Details

sample24.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
3.0ms	82×	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	(+ 1.0 (sqrt (+ x 1.0)))
0.0b	(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:

10.0ms	(+ 1.0 (sqrt (+ x 1.0)))
4.0ms	(sqrt (+ x 1.0))
16.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series209.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(+ 1.0 (sqrt (+ x 1.0)))
33.0ms	(sqrt (+ x 1.0))
135.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify37.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (30.0ms)

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

prune159.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ 1 (* (cbrt (+ 1.0 (sqrt (+ x 1.0)))) (cbrt (+ 1.0 (sqrt (+ x 1.0))))))
0.8b	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
0.8b	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
0.8b	(cbrt (+ 1.0 (sqrt (+ x 1.0))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
15×	`add-exp-log` `*-un-lft-identity`
12×	`pow1` `cbrt-prod`
9×	`add-sqr-sqrt` `add-cube-cbrt` `pow-flip` `flip3-+` `pow1/3` `flip-+`
8×	`associate-/r/`
7×	`add-cbrt-cube`
4×	`expm1-log1p-u` `frac-times` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `prod-exp` `distribute-lft-out` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `1-exp` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-2neg` `pow-plus` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv` `inv-pow`

Counts

4 → 93

Calls

4 calls:

37.0ms	(/ 1 (* (cbrt (+ 1.0 (sqrt (+ x 1.0)))) (cbrt (+ 1.0 (sqrt (+ x 1.0))))))
7.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
8.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
8.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))

series1.7s

Counts

4 → 12

Calls

4 calls:

1.0s	(/ 1 (* (cbrt (+ 1.0 (sqrt (+ x 1.0)))) (cbrt (+ 1.0 (sqrt (+ x 1.0))))))
244.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
237.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
236.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))

simplify79.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	622	1254
1	2509	1128
2	5002	1090

prune263.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.2b	(pow (sqrt (+ x 1.0)) 3)
5.8b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.3b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite104.0ms

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:

20.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
5.0ms	(pow (sqrt (+ x 1.0)) 3)
13.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
55.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
62.0ms	(pow (sqrt (+ x 1.0)) 3)
66.0ms	(- (* (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)))

simplify134.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 2 (115.0ms)

Iter	Nodes	Cost
0	825	1791
1	4130	1518
2	5001	1510

prune442.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
0.2b	(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
6.4b	(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
70×	`cbrt-prod`
51×	`times-frac`
48×	`add-sqr-sqrt`
45×	`add-cube-cbrt`
24×	`unpow-prod-down` `cube-prod`
17×	`associate-/r*`
13×	`distribute-lft-out`
7×	`add-exp-log`
6×	`pow1` `cube-div` `cube-mult` `unpow3` `add-cbrt-cube` `sqr-pow`
4×	`expm1-log1p-u` `cbrt-div` `flip3-+` `sqrt-prod` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `pow1/3` `div-exp` `pow-exp` `clear-num` `rem-cbrt-cube` `hypot-def` `div-inv` `rem-cube-cbrt`

Counts

4 → 162

Calls

4 calls:

4.0ms	(sqrt (+ x 1.0))
15.0ms	(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
36.0ms	(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
16.0ms	(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

series335.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt (+ x 1.0))
123.0ms	(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
142.0ms	(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
41.0ms	(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

simplify65.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	550	1479
1	2249	1341
2	5001	1311

prune270.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes24.0ms

Accuracy

99.5% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 1.9b

bsearch31.0ms

Steps

Iters	Range		Point
6	3.9715340067303715	33.11368705657117	5.562868238198095

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	26
1	29	26

end0.0ms

sample670.0ms

Algorithm

intervals

Results

430.0ms	7997×	body	80	valid
109.0ms	2688×	body	80	nan
1.0ms	3×	body	1280	valid