Details

sample16.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
1.0ms	94×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
12×	`times-frac`
6×	`distribute-lft-out`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `associate-/r*` `sqrt-prod`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `flip-+` `log1p-expm1-u` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `hypot-def` `div-inv`

Counts

3 → 71

Calls

3 calls:

4.0ms	(sqrt (+ x 1.0))
8.0ms	(+ 1.0 (sqrt (+ x 1.0)))
17.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series216.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(sqrt (+ x 1.0))
41.0ms	(+ 1.0 (sqrt (+ x 1.0)))
142.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify37.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	334	508
1	1222	457
2	5002	445

prune162.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.1b	(/ (+ 1.0 (sqrt (+ x 1.0))) x)
0.2b	(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
100×	`*-un-lft-identity`
67×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
19×	`associate-/r*`
18×	`distribute-lft-out`
17×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`div-exp`
7×	`associate-/l*`
6×	`pow1` `div-inv` `add-log-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `sqrt-prod` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `flip-+`
2×	`rec-exp` `frac-2neg` `sqrt-div` `1-exp` `clear-num` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `sum-log` `associate-/r/` `hypot-def` `inv-pow`

Counts

4 → 161

Calls

4 calls:

5.0ms	(sqrt (+ x 1.0))
9.0ms	(+ 1.0 (sqrt (+ x 1.0)))
28.0ms	(/ (+ 1.0 (sqrt (+ x 1.0))) x)
22.0ms	(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

series290.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt (+ x 1.0))
40.0ms	(+ 1.0 (sqrt (+ x 1.0)))
82.0ms	(/ (+ 1.0 (sqrt (+ x 1.0))) x)
139.0ms	(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

simplify70.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	615	1449
1	2708	1291
2	5001	1197

prune248.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
0.2b	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
0.2b	(cbrt (+ x 1.0))
0.2b	(cbrt (+ x 1.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
13×	`cbrt-prod`
10×	`associate-r`
9×	`times-frac` `sqrt-prod`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `cbrt-div`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r` `distribute-lft-out` `associate-/l` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 94

Calls

4 calls:

14.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
7.0ms	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
2.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt (+ x 1.0))

series480.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
209.0ms	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
86.0ms	(cbrt (+ x 1.0))
89.0ms	(cbrt (+ x 1.0))

simplify85.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	707	1346
1	3177	1264
2	5001	1230

prune323.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (sqrt (cbrt (+ x 1.0))) (fabs (cbrt (+ x 1.0))) 1.0)
0.2b	(/ x (fma (sqrt (cbrt (+ x 1.0))) (fabs (cbrt (+ x 1.0))) 1.0))
0.2b	(cbrt (+ x 1.0))
0.2b	(cbrt (+ x 1.0))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
14×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`times-frac`
8×	`cbrt-prod`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `cbrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

4 → 71

Calls

4 calls:

0.0ms	(fma (sqrt (cbrt (+ x 1.0))) (fabs (cbrt (+ x 1.0))) 1.0)
2.0ms	(/ x (fma (sqrt (cbrt (+ x 1.0))) (fabs (cbrt (+ x 1.0))) 1.0))
2.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt (+ x 1.0))

series490.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(fma (sqrt (cbrt (+ x 1.0))) (fabs (cbrt (+ x 1.0))) 1.0)
215.0ms	(/ x (fma (sqrt (cbrt (+ x 1.0))) (fabs (cbrt (+ x 1.0))) 1.0))
88.0ms	(cbrt (+ x 1.0))
86.0ms	(cbrt (+ x 1.0))

simplify69.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	610	1092
1	2616	1015
2	5001	999

prune283.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes34.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

end0.0ms

sample315.0ms

Algorithm

intervals

Results

154.0ms	7995×	body	80	valid
43.0ms	2667×	body	80	nan
1.0ms	5×	body	1280	valid