Details

Time bar (total: 3.9s)

sample25.0ms

Algorithm
intervals
Results
5.0ms55×body1280valid
4.0ms259×body80nan
3.0ms42×body640valid
3.0ms141×body80valid
1.0ms13×body320valid
0.0ms5×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: 27.8b

localize5.0ms

Local error

Found 1 expressions with local error:

1.6b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity sqrt-prod
4×difference-of-squares
3×distribute-lft-out-- add-log-exp
1×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log add-cbrt-cube flip-- distribute-lft-out
Counts
1 → 19
Calls
1 calls:
9.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series74.0ms

Counts
1 → 3
Calls
1 calls:
74.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify46.0ms

Algorithm
egg-herbie
Counts
22 → 22
Iterations

Useful iterations: 3 (43.0ms)

IterNodesCost
0132175
1400159
21559153
35001149

prune43.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
20×sqrt-prod distribute-lft-out
18×times-frac
13×add-sqr-sqrt add-cube-cbrt
6×associate-/r*
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/l*
2×pow1 flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 55
Calls
2 calls:
7.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
10.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series215.0ms

Counts
2 → 6
Calls
2 calls:
69.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
146.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify36.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0295535
11077482
25001453

prune126.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

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 (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.2b
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod
74×*-un-lft-identity
32×distribute-lft-out
30×add-sqr-sqrt
28×sqrt-div
21×pow1
16×add-cube-cbrt
15×swap-sqr
14×flip3-+ flip-+
11×add-exp-log add-cbrt-cube
10×sqrt-pow1 pow1/2
9×associate-*r* associate-*l*
8×frac-times associate-/r/
5×pow-prod-up
4×associate-*r/ associate-*l/ add-log-exp unswap-sqr
3×times-frac pow-prod-down pow-sqr associate-/l*
2×cbrt-undiv rem-sqrt-square div-exp prod-exp cbrt-unprod
1×pow2 frac-2neg pow-plus sqrt-unprod clear-num associate-/r* rem-square-sqrt *-commutative div-inv
Counts
4 → 135
Calls
4 calls:
8.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
22.0ms
(/ 1.0 (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
26.0ms
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series558.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
164.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
154.0ms
(/ 1.0 (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
72.0ms
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify77.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
05061612
123061409
250011358

prune308.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
297×*-un-lft-identity
274×sqrt-prod
157×times-frac
119×add-sqr-sqrt
116×distribute-lft-out
88×add-cube-cbrt
41×swap-sqr
27×associate-*r* associate-*l*
20×pow1
14×associate-/r/
12×associate-/r*
10×add-exp-log add-cbrt-cube
9×sqrt-pow1 pow1/2 unswap-sqr
7×flip3-+ flip-+ div-inv
6×associate-/l*
5×sqrt-div pow-prod-up
4×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 → 250
Calls
4 calls:
11.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
10.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
40.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series833.0ms

Counts
4 → 12
Calls
4 calls:
360.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
148.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
149.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
175.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify103.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
06472845
131522529
250022489

prune521.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes42.0ms

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
095
195

end0.0ms

sample687.0ms

Algorithm
intervals
Results
156.0ms1723×body1280valid
138.0ms8043×body80nan
86.0ms1235×body640valid
82.0ms4063×body80valid
35.0ms639×body320valid
12.0ms340×body160valid