Details

sample15.0ms

Algorithm

intervals

Results

10.0ms

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: 13.8b

localize4.0ms

Local error

Found 1 expressions with local error:

13.8b

(/ 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))

series60.0ms

Counts

1 → 3

Calls

1 calls:

60.0ms

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

simplify55.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (51.0ms)

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

prune68.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ 1 (fma x x 1.0))
13.6b	(* x (/ 1 (fma x x 1.0)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`times-frac`
19×	`*-un-lft-identity`
18×	`add-cube-cbrt`
15×	`add-exp-log`
13×	`associate-r`
9×	`add-cbrt-cube`
5×	`pow1`
4×	`div-exp` `prod-exp`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `expm1-log1p-u` `rec-exp` `1-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

2 → 71

Calls

2 calls:

2.0ms	(/ 1 (fma x x 1.0))
8.0ms	(* x (/ 1 (fma x x 1.0)))

series118.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ 1 (fma x x 1.0))
67.0ms	(* x (/ 1 (fma x x 1.0)))

simplify40.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	278	377
1	1193	340
2	5001	314

prune125.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

6.5b	(* (/ 1 (* (cbrt (+ (* x x) 1.0)) (cbrt (+ (* x x) 1.0)))) (/ x (cbrt (+ (* x x) 1.0))))
14.3b	(cbrt (+ (* x x) 1.0))
14.3b	(cbrt (+ (* x x) 1.0))
14.3b	(cbrt (+ (* x x) 1.0))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
43×	`add-sqr-sqrt`
33×	`times-frac`
25×	`*-un-lft-identity`
24×	`associate-r`
22×	`add-cube-cbrt`
21×	`cbrt-prod`
20×	`cbrt-div` `prod-exp`
18×	`add-cbrt-cube`
15×	`div-exp` `associate-l`
10×	`flip3-+` `associate-/r/` `flip-+`
9×	`unswap-sqr`
8×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`pow1`
5×	`frac-times`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-r/` `associate-l/`
2×	`div-inv`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 127

Calls

4 calls:

86.0ms	(* (/ 1 (* (cbrt (+ (* x x) 1.0)) (cbrt (+ (* x x) 1.0)))) (/ x (cbrt (+ (* x x) 1.0))))
2.0ms	(cbrt (+ (* x x) 1.0))
2.0ms	(cbrt (+ (* x x) 1.0))
3.0ms	(cbrt (+ (* x x) 1.0))

series570.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (/ 1 (* (cbrt (+ (* x x) 1.0)) (cbrt (+ (* x x) 1.0)))) (/ x (cbrt (+ (* x x) 1.0))))
170.0ms	(cbrt (+ (* x x) 1.0))
169.0ms	(cbrt (+ (* x x) 1.0))
169.0ms	(cbrt (+ (* x x) 1.0))

simplify82.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	678	1745
1	3125	1508
2	5002	1367

prune316.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 x) (* 1.0 (/ 1 (pow x 3))))
0.2b	(/ 1 (pow x 5))
0.3b	(/ 1 (pow x 3))
20.7b	(fma 1.0 (/ 1 (pow x 5)) (- (/ 1 x) (* 1.0 (/ 1 (pow x 3)))))

rewrite31.0ms

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:

17.0ms	(- (/ 1 x) (* 1.0 (/ 1 (pow x 3))))
4.0ms	(/ 1 (pow x 5))
5.0ms	(/ 1 (pow x 3))
0.0ms	(fma 1.0 (/ 1 (pow x 5)) (- (/ 1 x) (* 1.0 (/ 1 (pow x 3)))))

series186.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (/ 1 x) (* 1.0 (/ 1 (pow x 3))))
41.0ms	(/ 1 (pow x 5))
35.0ms	(/ 1 (pow x 3))
42.0ms	(fma 1.0 (/ 1 (pow x 5)) (- (/ 1 x) (* 1.0 (/ 1 (pow x 3)))))

simplify67.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (54.0ms)

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

prune295.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes25.0ms

Accuracy

99.9% (0.0b remaining)

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

bsearch53.0ms

Steps

Iters	Range		Point
9	22857.716182190634	7734910176.923709	23741.194574337824
5	-1.3137402406912225e+25	-5.426770360209421e+24	-1.033538641236291e+25

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	11
1	29	11

end0.0ms

sample400.0ms

Algorithm

intervals

Results

309.0ms

8000×

body

valid