Details

Time bar (total: 35.6s)

sample40.0ms

Algorithm
intervals
Results
14.0ms256×body80valid
9.0ms198×body80nan

simplify188.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01114
12114
24113
36913
49413
511813
613113
713313
done13313

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma (sqrt x) 4.0 (+ x 1.0))
0.0b
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
0.0b
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
103×add-sqr-sqrt *-un-lft-identity
71×add-cube-cbrt
26×associate-/r*
16×distribute-lft-out-- difference-of-squares
11×associate-/r/
10×add-exp-log add-cbrt-cube
6×div-inv associate-/l*
5×flip3-- flip--
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×fma-udef
Counts
3 → 153
Calls
3 calls:
0.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
26.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
29.0ms
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

series221.0ms

Counts
3 → 9
Calls
3 calls:
51.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
83.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
86.0ms
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

simplify1.4s

Counts
162 → 162
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02503612
15483468
218733294
done50003288

prune405.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0)))
0.0b
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- (sqrt x) (sqrt 1.0)))
0.0b
(/ (/ 6.0 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0)))) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- (sqrt x) (sqrt 1.0))))
0.0b
(/ 6.0 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0))))

rewrite2.0s

Algorithm
rewrite-expression-head
Rules
25326×times-frac
15653×*-un-lft-identity
13901×add-sqr-sqrt
12335×sqrt-prod
8373×add-cube-cbrt
2764×difference-of-squares
2258×distribute-lft-out
1382×distribute-lft-out--
669×associate-/r/
366×div-inv
188×flip3-+ flip-+
128×associate-/l*
115×flip3-- flip--
110×associate-/r*
34×add-exp-log add-cbrt-cube
20×cbrt-undiv div-exp
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
1×associate-/l/
Counts
4 → 7285
Calls
4 calls:
30.0ms
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0)))
31.0ms
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- (sqrt x) (sqrt 1.0)))
337.0ms
(/ (/ 6.0 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0)))) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- (sqrt x) (sqrt 1.0))))
33.0ms
(/ 6.0 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0))))

series1.9s

Counts
4 → 12
Calls
4 calls:
568.0ms
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0)))
520.0ms
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- (sqrt x) (sqrt 1.0)))
539.0ms
(/ (/ 6.0 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0)))) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- (sqrt x) (sqrt 1.0))))
305.0ms
(/ 6.0 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0))))

simplify4.0s

Counts
7297 → 7297
Iterations

Useful iterations: done (3.1s)

IterNodesCost
04275487464
done5000453122

prune17.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (+ (sqrt x) (sqrt 1.0)))
0.1b
(sqrt (+ (sqrt x) (sqrt 1.0)))
0.1b
(sqrt (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
0.1b
(sqrt (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
42×sqrt-prod
32×add-sqr-sqrt
18×*-un-lft-identity
10×pow1 add-cube-cbrt sqrt-pow1
8×hypot-def
6×rem-sqrt-square pow1/2
4×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u distribute-lft-out add-log-exp
2×flip3-+ flip-+
Counts
4 → 88
Calls
4 calls:
18.0ms
(sqrt (+ (sqrt x) (sqrt 1.0)))
24.0ms
(sqrt (+ (sqrt x) (sqrt 1.0)))
3.0ms
(sqrt (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
3.0ms
(sqrt (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

series649.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(sqrt (+ (sqrt x) (sqrt 1.0)))
194.0ms
(sqrt (+ (sqrt x) (sqrt 1.0)))
151.0ms
(sqrt (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
153.0ms
(sqrt (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

simplify2.8s

Counts
100 → 100
Iterations

Useful iterations: done (2.8s)

IterNodesCost
01481406
13411230
28771134
325621072
done50011052

prune532.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 6.0 (- x 1.0))
0.0b
(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.4b
(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt *-un-lft-identity
20×add-cube-cbrt
18×prod-diff
11×distribute-rgt-in distribute-lft-in
10×add-exp-log add-cbrt-cube
8×add-log-exp
5×pow1 associate-*r*
4×fma-def associate-*r/
3×expm1-log1p-u times-frac associate-*l* associate-/r* sum-log log1p-expm1-u
2×cbrt-undiv sub-neg flip3-- flip3-+ div-exp prod-exp associate-/r/ flip-- cbrt-unprod flip-+ associate-/l/
1×+-commutative associate-+l+ frac-2neg pow-prod-down clear-num *-commutative div-inv distribute-lft-out associate-/l* distribute-lft-out-- difference-of-squares unswap-sqr
Counts
3 → 92
Calls
3 calls:
25.0ms
(* 6.0 (- x 1.0))
53.0ms
(+ (+ x 1.0) (* 4.0 (sqrt x)))
73.0ms
(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

series190.0ms

Counts
3 → 9
Calls
3 calls:
51.0ms
(* 6.0 (- x 1.0))
37.0ms
(+ (+ x 1.0) (* 4.0 (sqrt x)))
103.0ms
(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

simplify1.3s

Counts
101 → 101
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01871534
14661342
214161067
done50001040

prune305.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes74.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01531
11731
done1731

end0.0ms

sample1.7s

Algorithm
intervals
Results
872.0ms8006×body80nan
498.0ms8000×body80valid