Details

Time bar (total: 5.7s)

sample39.0ms

Algorithm
intervals
Results
9.0ms56×body1280valid
8.0ms245×body80nan
6.0ms49×body640valid
4.0ms111×body80valid
3.0ms28×body320valid
1.0ms12×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize5.0ms

Local error

Found 1 expressions with local error:

3.2b
(- (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))

series6.0ms

Counts
1 → 3
Calls
1 calls:
6.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify45.0ms

Algorithm
egg-herbie
Counts
22 → 22
Iterations

Useful iterations: 3 (42.0ms)

IterNodesCost
0132175
1400159
21559153
35001149

prune94.0ms

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)))

rewrite42.0ms

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:
16.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
23.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series15.0ms

Counts
2 → 6
Calls
2 calls:
5.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
10.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify37.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0295535
11077482
25001453

prune310.0ms

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)))))

rewrite214.0ms

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))))
25.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
23.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
123.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series56.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(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)))
16.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify99.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
06472845
131522529
250022489

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize13.0ms

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

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
190×*-un-lft-identity sqrt-prod
110×times-frac
81×add-sqr-sqrt
71×add-cube-cbrt
68×distribute-lft-out
27×associate-*l*
15×associate-/r*
10×add-exp-log add-cbrt-cube
9×associate-/l*
8×associate-/r/
7×pow1
4×flip3-+ sqrt-div flip-+ div-inv add-log-exp
3×associate-*r* unswap-sqr
2×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num
1×sqrt-undiv sqrt-pow1 pow1/2 pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod
Counts
4 → 206
Calls
4 calls:
26.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
25.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
26.0ms
(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
60.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (fabs (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))

series84.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
10.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
20.0ms
(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
35.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (fabs (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))

simplify90.0ms

Algorithm
egg-herbie
Counts
218 → 218
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
07673172
129912974
250032791

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes76.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0138
1138

end0.0ms

sample1.1s

Algorithm
intervals
Results
280.0ms1752×body1280valid
258.0ms8078×body80nan
166.0ms1322×body640valid
132.0ms3992×body80valid
61.0ms628×body320valid
19.0ms306×body160valid