Details

Time bar (total: 4.2s)

sample23.0ms

Algorithm
intervals
Results
4.0ms56×body1280valid
4.0ms233×body80nan
3.0ms42×body640valid
2.0ms131×body80valid
1.0ms18×body320valid
0.0ms9×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize5.0ms

Local error

Found 1 expressions with local error:

2.2b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite55.0ms

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:
51.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series65.0ms

Counts
1 → 3
Calls
1 calls:
65.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify134.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 3 (126.0ms)

IterNodesCost
02521065
1759733
24363623
35001593

prune85.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
62×*-un-lft-identity
27×distribute-lft-out
24×times-frac
20×sqrt-prod
13×add-sqr-sqrt add-cube-cbrt
6×associate-/r*
4×associate-/l*
3×add-exp-log add-cbrt-cube
2×flip3-+ associate-/r/ flip-+ associate-/l/
1×pow1 cbrt-undiv expm1-log1p-u frac-2neg div-exp clear-num log1p-expm1-u div-inv add-log-exp
Counts
1 → 52
Calls
1 calls:
57.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series130.0ms

Counts
1 → 3
Calls
1 calls:
130.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify42.0ms

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0304558
11271513
25001476

prune101.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite337.0ms

Algorithm
rewrite-expression-head
Rules
1122×*-un-lft-identity
908×sqrt-prod
774×times-frac
460×distribute-lft-out
310×add-sqr-sqrt
292×add-cube-cbrt
46×associate-/l*
28×sqrt-div
24×associate-/r/
18×associate-/r*
15×flip3-+ flip-+
12×div-inv
11×add-exp-log add-cbrt-cube
8×hypot-def
6×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
Counts
4 → 563
Calls
4 calls:
42.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
42.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
59.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
139.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series744.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
152.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
309.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
131.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify162.0ms

Algorithm
egg-herbie
Counts
575 → 575
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
0110711446
145549783
250019783

prune613.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (+ x 1.0)) (sqrt x))
0.4b
(pow (sqrt x) 3/2)
0.5b
(* (sqrt x) (sqrt x))
1.9b
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
32×sqrt-prod
25×pow1
21×*-un-lft-identity
19×add-cube-cbrt
13×associate-*l*
12×associate-*r*
11×sqrt-pow1 pow1/2
9×add-exp-log
8×swap-sqr add-cbrt-cube unswap-sqr
6×unpow-prod-down pow-prod-down add-log-exp
5×pow-prod-up
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow pow-pow pow-sqr
2×sqrt-unprod sqrt-div associate-*l/ prod-exp *-commutative cbrt-unprod
1×pow2 pow-to-exp sub-neg flip3-- distribute-rgt-out-- flip3-+ pow-plus fma-neg diff-log prod-diff pow-exp rem-square-sqrt sqrt-pow2 flip-- flip-+ distribute-lft-out sqr-pow
Counts
4 → 128
Calls
4 calls:
28.0ms
(* (sqrt (+ x 1.0)) (sqrt x))
4.0ms
(pow (sqrt x) 3/2)
13.0ms
(* (sqrt x) (sqrt x))
12.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))

series258.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* (sqrt (+ x 1.0)) (sqrt x))
106.0ms
(pow (sqrt x) 3/2)
14.0ms
(* (sqrt x) (sqrt x))
82.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))

simplify71.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
0467687
12312601
25002588

prune494.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes30.0ms

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)

IterNodesCost
0126
1166
2166

end0.0ms

sample679.0ms

Algorithm
intervals
Results
138.0ms1741×body1280valid
129.0ms8007×body80nan
82.0ms1258×body640valid
71.0ms4058×body80valid
29.0ms638×body320valid
10.0ms305×body160valid