Details

sample14.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
2.0ms	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

localize9.0ms

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))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`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×	`flip3-+` `flip-+` `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` `div-inv`

Counts

3 → 61

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))))

series222.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(sqrt (+ x 1.0))
43.0ms	(+ 1.0 (sqrt (+ x 1.0)))
143.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify37.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	317	483
1	1159	435
2	5001	427

prune135.0ms

Pruning

3 alts after pruning (3 fresh and 0 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)))

rewrite110.0ms

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×	`sum-cubes` `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` `sqrt-unprod` `diff-log` `unpow3` `div-exp` `pow-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `sqrt-pow2` `flip--` `cbrt-unprod` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 184

Calls

4 calls:

21.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
7.0ms	(pow (sqrt (+ x 1.0)) 3)
14.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
57.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
71.0ms	(pow (sqrt (+ x 1.0)) 3)
67.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
195.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify133.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (114.0ms)

Iter	Nodes	Cost
0	771	1703
1	3873	1474
2	5002	1459

prune405.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize24.0ms

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)))

rewrite89.0ms

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×	`cbrt-div` `sum-cubes` `frac-sub`
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` `pow1/3` `diff-log` `unpow3` `div-exp` `clear-num` `sqrt-pow2` `flip--` `div-inv` `rem-cube-cbrt`

Counts

4 → 130

Calls

4 calls:

5.0ms	(pow (sqrt (+ x 1.0)) 3)
6.0ms	(pow (cbrt (sqrt (+ x 1.0))) 4)
15.0ms	(- (* (pow (cbrt (sqrt (+ x 1.0))) 4) (cbrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
58.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(pow (sqrt (+ x 1.0)) 3)
151.0ms	(pow (cbrt (sqrt (+ x 1.0))) 4)
70.0ms	(- (* (pow (cbrt (sqrt (+ x 1.0))) 4) (cbrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
195.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify97.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	788	1355
1	3158	1218
2	5001	1181

prune431.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
52×	`times-frac`
39×	`add-cube-cbrt` `sqrt-prod`
30×	`associate-r`
15×	`distribute-lft-out`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-l` `associate-/l*` `add-log-exp` `unswap-sqr`
4×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

4 → 132

Calls

4 calls:

4.0ms	(sqrt (+ x 1.0))
20.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
8.0ms	(+ 1.0 (sqrt (+ x 1.0)))
46.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series519.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (+ x 1.0))
304.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
48.0ms	(+ 1.0 (sqrt (+ x 1.0)))
136.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	529	1281
1	2243	1134
2	5001	1107

prune258.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes21.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 7.1b

bsearch26.0ms

Steps

Iters	Range		Point
6	4.358640797965703e-14	5.860557618502762e-13	2.735909407601672e-13

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	25
1	29	25

end0.0ms

sample321.0ms

Algorithm

intervals

Results

166.0ms	7999×	body	80	valid
42.0ms	2642×	body	80	nan
0.0ms	1×	body	1280	valid