Details

Time bar (total: 13.3s)

sample32.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
4.0ms91×body80nan

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
188
done88

prune4.0ms

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

rewrite105.0ms

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:
10.0ms
(sqrt (+ x 1.0))
25.0ms
(+ 1.0 (sqrt (+ x 1.0)))
67.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series289.0ms

Counts
3 → 9
Calls
3 calls:
49.0ms
(sqrt (+ x 1.0))
60.0ms
(+ 1.0 (sqrt (+ x 1.0)))
180.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify885.0ms

Counts
80 → 80
Iterations

Useful iterations: done (883.0ms)

IterNodesCost
0146959
1343886
21581822
done5001815

prune214.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize11.0ms

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

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity
34×add-sqr-sqrt
26×times-frac
24×add-cube-cbrt
18×associate-*r*
17×add-exp-log
11×add-cbrt-cube
9×distribute-lft-out
8×pow1
6×add-log-exp
4×expm1-log1p-u flip3-+ div-exp prod-exp associate-/r* sqrt-prod associate-/r/ flip-+ log1p-expm1-u
3×fma-def associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv rec-exp sqrt-div 1-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num sum-log un-div-inv *-commutative hypot-def inv-pow
Counts
4 → 118
Calls
4 calls:
9.0ms
(sqrt (+ x 1.0))
21.0ms
(+ 1.0 (sqrt (+ x 1.0)))
55.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
107.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

series421.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(sqrt (+ x 1.0))
60.0ms
(+ 1.0 (sqrt (+ x 1.0)))
125.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
200.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

simplify1.5s

Counts
130 → 130
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01941642
14961444
225621264
done50011255

prune366.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.4b
(/ x (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))))))
0.8b
(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite388.0ms

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:
35.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
72.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
227.0ms
(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
44.0ms
(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
196.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
618.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
194.0ms
(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
257.0ms
(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify640.0ms

Counts
227 → 227
Iterations

Useful iterations: done (629.0ms)

IterNodesCost
03104760
18694303
done50003880

prune617.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite212.0ms

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:
12.0ms
(sqrt (+ x 1.0))
18.0ms
(+ 1.0 (sqrt (+ x 1.0)))
51.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
125.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series741.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(sqrt (+ x 1.0))
55.0ms
(+ 1.0 (sqrt (+ x 1.0)))
422.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
221.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify4.1s

Counts
156 → 156
Iterations

Useful iterations: done (4.1s)

IterNodesCost
02242373
15822181
240821930
done50011905

prune461.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes29.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
11310
done1310

end0.0ms

sample750.0ms

Algorithm
intervals
Results
338.0ms8000×body80valid
153.0ms2641×body80nan