Details

Time bar (total: 4.1s)

sample22.0ms

Algorithm
intervals
Results
5.0ms58×body1280valid
4.0ms226×body80nan
3.0ms42×body640valid
2.0ms123×body80valid
1.0ms23×body320valid
0.0ms10×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: 31.7b

localize7.0ms

Local error

Found 1 expressions with local error:

3.0b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite23.0ms

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:
22.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series73.0ms

Counts
1 → 3
Calls
1 calls:
73.0ms
(- (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

prune41.0ms

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

rewrite44.0ms

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:
17.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
25.0ms
(/ 1.0 (+ (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 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify36.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0295535
11077482
25001453

prune117.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

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

rewrite189.0ms

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:
24.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
23.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
31.0ms
(/ 1.0 (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
105.0ms
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series538.0ms

Counts
4 → 12
Calls
4 calls:
164.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
165.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
146.0ms
(/ 1.0 (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
64.0ms
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify71.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
05061618
124281409
250021358

prune300.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (fabs (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(* (* (fabs (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.3b
(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b
(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
32×sqrt-prod
21×associate-*r*
18×cbrt-prod
16×add-sqr-sqrt distribute-lft-out
14×sqrt-div
12×add-cube-cbrt
11×pow1 add-exp-log add-cbrt-cube
10×cbrt-div associate-*r/
9×flip3-+ flip-+
4×frac-times associate-*l* pow-prod-down prod-exp cbrt-unprod add-log-exp
2×pow1/3 associate-*l/ *-commutative unswap-sqr
Counts
4 → 94
Calls
4 calls:
50.0ms
(* (fabs (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
100.0ms
(* (* (fabs (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
12.0ms
(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))
12.0ms
(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))

series1.1s

Counts
4 → 12
Calls
4 calls:
176.0ms
(* (fabs (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
335.0ms
(* (* (fabs (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
298.0ms
(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))
296.0ms
(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify90.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
07302087
132001918
250011896

prune354.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes28.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify5.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
095
195

end0.0ms

sample620.0ms

Algorithm
intervals
Results
136.0ms1746×body1280valid
127.0ms7984×body80nan
82.0ms1276×body640valid
73.0ms4049×body80valid
28.0ms615×body320valid
12.0ms314×body160valid