Details

sample23.0ms

Algorithm

intervals

Results

4.0ms	55×	body	1280	valid
4.0ms	259×	body	80	nan
3.0ms	42×	body	640	valid
2.0ms	141×	body	80	valid
1.0ms	13×	body	320	valid
0.0ms	5×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 27.8b

localize5.0ms

Local error

Found 1 expressions with local error:

1.6b	(- (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))

series73.0ms

Counts

1 → 3

Calls

1 calls:

73.0ms

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

simplify135.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (126.0ms)

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

prune92.0ms

Pruning

2 alts after pruning (2 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)))

series211.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
143.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify45.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (38.0ms)

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

prune171.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

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))

rewrite22.0ms

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:

10.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))

series357.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
85.0ms	(cbrt (+ x 1.0))
88.0ms	(cbrt (+ x 1.0))
86.0ms	(cbrt (+ x 1.0))

simplify150.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 3 (141.0ms)

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

prune385.0ms

Pruning

11 alts after pruning (9 fresh and 2 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 (sqrt (+ x 1.0)))
0.3b	(cbrt (sqrt (+ x 1.0)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod`
18×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`cbrt-div` `sqrt-prod`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3-+` `pow1/3` `sqrt-div` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`

Counts

4 → 70

Calls

4 calls:

3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))
4.0ms	(cbrt (sqrt (+ x 1.0)))
4.0ms	(cbrt (sqrt (+ x 1.0)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(cbrt (+ x 1.0))
86.0ms	(cbrt (+ x 1.0))
86.0ms	(cbrt (sqrt (+ x 1.0)))
86.0ms	(cbrt (sqrt (+ x 1.0)))

simplify89.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	307	600
1	892	564
2	3151	524
3	5001	510

prune370.0ms

Pruning

11 alts after pruning (8 fresh and 3 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

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	16	6

end0.0ms

sample641.0ms

Algorithm

intervals

Results

141.0ms	1723×	body	1280	valid
130.0ms	8043×	body	80	nan
79.0ms	4063×	body	80	valid
78.0ms	1235×	body	640	valid
30.0ms	639×	body	320	valid
11.0ms	340×	body	160	valid