Details

Time bar (total: 9.0s)

sample27.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
3.0ms91×body80nan

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
188
done88

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite84.0ms

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:
8.0ms
(sqrt (+ x 1.0))
16.0ms
(+ 1.0 (sqrt (+ x 1.0)))
58.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series307.0ms

Counts
3 → 9
Calls
3 calls:
49.0ms
(sqrt (+ x 1.0))
68.0ms
(+ 1.0 (sqrt (+ x 1.0)))
190.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify916.0ms

Counts
80 → 80
Iterations

Useful iterations: done (913.0ms)

IterNodesCost
0146959
1343886
21581822
done5001815

prune212.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize24.0ms

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)
5.6b
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))
5.8b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))

rewrite172.0ms

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:
39.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
11.0ms
(pow (sqrt (+ x 1.0)) 3)
85.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))
29.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))

series341.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
66.0ms
(pow (sqrt (+ x 1.0)) 3)
192.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))
65.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))

simplify598.0ms

Counts
206 → 206
Iterations

Useful iterations: done (587.0ms)

IterNodesCost
03264145
19533032
done50002796

prune739.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize17.0ms

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)))

rewrite186.0ms

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:
11.0ms
(sqrt (+ x 1.0))
22.0ms
(+ 1.0 (sqrt (+ x 1.0)))
67.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))
48.0ms
(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))

series504.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(sqrt (+ x 1.0))
62.0ms
(+ 1.0 (sqrt (+ x 1.0)))
237.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))
168.0ms
(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))

simplify680.0ms

Counts
317 → 317
Iterations

Useful iterations: done (664.0ms)

IterNodesCost
03846996
110216387
done50006149

prune758.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt x) (/ (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))) (sqrt x)))
0.1b
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
0.2b
(cbrt (+ x 1.0))
0.2b
(cbrt (+ x 1.0))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
258×times-frac
153×add-sqr-sqrt *-un-lft-identity
147×add-cube-cbrt
141×sqrt-prod
22×associate-/r*
13×cbrt-prod
11×add-exp-log add-cbrt-cube
10×associate-*r*
8×div-inv
6×pow1 cbrt-div associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv flip3-+ div-exp associate-*l* flip-+ distribute-lft-out unswap-sqr
2×pow1/3 sqrt-div associate-*r/
1×frac-2neg pow-prod-down prod-exp clear-num associate-/r/ *-commutative cbrt-unprod
Counts
4 → 240
Calls
4 calls:
23.0ms
(/ (sqrt x) (/ (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))) (sqrt x)))
42.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
7.0ms
(cbrt (+ x 1.0))
8.0ms
(cbrt (+ x 1.0))

series564.0ms

Counts
4 → 12
Calls
4 calls:
235.0ms
(/ (sqrt x) (/ (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))) (sqrt x)))
116.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
116.0ms
(cbrt (+ x 1.0))
97.0ms
(cbrt (+ x 1.0))

simplify684.0ms

Counts
252 → 252
Iterations

Useful iterations: done (669.0ms)

IterNodesCost
04848478
113197973
done50007417

prune1.0s

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes50.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
188
done88

end0.0ms

sample957.0ms

Algorithm
intervals
Results
689.0ms7998×body80valid
61.0ms2683×body80nan
0.0ms2×body1280valid