ms	(* (/ x (+ (- (* 1.0 1.0)) (pow x 4))) (- (* x x) 1.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	427	860
1	1887	778
2	5003	745

prune180.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes27.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.8b

bsearch57.0ms

Steps

Iters	Range		Point
6	145.42571904303156	1078.5849367128544	460.75784523236763
9	-4696503048995838.0	-66949431.36780037	-159825393.0444623

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	17
1	42	17

end0.0ms

sample218.0ms

Algorithm

intervals

Results

137.0ms

8000×

body

valid