Details

Time bar (total: 4.4s)

sample24.0ms

Algorithm
intervals
Results
5.0ms276×body80nan
4.0ms51×body1280valid
3.0ms139×body80valid
2.0ms29×body640valid
1.0ms26×body320valid
0.0ms11×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: 27.1b

localize5.0ms

Local error

Found 1 expressions with local error:

3.2b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite31.0ms

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:
27.0ms
(- (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 (123.0ms)

IterNodesCost
02521065
1759733
24363623
35001593

prune91.0ms

Pruning

2 alts after pruning (2 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)))

rewrite54.0ms

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:
21.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
29.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series213.0ms

Counts
2 → 6
Calls
2 calls:
71.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
142.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify46.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0356693
11446627
25001586

prune164.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

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)))
0.1b
(/ (+ 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))))

rewrite227.0ms

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:
24.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
27.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
31.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
84.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series862.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
175.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
361.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
158.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify182.0ms

Algorithm
egg-herbie
Counts
575 → 575
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
0110711444
145519783
250019783

prune636.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.4b
(pow (sqrt x) 3/2)
0.5b
(* (sqrt x) (sqrt x))
2.9b
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt sqrt-prod
37×*-un-lft-identity
36×pow1
23×add-cube-cbrt
19×swap-sqr
17×sqrt-pow1 pow1/2
13×associate-*r* associate-*l*
12×sqrt-div
10×pow-prod-up
9×add-exp-log
8×add-cbrt-cube unswap-sqr
6×unpow-prod-down flip3-+ pow-prod-down pow-sqr flip-+ distribute-lft-out add-log-exp
4×expm1-log1p-u frac-times log1p-expm1-u
3×pow-unpow pow-pow
2×pow2 pow-plus sqrt-unprod associate-*r/ associate-*l/ prod-exp rem-square-sqrt *-commutative cbrt-unprod
1×pow-to-exp sub-neg flip3-- distribute-rgt-out-- fma-neg diff-log prod-diff pow-exp sqrt-pow2 flip-- sqr-pow
Counts
4 → 157
Calls
4 calls:
25.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
2.0ms
(pow (sqrt x) 3/2)
7.0ms
(* (sqrt x) (sqrt x))
5.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))

series258.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
121.0ms
(pow (sqrt x) 3/2)
16.0ms
(* (sqrt x) (sqrt x))
96.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))

simplify84.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
0503743
12458632
25002611

prune489.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes33.0ms

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

sample668.0ms

Algorithm
intervals
Results
152.0ms1797×body1280valid
136.0ms7781×body80nan
87.0ms1283×body640valid
73.0ms3999×body80valid
33.0ms621×body320valid
10.0ms300×body160valid