Details

sample9.0ms

Algorithm

intervals

Results

4.0ms

256×

body

valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	3
1	7	3

prune1.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.7b

localize4.0ms

Local error

Found 1 expressions with local error:

17.7b

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

rewrite7.0ms

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` `expm1-log1p-u` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 31

Calls

1 calls:

6.0ms

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

series54.0ms

Counts

1 → 3

Calls

1 calls:

54.0ms

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

simplify57.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	171	215
1	589	196
2	1979	191
3	5002	186

prune72.0ms

Filtered

34 candidates to 29 candidates (85.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
0.0b	(/ x (sqrt (+ (* x x) 1.0)))
17.7b	(sqrt (+ (* x x) 1.0))
17.7b	(sqrt (+ (* x x) 1.0))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

97×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`sqrt-div`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`associate-/r*` `associate-/r/`
5×	`cbrt-undiv` `flip3-+` `flip-+`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `hypot-def`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 168

Calls

4 calls:

24.0ms	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (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))

series264.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
116.0ms	(/ x (sqrt (+ (* x x) 1.0)))
47.0ms	(sqrt (+ (* x x) 1.0))
43.0ms	(sqrt (+ (* x x) 1.0))

simplify79.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	634	1778
1	2978	1575
2	5001	1440

prune335.0ms

Filtered

180 candidates to 125 candidates (69.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ x (sqrt (sqrt (+ (* x x) 1.0))))
17.7b	(sqrt (+ (* x x) 1.0))
17.7b	(sqrt (+ (* x x) 1.0))
17.7b	(sqrt (+ (* x x) 1.0))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
35×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
10×	`sqrt-div`
9×	`associate-/r*`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 109

Calls

4 calls:

8.0ms	(/ x (sqrt (sqrt (+ (* x x) 1.0))))
4.0ms	(sqrt (+ (* x x) 1.0))
4.0ms	(sqrt (+ (* x x) 1.0))
4.0ms	(sqrt (+ (* x x) 1.0))

series392.0ms

Counts

4 → 12

Calls

4 calls:

261.0ms	(/ x (sqrt (sqrt (+ (* x x) 1.0))))
45.0ms	(sqrt (+ (* x x) 1.0))
40.0ms	(sqrt (+ (* x x) 1.0))
45.0ms	(sqrt (+ (* x x) 1.0))

simplify41.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	354	938
1	1230	897
2	5001	881

prune335.0ms

Filtered

121 candidates to 102 candidates (84.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 x) (* 1.0 (/ 1 (pow x 3))))
0.0b	(/ 1 (pow x 5))
0.1b	(/ 1 (pow x 3))
17.9b	(fma 1.0 (/ 1 (pow x 5)) (- (/ 1 x) (* 1.0 (/ 1 (pow x 3)))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
59×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
22×	`add-exp-log`
19×	`associate-/r*`
13×	`fma-neg` `prod-diff`
12×	`cube-prod` `div-exp`
8×	`add-cbrt-cube` `sqr-pow`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `cube-mult` `unpow3` `log1p-expm1-u` `div-inv`
2×	`cbrt-undiv` `pow-flip` `frac-2neg` `clear-num` `frac-sub` `inv-pow`
1×	`sub-neg` `flip3--` `diff-log` `associate-*r/` `un-div-inv` `flip--` `fma-udef`

Counts

4 → 182

Calls

4 calls:

8.0ms	(- (/ 1 x) (* 1.0 (/ 1 (pow x 3))))
5.0ms	(/ 1 (pow x 5))
5.0ms	(/ 1 (pow x 3))
1.0ms	(fma 1.0 (/ 1 (pow x 5)) (- (/ 1 x) (* 1.0 (/ 1 (pow x 3)))))

series190.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (/ 1 x) (* 1.0 (/ 1 (pow x 3))))
42.0ms	(/ 1 (pow x 5))
37.0ms	(/ 1 (pow x 3))
43.0ms	(fma 1.0 (/ 1 (pow x 5)) (- (/ 1 x) (* 1.0 (/ 1 (pow x 3)))))

simplify68.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	469	1124
1	2427	837
2	5001	831

prune296.0ms

Filtered

194 candidates to 91 candidates (46.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes43.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.3b

bsearch55.0ms

Steps

Iters	Range		Point
8	136.14768989527596	4873390.516357292	683.1562417368807
8	-2693.2368339428763	-0.10280128843953673	-743.7438403542988

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	11
1	29	11

end0.0ms

sample214.0ms

Algorithm

intervals

Results

132.0ms

8000×

body

valid