Details

Time bar (total: 5.6s)

sample24.0ms

Algorithm
intervals
Results
5.0ms58×body1280valid
5.0ms284×body80nan
2.0ms136×body80valid
2.0ms38×body640valid
1.0ms14×body320valid
0.0ms10×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite25.0ms

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:
25.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series72.0ms

Counts
1 → 3
Calls
1 calls:
72.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify48.0ms

Algorithm
egg-herbie
Counts
22 → 22
Iterations

Useful iterations: 3 (45.0ms)

IterNodesCost
0132175
1400159
21559153
35001149

prune41.0ms

Pruning

2 alts after pruning (2 fresh and 0 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)))

rewrite47.0ms

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))
28.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series209.0ms

Counts
2 → 6
Calls
2 calls:
65.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
144.0ms
(/ 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

prune113.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

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)))))

rewrite231.0ms

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:
26.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
26.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
24.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
139.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series821.0ms

Counts
4 → 12
Calls
4 calls:
356.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
147.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
148.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
169.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify107.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
06472845
131522529
250022489

prune526.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.3b
(* (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.3b
(* (sqrt (* (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite485.0ms

Algorithm
rewrite-expression-head
Rules
884×sqrt-prod
683×*-un-lft-identity
517×times-frac
435×add-sqr-sqrt
244×distribute-lft-out
240×add-cube-cbrt
127×swap-sqr
87×associate-*r*
64×associate-*l*
31×unswap-sqr
22×add-exp-log sqrt-div add-cbrt-cube
18×pow1 associate-/r*
14×associate-/r/
12×associate-/l*
7×flip3-+ flip-+ div-inv
6×cbrt-undiv frac-times sqrt-undiv div-exp pow-prod-down associate-*l/
5×prod-exp cbrt-unprod
4×sqrt-pow1 associate-*r/ add-log-exp
2×frac-2neg pow1/2 sqrt-unprod clear-num *-commutative
1×pow2 pow-plus rem-square-sqrt pow-sqr pow-prod-up
Counts
4 → 525
Calls
4 calls:
27.0ms
(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
27.0ms
(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
173.0ms
(* (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
211.0ms
(* (sqrt (* (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
368.0ms
(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
366.0ms
(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
179.0ms
(* (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
182.0ms
(* (sqrt (* (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify108.0ms

Algorithm
egg-herbie
Counts
537 → 537
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
0116610721
150028969

prune904.0ms

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 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
095
195

end0.0ms

sample649.0ms

Algorithm
intervals
Results
144.0ms1716×body1280valid
136.0ms8040×body80nan
87.0ms1282×body640valid
77.0ms4104×body80valid
27.0ms573×body320valid
11.0ms325×body160valid