Details

Time bar (total: 4.8s)

sample14.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
1.0ms77×body80nan

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
084
184
done84

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize5.0ms

Local error

Found 3 expressions with local error:

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

rewrite58.0ms

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:
16.0ms
(+ 1.0 (sqrt (+ x 1.0)))
10.0ms
(sqrt (+ x 1.0))
30.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series205.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(+ 1.0 (sqrt (+ x 1.0)))
32.0ms
(sqrt (+ x 1.0))
133.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify35.0ms

Counts
80 → 80
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0334508
11222457
25002445
done5002445

prune152.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize6.0ms

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))) x)
0.2b
(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
108×times-frac
100×*-un-lft-identity
67×add-sqr-sqrt
64×add-cube-cbrt
19×associate-/r*
18×distribute-lft-out
17×add-exp-log
11×add-cbrt-cube
8×div-exp
7×associate-/l*
6×pow1 div-inv add-log-exp
4×cbrt-undiv expm1-log1p-u sqrt-prod log1p-expm1-u
3×fma-def flip3-+ flip-+
2×rec-exp frac-2neg sqrt-div 1-exp clear-num associate-/l/
1×+-commutative rem-sqrt-square pow-flip sqrt-pow1 pow1/2 sum-log associate-/r/ hypot-def inv-pow
Counts
4 → 161
Calls
4 calls:
7.0ms
(sqrt (+ x 1.0))
15.0ms
(+ 1.0 (sqrt (+ x 1.0)))
50.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) x)
39.0ms
(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

series285.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(sqrt (+ x 1.0))
39.0ms
(+ 1.0 (sqrt (+ x 1.0)))
80.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) x)
134.0ms
(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

simplify66.0ms

Counts
173 → 173
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
06151449
127081291
250011197
done50011197

prune230.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize8.0ms

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)))))

rewrite141.0ms

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))
15.0ms
(+ 1.0 (sqrt (+ x 1.0)))
32.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
80.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series470.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(sqrt (+ x 1.0))
45.0ms
(+ 1.0 (sqrt (+ x 1.0)))
272.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
124.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify63.0ms

Counts
156 → 156
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05541324
123241174
250011140
done50011140

prune284.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2)))
0.0b
(/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))
0.0b
(fma 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))) (+ (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (/ x (+ (sqrt 1.0) 1.0))))
9.4b
(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))) (+ (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (/ x (+ (sqrt 1.0) 1.0)))))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
89×add-exp-log
42×div-exp
36×prod-exp
35×pow-to-exp pow-exp
20×times-frac associate-/l*
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
12×unpow-prod-down
6×cube-prod
4×pow1 cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
2×cube-mult frac-2neg unpow3 clear-num associate-/r* cbrt-unprod fma-udef div-inv unpow2
Counts
4 → 132
Calls
4 calls:
30.0ms
(/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2)))
25.0ms
(/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))
0.0ms
(fma 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))) (+ (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (/ x (+ (sqrt 1.0) 1.0))))
0.0ms
(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))) (+ (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (/ x (+ (sqrt 1.0) 1.0)))))

series1.6s

Counts
4 → 12
Calls
4 calls:
255.0ms
(/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2)))
179.0ms
(/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))
734.0ms
(fma 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))) (+ (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (/ x (+ (sqrt 1.0) 1.0))))
471.0ms
(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))) (+ (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (/ x (+ (sqrt 1.0) 1.0)))))

simplify87.0ms

Counts
144 → 144
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
04621841
125901660
250021654
done50021654

prune448.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes16.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0125
1125
done125

end0.0ms

sample340.0ms

Algorithm
intervals
Results
153.0ms8000×body80valid
37.0ms2640×body80nan