Details

Time bar (total: 5.1s)

sample24.0ms

Algorithm
intervals
Results
5.0ms284×body80nan
5.0ms58×body1280valid
2.0ms136×body80valid
2.0ms38×body640valid
1.0ms14×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: 29.0b

localize5.0ms

Local error

Found 1 expressions with local error:

2.9b
(- (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))

series73.0ms

Counts
1 → 3
Calls
1 calls:
73.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify47.0ms

Algorithm
egg-herbie
Counts
22 → 22
Iterations

Useful iterations: 3 (44.0ms)

IterNodesCost
0132175
1400159
21559153
35001149

prune42.0ms

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)))

rewrite45.0ms

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:
19.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
24.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series207.0ms

Counts
2 → 6
Calls
2 calls:
67.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
140.0ms
(/ 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

localize11.0ms

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)))))

rewrite218.0ms

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))))
24.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
26.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
124.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series825.0ms

Counts
4 → 12
Calls
4 calls:
367.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
149.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
139.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
170.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify113.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
06472845
131522529
250022489

prune525.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.3b
(* (sqrt (* (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.3b
(* (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite390.0ms

Algorithm
rewrite-expression-head
Rules
210×*-un-lft-identity
192×sqrt-prod
150×times-frac
138×add-sqr-sqrt
84×add-cube-cbrt
68×distribute-lft-out
60×associate-*r*
37×associate-*l*
34×add-exp-log
22×add-cbrt-cube
18×sqrt-div associate-/r* unswap-sqr
15×pow1
11×div-exp
10×associate-/r/
9×prod-exp
6×cbrt-undiv frac-times pow-prod-down associate-*l/ associate-/l*
5×sqrt-pow1 flip3-+ cbrt-unprod flip-+ div-inv
4×associate-*r/ add-log-exp
3×rec-exp pow-flip pow1/2 1-exp
2×frac-2neg clear-num *-commutative
1×sqrt-unprod swap-sqr inv-pow
Counts
4 → 274
Calls
4 calls:
25.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
28.0ms
(/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
190.0ms
(* (sqrt (* (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))
133.0ms
(* (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

series957.0ms

Counts
4 → 12
Calls
4 calls:
351.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
273.0ms
(/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
180.0ms
(* (sqrt (* (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))
153.0ms
(* (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify69.0ms

Algorithm
egg-herbie
Counts
286 → 286
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
010424506
150013699

prune646.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes26.0ms

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

sample656.0ms

Algorithm
intervals
Results
147.0ms1716×body1280valid
144.0ms8040×body80nan
83.0ms1282×body640valid
76.0ms4104×body80valid
28.0ms573×body320valid
11.0ms325×body160valid