Details

Time bar (total: 15.0s)

sample31.0ms

Algorithm
intervals
Results
18.0ms255×body80valid
3.0ms85×body80nan
0.0ms1×body1280valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
188
done88

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.1b
(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
17×add-sqr-sqrt
14×add-cube-cbrt
12×times-frac
6×distribute-lft-out
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 associate-/r* sqrt-prod
3×expm1-log1p-u fma-def flip3-+ flip-+ log1p-expm1-u associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log hypot-def div-inv
Counts
3 → 71
Calls
3 calls:
9.0ms
(sqrt (+ x 1.0))
32.0ms
(+ 1.0 (sqrt (+ x 1.0)))
32.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series321.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(sqrt (+ x 1.0))
48.0ms
(+ 1.0 (sqrt (+ x 1.0)))
227.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify2.5s

Counts
80 → 80
Iterations

Useful iterations: 3 (998.0ms)

IterNodesCost
0146959
1333886
2955819
33899808
done5000808

prune283.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.2b
(pow (sqrt (+ x 1.0)) 3)
4.7b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.3b
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite292.0ms

Algorithm
rewrite-expression-head
Rules
89×*-un-lft-identity
62×sqrt-div
43×add-sqr-sqrt
34×sqrt-prod
32×flip3-+ flip-+
31×add-cube-cbrt
28×associate-*r/ distribute-lft-out
27×times-frac
23×unpow-prod-down cube-prod
21×pow1
16×frac-sub
12×frac-times
11×swap-sqr
9×add-exp-log sqrt-pow1 pow1/2 associate-/r* add-cbrt-cube
8×associate-*l/
7×associate-*r* associate-*l*
6×add-log-exp
5×pow-prod-up
4×expm1-log1p-u sum-cubes log1p-expm1-u sub-div unswap-sqr
3×pow-unpow pow-pow pow-prod-down pow-sqr associate-/l*
2×cube-div associate-/r/
1×cbrt-undiv pow2 cube-mult pow-to-exp sub-neg flip3-- distribute-rgt-out-- frac-2neg pow-plus fma-neg sqrt-unprod diff-log unpow3 div-exp prod-diff pow-exp prod-exp clear-num rem-square-sqrt *-commutative sqrt-pow2 flip-- cbrt-unprod div-inv rem-cube-cbrt sqr-pow
Counts
4 → 194
Calls
4 calls:
54.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
20.0ms
(pow (sqrt (+ x 1.0)) 3)
59.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
143.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series469.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
94.0ms
(pow (sqrt (+ x 1.0)) 3)
75.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
279.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify2.2s

Counts
206 → 206
Iterations

Useful iterations: done (2.2s)

IterNodesCost
03264145
18032987
229592729
done50002724

prune752.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sqrt (+ x 1.0)) 3)
0.2b
(/ 1 (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))
4.7b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.1b
(* x (/ 1 (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3))))

rewrite614.0ms

Algorithm
rewrite-expression-head
Rules
112×*-un-lft-identity
56×times-frac
50×sqrt-div
44×add-sqr-sqrt
37×add-cube-cbrt distribute-lft-out
35×unpow-prod-down cube-prod
33×associate-*r*
27×flip3-+ associate-*r/ flip-+
18×add-exp-log
16×frac-sub
12×add-cbrt-cube
9×pow1 associate-/r*
8×frac-times sqrt-prod
7×sum-cubes
6×associate-*l/ add-log-exp
4×expm1-log1p-u div-exp prod-exp associate-/r/ log1p-expm1-u sub-div
3×pow-unpow pow-pow associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv cube-div rec-exp 1-exp cbrt-unprod div-inv
1×cube-mult pow-to-exp sub-neg flip3-- distribute-rgt-out-- pow-flip frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log unpow3 prod-diff pow-prod-down pow-exp clear-num un-div-inv *-commutative sqrt-pow2 flip-- inv-pow rem-cube-cbrt sqr-pow
Counts
4 → 192
Calls
4 calls:
20.0ms
(pow (sqrt (+ x 1.0)) 3)
166.0ms
(/ 1 (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))
37.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
371.0ms
(* x (/ 1 (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3))))

series705.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(pow (sqrt (+ x 1.0)) 3)
216.0ms
(/ 1 (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))
90.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
290.0ms
(* x (/ 1 (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3))))

simplify2.6s

Counts
204 → 204
Iterations

Useful iterations: done (2.6s)

IterNodesCost
03534361
19243291
230362956
done50002947

prune730.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.1b
(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))
0.1b
(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
360×times-frac
288×*-un-lft-identity
190×sqrt-prod
189×add-sqr-sqrt
186×add-cube-cbrt
51×distribute-lft-out
34×associate-/r*
11×add-exp-log add-cbrt-cube
10×associate-/l*
9×div-inv
6×add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×fma-def flip3-+ flip-+
2×frac-2neg sqrt-div clear-num associate-/l/
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log associate-/r/ hypot-def
Counts
4 → 305
Calls
4 calls:
16.0ms
(sqrt (+ x 1.0))
23.0ms
(+ 1.0 (sqrt (+ x 1.0)))
67.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))
81.0ms
(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))

series507.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(sqrt (+ x 1.0))
49.0ms
(+ 1.0 (sqrt (+ x 1.0)))
239.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))
182.0ms
(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))

simplify1.9s

Counts
317 → 317
Iterations

Useful iterations: done (1.9s)

IterNodesCost
03846996
18796291
228615814
done50005716

prune732.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes1.0ms