Details

sample17.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
5.0ms	99×	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)))
0.1b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite33.0ms

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))
9.0ms	(+ 1.0 (sqrt (+ x 1.0)))
18.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series221.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(sqrt (+ x 1.0))
41.0ms	(+ 1.0 (sqrt (+ x 1.0)))
144.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify39.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (32.0ms)

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

prune162.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.2b	(pow (sqrt (+ x 1.0)) 3)
5.0b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
5.6b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite117.0ms

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:

25.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
6.0ms	(pow (sqrt (+ x 1.0)) 3)
15.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
63.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
69.0ms	(pow (sqrt (+ x 1.0)) 3)
67.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
192.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify140.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 2 (121.0ms)

Iter	Nodes	Cost
0	825	1791
1	4126	1518
2	5001	1510

prune450.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sqrt (+ x 1.0)) 3)
0.3b	(pow (cbrt (sqrt (+ x 1.0))) 4)
5.0b	(- (* (pow (cbrt (sqrt (+ x 1.0))) 4) (cbrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
5.6b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity`
33×	`unpow-prod-down`
27×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
23×	`cube-prod` `distribute-lft-out`
12×	`sqrt-prod`
9×	`associate-/r*`
8×	`add-exp-log` `associate-*r/`
7×	`pow1` `cbrt-prod` `add-cbrt-cube`
6×	`pow-unpow` `flip3-+` `sqrt-div` `flip-+` `add-log-exp`
5×	`pow-pow`
4×	`expm1-log1p-u` `cbrt-div` `sum-cubes` `frac-sub` `log1p-expm1-u`
3×	`associate-/l*`
2×	`cube-div` `pow-to-exp` `pow-exp` `associate-/r/` `sqr-pow`
1×	`cbrt-undiv` `cube-mult` `sub-neg` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `pow1/3` `diff-log` `unpow3` `div-exp` `prod-diff` `clear-num` `sqrt-pow2` `flip--` `div-inv` `rem-cube-cbrt`

Counts

4 → 140

Calls

4 calls:

6.0ms	(pow (sqrt (+ x 1.0)) 3)
6.0ms	(pow (cbrt (sqrt (+ x 1.0))) 4)
16.0ms	(- (* (pow (cbrt (sqrt (+ x 1.0))) 4) (cbrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
63.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series476.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(pow (sqrt (+ x 1.0)) 3)
148.0ms	(pow (cbrt (sqrt (+ x 1.0))) 4)
61.0ms	(- (* (pow (cbrt (sqrt (+ x 1.0))) 4) (cbrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
198.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify96.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	827	1430
1	3357	1285
2	5002	1216

prune457.0ms

Pruning

4 alts after pruning (1 fresh and 3 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))) (sqrt x))
0.1b	(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

360×	`times-frac`
288×	`*-un-lft-identity`
190×	`sqrt-prod`
189×	`add-sqr-sqrt`
186×	`add-cube-cbrt`
51×	`distribute-lft-out`
34×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/l*`
9×	`div-inv`
6×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `flip-+`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log` `associate-/r/` `hypot-def`

Counts

4 → 305

Calls

4 calls:

4.0ms	(sqrt (+ x 1.0))
9.0ms	(+ 1.0 (sqrt (+ x 1.0)))
31.0ms	(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))
27.0ms	(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))

series357.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt (+ x 1.0))
41.0ms	(+ 1.0 (sqrt (+ x 1.0)))
148.0ms	(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))
139.0ms	(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))

simplify122.0ms

Algorithm

egg-herbie

Counts

317 → 317

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	898	4087
1	4302	3656
2	5001	3645

prune421.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes41.0ms

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

sample299.0ms

Algorithm

intervals

Results

153.0ms	7999×	body	80	valid
38.0ms	2642×	body	80	nan
0.0ms	1×	body	1280	valid