Details

Time bar (total: 15.3s)

sample30.0ms

Algorithm
intervals
Results
12.0ms255×body80valid
3.0ms85×body80nan
0.0ms1×body1280valid

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

localize13.0ms

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))))

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:
8.0ms
(sqrt (+ x 1.0))
39.0ms
(+ 1.0 (sqrt (+ x 1.0)))
59.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series354.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(sqrt (+ x 1.0))
73.0ms
(+ 1.0 (sqrt (+ x 1.0)))
240.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify2.5s

Counts
80 → 80
Iterations

Useful iterations: 3 (1.0s)

IterNodesCost
0146959
1333886
2955819
33899808
done5000808

prune248.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.4b
(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
0.4b
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.7b
(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite399.0ms

Algorithm
rewrite-expression-head
Rules
116×add-sqr-sqrt
106×times-frac
101×*-un-lft-identity
72×sqrt-prod
65×add-cube-cbrt
32×add-exp-log
27×associate-*r* associate-*l*
20×add-cbrt-cube
15×distribute-lft-out unswap-sqr
14×associate-/r*
11×div-exp
10×sqrt-div
9×pow1
8×prod-exp associate-/r/
6×cbrt-undiv associate-/l*
5×flip3-+ flip-+
4×expm1-log1p-u cbrt-unprod log1p-expm1-u div-inv add-log-exp
3×rec-exp pow-flip 1-exp
2×frac-2neg sqrt-pow1 pow1/2 clear-num hypot-def
1×frac-times rem-sqrt-square associate-*r/ pow-prod-down associate-*l/ *-commutative inv-pow
Counts
4 → 215
Calls
4 calls:
58.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
208.0ms
(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
65.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
46.0ms
(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
163.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
195.0ms
(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
647.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
298.0ms
(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify1.8s

Counts
227 → 227
Iterations

Useful iterations: done (1.8s)

IterNodesCost
03104760
17944193
224383556
done50003512

prune526.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize48.0ms

Local error

Found 2 expressions with local error:

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))))
8.6b
(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)))))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
2×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
2 → 20
Calls
2 calls:
1.0ms
(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))))
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)))))

series1.8s

Counts
2 → 6
Calls
2 calls:
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))))
743.0ms
(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)))))

simplify2.1s

Counts
26 → 26
Iterations

Useful iterations: done (2.1s)

IterNodesCost
0521394
11111388
24331210
328041177
done50001171

prune214.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite190.0ms

Algorithm
rewrite-expression-head
Rules
70×*-un-lft-identity
59×add-sqr-sqrt
52×times-frac
40×add-cube-cbrt
39×sqrt-prod
30×associate-*r*
15×distribute-lft-out
11×add-exp-log add-cbrt-cube
7×pow1
6×associate-*l* associate-/l* add-log-exp unswap-sqr
4×expm1-log1p-u flip3-+ associate-/r* associate-/r/ flip-+ log1p-expm1-u
3×fma-def
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 → 144
Calls
4 calls:
8.0ms
(sqrt (+ x 1.0))
45.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
17.0ms
(+ 1.0 (sqrt (+ x 1.0)))
114.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series788.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(sqrt (+ x 1.0))
448.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
55.0ms
(+ 1.0 (sqrt (+ x 1.0)))
238.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify1.5s

Counts
156 → 156
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02242373
15452089
217801913
done50001885

prune552.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes64.0ms

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

sample740.0ms

Algorithm
intervals
Results
439.0ms7997×body80valid
76.0ms2731×body80nan
1.0ms3×body1280valid