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	7	3
1	7	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` `expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 45

Calls

2 calls:

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

series90.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(+ (* x x) 1.0)
58.0ms	(/ x (+ (* x x) 1.0))

simplify116.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (112.0ms)

Iter	Nodes	Cost
0	205	273
1	756	247
2	3230	239
3	5002	237

prune100.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize10.0ms

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))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
166×	`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` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `hypot-def`
1×	`associate-/l/`

Counts

4 → 272

Calls

4 calls:

16.0ms	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
7.0ms	(/ x (sqrt (+ (* x x) 1.0)))
4.0ms	(sqrt (+ (* x x) 1.0))
5.0ms	(sqrt (+ (* x x) 1.0))

series269.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
125.0ms	(/ x (sqrt (+ (* x x) 1.0)))
41.0ms	(sqrt (+ (* x x) 1.0))
48.0ms	(sqrt (+ (* x x) 1.0))

simplify89.0ms

Algorithm

egg-herbie

Counts

284 → 284

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	793	3897
1	3057	3471
2	5001	3383

prune443.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

6.7b	(sqrt (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))
13.4b	(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
15.6b	(sqrt (+ (* x x) 1.0))
20.7b	(/ (hypot (pow 1.0 3/2) (pow x 3)) (sqrt (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
9×	`add-log-exp`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`associate-+r+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log` `associate-/r/` `hypot-def`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `sub-neg` `sqrt-undiv` `hypot-udef` `fma-def` `frac-2neg` `diff-log` `div-exp` `prod-diff` `clear-num` `div-inv`

Counts

4 → 99

Calls

4 calls:

12.0ms	(sqrt (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))
12.0ms	(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
4.0ms	(sqrt (+ (* x x) 1.0))
15.0ms	(/ (hypot (pow 1.0 3/2) (pow x 3)) (sqrt (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))))

series420.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(sqrt (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))
40.0ms	(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
47.0ms	(sqrt (+ (* x x) 1.0))
253.0ms	(/ (hypot (pow 1.0 3/2) (pow x 3)) (sqrt (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	421	1548
1	1558	1415
2	5001	1380

prune431.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (pow x 5))
0.4b	(/ 1 (pow x 3))
20.5b	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

1934×	`times-frac`
1319×	`add-sqr-sqrt`
1235×	`*-un-lft-identity`
1170×	`add-cube-cbrt`
1000×	`prod-diff`
650×	`unpow-prod-down`
251×	`cube-prod`
238×	`sqr-pow`
79×	`cube-mult` `unpow3`
72×	`div-inv`
63×	`difference-of-squares`
25×	`fma-neg`
21×	`add-exp-log`
19×	`associate-/r*`
12×	`div-exp`
7×	`add-cbrt-cube` `distribute-lft-out--`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `pow-flip` `frac-2neg` `clear-num` `inv-pow`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

3 → 1240

Calls

3 calls:

5.0ms	(/ 1 (pow x 5))
6.0ms	(/ 1 (pow x 3))
75.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

series177.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ 1 (pow x 5))
38.0ms	(/ 1 (pow x 3))
96.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

simplify272.0ms

Algorithm

egg-herbie

Counts

1249 → 1249

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	2381	31548
1	5001	18062

prune449.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes20.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 24.2b

bsearch79.0ms

Steps

Iters	Range		Point
10	4.9177062248324165e-05	42925490.781275615	764.6675213818143
9	-234806929230.2476	-1816.595590764893	-14917877722.165144

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	25
1	41	25

end0.0ms

sample228.0ms

Algorithm

intervals

Results

137.0ms

8000×

body

valid