Details

Time bar (total: 12.7s)

sample26.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
3.0ms90×body80nan

simplify5.0ms

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: 0.1b

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))))

rewrite80.0ms

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:
13.0ms
(sqrt (+ x 1.0))
28.0ms
(+ 1.0 (sqrt (+ x 1.0)))
37.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series306.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(sqrt (+ x 1.0))
69.0ms
(+ 1.0 (sqrt (+ x 1.0)))
190.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify2.0s

Counts
80 → 80
Iterations

Useful iterations: 3 (949.0ms)

IterNodesCost
0146959
1333886
2955819
33899808
done5000808

prune199.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3)))
0.1b
(/ x (+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3))))
0.2b
(pow (sqrt (+ x 1.0)) 3)
4.0b
(cbrt (pow (sqrt (+ x 1.0)) 3))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
24×add-sqr-sqrt add-cube-cbrt
20×cbrt-prod
16×sqrt-prod
14×unpow-prod-down cube-prod
12×times-frac
9×distribute-lft-out
7×add-exp-log add-cbrt-cube
6×pow1 add-log-exp
4×cube-div expm1-log1p-u flip3-+ sqrt-div associate-/r* flip-+ log1p-expm1-u
3×pow-unpow pow-pow fma-def associate-/l*
2×cube-mult cbrt-div unpow3 associate-/r/ sqr-pow
1×cbrt-undiv +-commutative pow-to-exp frac-2neg sqrt-pow1 pow1/2 pow1/3 div-exp pow-exp clear-num sum-log sqrt-pow2 rem-cbrt-cube div-inv rem-cube-cbrt
Counts
4 → 123
Calls
4 calls:
57.0ms
(+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3)))
92.0ms
(/ x (+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3))))
11.0ms
(pow (sqrt (+ x 1.0)) 3)
11.0ms
(cbrt (pow (sqrt (+ x 1.0)) 3))

series397.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3)))
193.0ms
(/ x (+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3))))
88.0ms
(pow (sqrt (+ x 1.0)) 3)
41.0ms
(cbrt (pow (sqrt (+ x 1.0)) 3))

simplify928.0ms

Counts
135 → 135
Iterations

Useful iterations: done (921.0ms)

IterNodesCost
02071951
14781365
214091282
done50001273

prune352.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (pow x 3) (* (pow (+ (sqrt 1.0) 1.0) 3) 1.0))
0.0b
(fma 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))) (fma 1/4 (/ (pow x 3) (* (pow (+ (sqrt 1.0) 1.0) 3) 1.0)) (/ x (+ (sqrt 1.0) 1.0))))
0.0b
(fma 1/4 (/ (pow x 3) (* (pow (+ (sqrt 1.0) 1.0) 3) 1.0)) (/ x (+ (sqrt 1.0) 1.0)))
6.0b
(fma -1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))) (fma 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))) (fma 1/4 (/ (pow x 3) (* (pow (+ (sqrt 1.0) 1.0) 3) 1.0)) (/ x (+ (sqrt 1.0) 1.0)))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
30×add-exp-log
12×times-frac div-exp associate-/l*
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×prod-exp add-cbrt-cube
7×pow-to-exp pow-exp
6×unpow-prod-down cube-prod
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×fma-udef
2×cbrt-undiv cube-div cube-mult unpow3 associate-*l/ associate-/r/ sqr-pow
1×frac-2neg flip3-+ clear-num associate-/r* cbrt-unprod flip-+ div-inv
Counts
4 → 83
Calls
4 calls:
41.0ms
(/ (pow x 3) (* (pow (+ (sqrt 1.0) 1.0) 3) 1.0))
0.0ms
(fma 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))) (fma 1/4 (/ (pow x 3) (* (pow (+ (sqrt 1.0) 1.0) 3) 1.0)) (/ x (+ (sqrt 1.0) 1.0))))
0.0ms
(fma 1/4 (/ (pow x 3) (* (pow (+ (sqrt 1.0) 1.0) 3) 1.0)) (/ x (+ (sqrt 1.0) 1.0)))
1.0ms
(fma -1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))) (fma 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))) (fma 1/4 (/ (pow x 3) (* (pow (+ (sqrt 1.0) 1.0) 3) 1.0)) (/ x (+ (sqrt 1.0) 1.0)))))

series2.8s

Counts
4 → 12
Calls
4 calls:
233.0ms
(/ (pow x 3) (* (pow (+ (sqrt 1.0) 1.0) 3) 1.0))
1.1s
(fma 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))) (fma 1/4 (/ (pow x 3) (* (pow (+ (sqrt 1.0) 1.0) 3) 1.0)) (/ x (+ (sqrt 1.0) 1.0))))
864.0ms
(fma 1/4 (/ (pow x 3) (* (pow (+ (sqrt 1.0) 1.0) 3) 1.0)) (/ x (+ (sqrt 1.0) 1.0)))
631.0ms
(fma -1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))) (fma 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))) (fma 1/4 (/ (pow x 3) (* (pow (+ (sqrt 1.0) 1.0) 3) 1.0)) (/ x (+ (sqrt 1.0) 1.0)))))

simplify936.0ms

Counts
95 → 95
Iterations

Useful iterations: done (931.0ms)

IterNodesCost
01522591
13422494
215822224
done50002215

prune623.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0))
0.0b
(sqrt (+ x 1.0))
0.0b
(+ (sqrt (+ x 1.0)) 1.0)
0.2b
(* (sqrt x) (/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0)))

rewrite326.0ms

Algorithm
rewrite-expression-head
Rules
73×*-un-lft-identity
60×add-sqr-sqrt
52×times-frac
43×sqrt-prod
41×add-cube-cbrt
30×associate-*r*
16×distribute-lft-out
11×add-exp-log add-cbrt-cube
7×pow1 fma-def
6×associate-*l* associate-/l* add-log-exp unswap-sqr
4×expm1-log1p-u flip3-+ associate-/r* associate-/r/ flip-+ log1p-expm1-u
2×cbrt-undiv sqrt-div div-exp prod-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num sum-log *-commutative hypot-def
Counts
4 → 148
Calls
4 calls:
67.0ms
(/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0))
17.0ms
(sqrt (+ x 1.0))
66.0ms
(+ (sqrt (+ x 1.0)) 1.0)
170.0ms
(* (sqrt x) (/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0)))

series719.0ms

Counts
4 → 12
Calls
4 calls:
411.0ms
(/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0))
48.0ms
(sqrt (+ x 1.0))
57.0ms
(+ (sqrt (+ x 1.0)) 1.0)
203.0ms
(* (sqrt x) (/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0)))

simplify1.4s

Counts
160 → 160
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02242373
15442088
217801911
done50001884

prune469.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes85.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
188
done88

end0.0ms

sample706.0ms

Algorithm
intervals
Results
352.0ms7998×body80valid
110.0ms2659×body80nan
0.0ms2×body1280valid