Details

Time bar (total: 5.1s)

sample30.0ms

Algorithm
intervals
Results
6.0ms64×body640valid
5.0ms252×body80nan
5.0ms41×body1280valid
3.0ms132×body80valid
1.0ms13×body320valid
0.0ms6×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0116
1146
2146

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.4b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
1.2b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
75×*-un-lft-identity
73×add-sqr-sqrt
69×times-frac
50×sqrt-prod
42×add-cube-cbrt
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
8×add-exp-log add-cbrt-cube distribute-lft-out
6×associate-/l* add-log-exp
5×pow1
4×sqrt-div div-inv
2×cbrt-undiv frac-2neg flip3-+ div-exp clear-num associate-/r/ flip-+
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 pow1/2 diff-log frac-sub flip--
Counts
4 → 133
Calls
4 calls:
3.0ms
(sqrt (+ x 1.0))
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
4.0ms
(/ 1.0 (sqrt x))
34.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series278.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(sqrt (+ x 1.0))
76.0ms
(/ 1.0 (sqrt (+ x 1.0)))
38.0ms
(/ 1.0 (sqrt x))
135.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify50.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04431097
114341038
25001992

prune314.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
1.2b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
2.5b
(exp (log (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
109×add-sqr-sqrt
103×*-un-lft-identity
99×times-frac
64×sqrt-prod
49×add-cube-cbrt
23×log-prod exp-sum
22×distribute-lft-out--
18×difference-of-squares
13×associate-/r*
10×distribute-lft-out
8×add-exp-log add-cbrt-cube
6×div-inv associate-/l* add-log-exp
5×pow1
4×exp-prod
3×log-div exp-diff
2×cbrt-undiv flip3-- frac-2neg sqrt-div div-exp clear-num associate-/r/ frac-sub flip--
1×sub-neg flip3-+ diff-log log-pow flip-+ rem-exp-log
Counts
4 → 155
Calls
4 calls:
9.0ms
(/ 1.0 (sqrt (+ x 1.0)))
4.0ms
(/ 1.0 (sqrt x))
30.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
35.0ms
(exp (log (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))))

series381.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(/ 1.0 (sqrt (+ x 1.0)))
39.0ms
(/ 1.0 (sqrt x))
134.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
133.0ms
(exp (log (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))))

simplify56.0ms

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04981515
114831440
250011366

prune389.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 16.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
1.2b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
2.7b
(pow E (log (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
110×add-sqr-sqrt
104×*-un-lft-identity
99×times-frac
64×sqrt-prod
50×add-cube-cbrt
23×unpow-prod-up log-prod
22×distribute-lft-out--
18×difference-of-squares
13×associate-/r*
10×distribute-lft-out
9×add-exp-log
8×add-cbrt-cube
6×pow1 div-inv associate-/l* add-log-exp
4×pow-unpow
3×unpow-prod-down log-div pow-sub
2×cbrt-undiv flip3-- frac-2neg sqrt-div div-exp pow-exp clear-num associate-/r/ frac-sub flip--
1×pow-to-exp sub-neg e-exp-1 pow-pow flip3-+ diff-log log-pow flip-+ sqr-pow
Counts
4 → 162
Calls
4 calls:
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
4.0ms
(/ 1.0 (sqrt x))
29.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
35.0ms
(pow E (log (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))))

series773.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(/ 1.0 (sqrt (+ x 1.0)))
37.0ms
(/ 1.0 (sqrt x))
136.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
522.0ms
(pow E (log (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))))

simplify70.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
08031825
127801714
250011698

prune474.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 16.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt x) (sqrt (+ x 1.0)))
1.2b
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
5.8b
(pow E (log (* (sqrt x) (sqrt (+ x 1.0)))))
6.3b
(log (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
15×pow1
13×*-un-lft-identity
11×add-cube-cbrt sqrt-prod
8×add-exp-log
7×pow-unpow associate-*r*
6×associate-*l* pow-prod-down add-cbrt-cube add-log-exp
5×log-pow
4×log-div log-prod sqrt-pow1 pow1/2 sqrt-div associate-*r/ unswap-sqr
3×unpow-prod-down
2×flip3-- flip3-+ pow-exp flip-- flip-+ pow-sub
1×unpow-prod-up pow-to-exp sub-neg e-exp-1 pow-pow sqrt-unprod diff-log rem-log-exp prod-exp *-commutative cbrt-unprod distribute-lft-out sqr-pow
Counts
4 → 84
Calls
4 calls:
8.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
7.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
8.0ms
(pow E (log (* (sqrt x) (sqrt (+ x 1.0)))))
7.0ms
(log (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))

series542.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
101.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
154.0ms
(pow E (log (* (sqrt x) (sqrt (+ x 1.0)))))
225.0ms
(log (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))

simplify58.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0551842
12118761
25001758

prune320.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 15.7b

regimes173.0ms

Accuracy

84% (0.5b remaining)

Error of 18.7b against oracle of 18.2b and baseline of 21.1b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04639
15039
25039

end0.0ms

sample846.0ms

Algorithm
intervals
Results
181.0ms1857×body640valid
179.0ms7850×body80nan
141.0ms1130×body1280valid
111.0ms4116×body80valid
42.0ms585×body320valid
15.0ms312×body160valid