Details

sample15.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
2.0ms	105×	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: 0.1b

localize5.0ms

Local error

Found 3 expressions with local error:

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

rewrite59.0ms

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:

8.0ms	(sqrt (+ x 1.0))
16.0ms	(+ 1.0 (sqrt (+ x 1.0)))
34.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series203.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(sqrt (+ x 1.0))
39.0ms	(+ 1.0 (sqrt (+ x 1.0)))
135.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify39.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (30.0ms)

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

prune161.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

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 (+ 1.0 (sqrt (+ x 1.0))))
0.1b	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
26×	`times-frac`
24×	`add-cube-cbrt`
18×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`distribute-lft-out`
8×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `div-exp` `prod-exp` `associate-/r*` `sqrt-prod` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`fma-def` `associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `sqrt-div` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `hypot-def` `inv-pow`

Counts

4 → 118

Calls

4 calls:

8.0ms	(sqrt (+ x 1.0))
17.0ms	(+ 1.0 (sqrt (+ x 1.0)))
32.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
72.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

series300.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt (+ x 1.0))
43.0ms	(+ 1.0 (sqrt (+ x 1.0)))
96.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
132.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

simplify54.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	472	857
1	2046	741
2	5002	696

prune220.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.0b	(expm1 (log1p (/ 1 (+ 1.0 (sqrt (+ x 1.0))))))
0.1b	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
0.1b	(* x (expm1 (log1p (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
12×	`times-frac`
10×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`pow1`
6×	`add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`fma-def` `associate-r` `associate-l` `associate-/l*`
2×	`flip3-+` `div-exp` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `expm1-log1p` `pow-flip` `frac-2neg` `1-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `div-inv` `inv-pow` `expm1-udef` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

16.0ms	(+ 1.0 (sqrt (+ x 1.0)))
0.0ms	(expm1 (log1p (/ 1 (+ 1.0 (sqrt (+ x 1.0))))))
33.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
7.0ms	(* x (expm1 (log1p (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ 1.0 (sqrt (+ x 1.0)))
404.0ms	(expm1 (log1p (/ 1 (+ 1.0 (sqrt (+ x 1.0))))))
100.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
922.0ms	(* x (expm1 (log1p (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))))

simplify67.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	484	845
1	2306	724
2	5002	693

prune225.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (sqrt (+ x 1.0)) 3)
0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
4.3b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
8.0b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
62×	`sqrt-div`
43×	`add-sqr-sqrt`
34×	`sqrt-prod`
32×	`flip3-+` `flip-+`
31×	`add-cube-cbrt`
28×	`associate-*r/` `distribute-lft-out`
27×	`times-frac`
23×	`unpow-prod-down` `cube-prod`
21×	`pow1`
16×	`frac-sub`
12×	`frac-times`
11×	`swap-sqr`
9×	`add-exp-log` `sqrt-pow1` `pow1/2` `associate-/r*` `add-cbrt-cube`
8×	`associate-*l/`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `sum-cubes` `log1p-expm1-u` `sub-div` `unswap-sqr`
3×	`pow-unpow` `pow-pow` `pow-prod-down` `pow-sqr` `associate-/l*`
2×	`cube-div` `associate-/r/`
1×	`cbrt-undiv` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `distribute-rgt-out--` `frac-2neg` `pow-plus` `fma-neg` `sqrt-unprod` `diff-log` `unpow3` `div-exp` `prod-diff` `pow-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `sqrt-pow2` `flip--` `cbrt-unprod` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 194

Calls

4 calls:

10.0ms	(pow (sqrt (+ x 1.0)) 3)
39.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
29.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
89.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series332.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(pow (sqrt (+ x 1.0)) 3)
24.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
60.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
189.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify136.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 2 (112.0ms)

Iter	Nodes	Cost
0	825	1791
1	4127	1518
2	5001	1510

prune453.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes38.0ms

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

sample352.0ms

Algorithm

intervals

Results

157.0ms	7996×	body	80	valid
41.0ms	2756×	body	80	nan
0.0ms	4×	body	1280	valid