Details

sample26.0ms

Algorithm

intervals

Results

6.0ms	58×	body	1280	valid
5.0ms	284×	body	80	nan
3.0ms	136×	body	80	valid
2.0ms	38×	body	640	valid
1.0ms	14×	body	320	valid
0.0ms	10×	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: 29.0b

localize8.0ms

Local error

Found 1 expressions with local error:

2.9b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite33.0ms

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:

30.0ms

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

series74.0ms

Counts

1 → 3

Calls

1 calls:

73.0ms

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

simplify133.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (124.0ms)

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

prune93.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

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)))

rewrite55.0ms

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:

20.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
31.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series216.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
146.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify46.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (37.0ms)

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

prune164.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (sqrt x) (sqrt (+ x 1.0)))
0.1b	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity`
31×	`distribute-lft-out`
27×	`sqrt-prod`
24×	`times-frac`
16×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`fma-def` `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 → 74

Calls

2 calls:

12.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
31.0ms	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

series209.0ms

Counts

2 → 6

Calls

2 calls:

69.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
140.0ms	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

simplify44.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	356	694
1	1445	627
2	5002	587

prune161.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0)))))
0.1b	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))
0.1b	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt (/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))))

rewrite252.0ms

Algorithm

rewrite-expression-head

Rules

597×	`*-un-lft-identity`
420×	`sqrt-prod`
256×	`distribute-lft-out`
247×	`times-frac`
130×	`add-sqr-sqrt`
99×	`add-cube-cbrt`
71×	`swap-sqr`
33×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `unswap-sqr`
8×	`associate-/l*`
7×	`div-inv`
5×	`sqrt-div` `pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 324

Calls

4 calls:

30.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0)))))
28.0ms	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))
28.0ms	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))
141.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))))

series819.0ms

Counts

4 → 12

Calls

4 calls:

358.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0)))))
140.0ms	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))
146.0ms	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))
174.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))))

simplify129.0ms

Algorithm

egg-herbie

Counts

336 → 336

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	723	3900
1	3735	3364
2	5002	3360

prune585.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes27.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b 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

sample647.0ms

Algorithm

intervals

Results

141.0ms	1716×	body	1280	valid
135.0ms	8040×	body	80	nan
80.0ms	1282×	body	640	valid
77.0ms	4104×	body	80	valid
27.0ms	573×	body	320	valid
13.0ms	325×	body	160	valid