Details

Time bar (total: 4.8s)

sample25.0ms

Algorithm
intervals
Results
5.0ms56×body1280valid
4.0ms245×body80nan
3.0ms49×body640valid
2.0ms111×body80valid
1.0ms28×body320valid
0.0ms12×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: 34.1b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite22.0ms

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))

series70.0ms

Counts
1 → 3
Calls
1 calls:
69.0ms
(- (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

prune42.0ms

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 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite43.0ms

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

series193.0ms

Counts
2 → 6
Calls
2 calls:
63.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
130.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify35.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0295535
11077482
25001453

prune121.0ms

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)))))

rewrite204.0ms

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))))
22.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
22.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
117.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series771.0ms

Counts
4 → 12
Calls
4 calls:
337.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
135.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
135.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
163.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify101.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
06472845
131522529
250022489

prune504.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize15.0ms

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)))) (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
298×sqrt-prod
262×*-un-lft-identity
181×times-frac
154×add-sqr-sqrt
101×add-cube-cbrt
92×distribute-lft-out
60×associate-*r*
27×associate-*l*
15×associate-/r* unswap-sqr
13×add-exp-log add-cbrt-cube
10×associate-/r/
9×associate-/l*
7×pow1 sqrt-div
5×flip3-+ flip-+ div-inv
4×add-log-exp
3×cbrt-undiv sqrt-undiv div-exp
2×rem-sqrt-square frac-2neg prod-exp clear-num cbrt-unprod
1×frac-times sqrt-pow1 pow1/2 sqrt-unprod associate-*r/ swap-sqr pow-prod-down associate-*l/ rem-square-sqrt *-commutative
Counts
4 → 282
Calls
4 calls:
27.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
22.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
25.0ms
(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
134.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

series996.0ms

Counts
4 → 12
Calls
4 calls:
340.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
142.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
341.0ms
(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
172.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify123.0ms

Algorithm
egg-herbie
Counts
294 → 294
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
08454186
139133969
250013783

prune567.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes30.0ms

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

sample686.0ms

Algorithm
intervals
Results
156.0ms1752×body1280valid
141.0ms8078×body80nan
91.0ms1322×body640valid
76.0ms3992×body80valid
32.0ms628×body320valid
10.0ms306×body160valid