Details

sample23.0ms

Algorithm

intervals

Results

4.0ms	49×	body	1280	valid
4.0ms	233×	body	80	nan
2.0ms	130×	body	80	valid
2.0ms	37×	body	640	valid
1.0ms	23×	body	320	valid
1.0ms	17×	body	160	valid

simplify5.0ms

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: 29.5b

localize5.0ms

Local error

Found 1 expressions with local error:

3.7b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite13.0ms

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:

9.0ms

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

series72.0ms

Counts

1 → 3

Calls

1 calls:

72.0ms

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

simplify130.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (122.0ms)

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

prune92.0ms

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

rewrite23.0ms

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:

8.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series207.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
140.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (37.0ms)

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

prune169.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.0b	(log1p (expm1 (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.5b	(expm1 (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

8.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
1.0ms	(log1p (expm1 (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
13.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.0ms	(expm1 (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.0s

Counts

4 → 12

Calls

4 calls:

71.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
510.0ms	(log1p (expm1 (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
145.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
309.0ms	(expm1 (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify63.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	542	1045
1	2186	929
2	5002	899

prune293.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.5b	(expm1 (/ (+ 1.0 0) (fma (sqrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (sqrt (cbrt (+ x 1.0))) (sqrt x))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
5×	`log1p-expm1-u`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`expm1-log1p` `expm1-udef`

Counts

4 → 59

Calls

4 calls:

3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))
1.0ms	(expm1 (/ (+ 1.0 0) (fma (sqrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (sqrt (cbrt (+ x 1.0))) (sqrt x))))

series1.0s

Counts

4 → 12

Calls

4 calls:

85.0ms	(cbrt (+ x 1.0))
287.0ms	(cbrt (+ x 1.0))
92.0ms	(cbrt (+ x 1.0))
539.0ms	(expm1 (/ (+ 1.0 0) (fma (sqrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (sqrt (cbrt (+ x 1.0))) (sqrt x))))

simplify77.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	708	1236
1	3125	1158
2	5001	1149

prune326.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes38.0ms

Accuracy

0% (0.1b 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 (1.0ms)

Iter	Nodes	Cost
0	14	8
1	18	8
2	18	8

end0.0ms

sample643.0ms

Algorithm

intervals

Results

142.0ms	8115×	body	80	nan
139.0ms	1696×	body	1280	valid
77.0ms	1203×	body	640	valid
74.0ms	4149×	body	80	valid
29.0ms	607×	body	320	valid
12.0ms	345×	body	160	valid