Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	60×	body	1280	valid
4.0ms	243×	body	80	nan
3.0ms	139×	body	80	valid
2.0ms	36×	body	640	valid
1.0ms	15×	body	320	valid
0.0ms	6×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize6.0ms

Local error

Found 1 expressions with local error:

1.7b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

57×	`sqrt-prod`
50×	`*-un-lft-identity`
42×	`prod-diff`
37×	`add-sqr-sqrt`
29×	`add-cube-cbrt`
8×	`distribute-lft-out`
7×	`fma-neg`
4×	`difference-of-squares`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

1 → 70

Calls

1 calls:

29.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

series70.0ms

Counts

1 → 3

Calls

1 calls:

70.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

simplify139.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (130.0ms)

Iter	Nodes	Cost
0	252	1065
1	759	733
2	4363	623
3	5001	593

prune95.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

74×	`*-un-lft-identity`
32×	`distribute-lft-out`
28×	`sqrt-prod`
24×	`times-frac`
16×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`fma-def`
6×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 75

Calls

2 calls:

22.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
31.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series203.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
137.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify49.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	356	693
1	1446	627
2	5001	586

prune177.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ x 1.0)))
0.1b	(sqrt (sqrt (+ x 1.0)))
0.1b	(fma (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))) (sqrt x))
0.2b	(/ (+ 1.0 0) (fma (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))) (sqrt x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

5.0ms	(sqrt (sqrt (+ x 1.0)))
5.0ms	(sqrt (sqrt (+ x 1.0)))
0.0ms	(fma (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))) (sqrt x))
8.0ms	(/ (+ 1.0 0) (fma (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))) (sqrt x)))

series707.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(sqrt (sqrt (+ x 1.0)))
90.0ms	(sqrt (sqrt (+ x 1.0)))
219.0ms	(fma (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))) (sqrt x))
306.0ms	(/ (+ 1.0 0) (fma (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))) (sqrt x)))

simplify84.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	743	1312
1	3230	1218
2	5003	1183

prune355.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 103

Calls

4 calls:

20.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
2.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt (+ x 1.0))

series380.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
93.0ms	(cbrt (+ x 1.0))
90.0ms	(cbrt (+ x 1.0))
90.0ms	(cbrt (+ x 1.0))

simplify166.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 3 (150.0ms)

Iter	Nodes	Cost
0	321	818
1	1064	769
2	4750	694
3	5001	688

prune377.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes77.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	10
1	16	10
2	16	10

end0.0ms

sample696.0ms

Algorithm

intervals

Results

151.0ms	1762×	body	1280	valid
150.0ms	8106×	body	80	nan
85.0ms	1184×	body	640	valid
83.0ms	4134×	body	80	valid
32.0ms	586×	body	320	valid
12.0ms	334×	body	160	valid