Details

Time bar (total: 9.0s)

sample19.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
2.0ms72×body80nan

simplify3.0ms

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

localize11.0ms

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))))

rewrite108.0ms

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:
14.0ms
(sqrt (+ x 1.0))
37.0ms
(+ 1.0 (sqrt (+ x 1.0)))
54.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series267.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(sqrt (+ x 1.0))
50.0ms
(+ 1.0 (sqrt (+ x 1.0)))
177.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify1.1s

Counts
80 → 80
Iterations

Useful iterations: done (1.1s)

IterNodesCost
0146959
1343886
21581822
done5001815

prune289.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
38×*-un-lft-identity
30×associate-*r*
28×times-frac
24×sqrt-prod
22×add-cube-cbrt
8×add-exp-log add-cbrt-cube distribute-lft-out
6×pow1 associate-*l* unswap-sqr
5×add-log-exp
3×expm1-log1p-u fma-def flip3-+ flip-+ log1p-expm1-u
2×sqrt-div prod-exp associate-/r/ cbrt-unprod
1×cbrt-undiv +-commutative rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ div-exp pow-prod-down sum-log *-commutative hypot-def div-inv
Counts
3 → 94
Calls
3 calls:
13.0ms
(sqrt (+ x 1.0))
23.0ms
(+ 1.0 (sqrt (+ x 1.0)))
111.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series256.0ms

Counts
3 → 9
Calls
3 calls:
32.0ms
(sqrt (+ x 1.0))
60.0ms
(+ 1.0 (sqrt (+ x 1.0)))
164.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify2.6s

Counts
103 → 103
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01791422
14771295
233621087
done50021058

prune421.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize67.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma (/ (pow x 3) (* (pow (+ (sqrt 1.0) 1.0) 3) 1.0)) 1/4 (fma 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))) (/ x (+ (sqrt 1.0) 1.0))))
0.2b
(/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))
9.0b
(fma -1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))) (fma (/ (pow x 3) (* (pow (+ (sqrt 1.0) 1.0) 3) 1.0)) 1/4 (fma 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))) (/ x (+ (sqrt 1.0) 1.0)))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
29×add-exp-log
12×div-exp
9×prod-exp
8×times-frac add-cbrt-cube associate-/l*
7×add-sqr-sqrt pow-to-exp add-cube-cbrt *-un-lft-identity pow-exp
6×unpow-prod-down
3×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×cbrt-undiv fma-udef unpow2 sqr-pow
1×frac-2neg clear-num associate-/r* cbrt-unprod div-inv
Counts
3 → 63
Calls
3 calls:
1.0ms
(fma (/ (pow x 3) (* (pow (+ (sqrt 1.0) 1.0) 3) 1.0)) 1/4 (fma 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))) (/ x (+ (sqrt 1.0) 1.0))))
48.0ms
(/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))
1.0ms
(fma -1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))) (fma (/ (pow x 3) (* (pow (+ (sqrt 1.0) 1.0) 3) 1.0)) 1/4 (fma 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))) (/ x (+ (sqrt 1.0) 1.0)))))

series1.8s

Counts
3 → 9
Calls
3 calls:
918.0ms
(fma (/ (pow x 3) (* (pow (+ (sqrt 1.0) 1.0) 3) 1.0)) 1/4 (fma 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))) (/ x (+ (sqrt 1.0) 1.0))))
190.0ms
(/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))
644.0ms
(fma -1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))) (fma (/ (pow x 3) (* (pow (+ (sqrt 1.0) 1.0) 3) 1.0)) 1/4 (fma 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))) (/ x (+ (sqrt 1.0) 1.0)))))

simplify692.0ms

Counts
72 → 72
Iterations

Useful iterations: done (689.0ms)

IterNodesCost
01282163
12812097
214481852
done50011785

prune409.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes69.0ms

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

sample658.0ms

Algorithm
intervals
Results
313.0ms7998×body80valid
116.0ms2672×body80nan
0.0ms2×body1280valid