Details

Time bar (total: 1.2m)

sample33.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
9.0ms245×body80nan

simplify135.0ms

Counts
1 → 1
Iterations
IterNodes
done129
8129
7128
6126
5109
484
362
238
121
011

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

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)))

rewrite27.0ms

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-cbrt-cube add-exp-log
6×div-inv associate-/l*
5×flip3-- flip--
4×cbrt-undiv div-exp
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×fma-udef
Counts
3 → 156
Calls
3 calls:
0.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
8.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
15.0ms
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

series230.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
78.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
106.0ms
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

simplify1.7s

Counts
165 → 165
Iterations
IterNodes
done5000
22097
1631
0254

prune679.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (fma (sqrt x) 4.0 (+ x 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))))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
25296×times-frac
15607×*-un-lft-identity
13884×add-sqr-sqrt
12306×sqrt-prod
8355×add-cube-cbrt
2764×difference-of-squares
2244×distribute-lft-out
1382×distribute-lft-out--
667×associate-/r/
365×div-inv
187×flip3-+ flip-+
122×associate-/l*
115×flip3-- flip--
105×associate-/r*
32×add-cbrt-cube add-exp-log
19×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 7247
Calls
4 calls:
2.0ms
(sqrt (fma (sqrt x) 4.0 (+ x 1.0)))
29.0ms
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- (sqrt x) (sqrt 1.0)))
55.0ms
(/ (/ 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))))
26.0ms
(/ 6.0 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0))))

series1.7s

Counts
4 → 12
Calls
4 calls:
99.0ms
(sqrt (fma (sqrt x) 4.0 (+ x 1.0)))
653.0ms
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- (sqrt x) (sqrt 1.0)))
581.0ms
(/ (/ 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))))
356.0ms
(/ 6.0 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0))))

simplify11.7s

Counts
7259 → 7259
Iterations
IterNodes
done5000
04283

prune18.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (fma (sqrt x) 4.0 (+ x 1.0)))
0.0b
(/ (/ 1 (/ (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
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- (sqrt x) (sqrt 1.0)))
0.0b
(/ 1 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0))))

rewrite801.0ms

Algorithm
rewrite-expression-head
Rules
25296×times-frac
15607×*-un-lft-identity
13884×add-sqr-sqrt
12306×sqrt-prod
8355×add-cube-cbrt
2764×difference-of-squares
2244×distribute-lft-out
1382×distribute-lft-out--
667×associate-/r/
365×div-inv
187×flip3-+ flip-+
122×associate-/l*
115×flip3-- flip--
105×associate-/r*
62×add-exp-log
43×div-exp
32×add-cbrt-cube
19×cbrt-undiv
6×pow1 rec-exp 1-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×rem-sqrt-square sqrt-pow1 pow1/2 pow-flip inv-pow associate-/l/
Counts
4 → 7261
Calls
4 calls:
1.0ms
(sqrt (fma (sqrt x) 4.0 (+ x 1.0)))
59.0ms
(/ (/ 1 (/ (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))))
20.0ms
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- (sqrt x) (sqrt 1.0)))
21.0ms
(/ 1 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0))))

series1.7s

Counts
4 → 12
Calls
4 calls:
105.0ms
(sqrt (fma (sqrt x) 4.0 (+ x 1.0)))
536.0ms
(/ (/ 1 (/ (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))))
710.0ms
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- (sqrt x) (sqrt 1.0)))
381.0ms
(/ 1 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0))))

simplify14.0s

Counts
7273 → 7273
Iterations
IterNodes
done5001
04189

prune16.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 6.0 (- x 1.0))
0.0b
(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.1b
(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

rewrite71.0ms

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-cbrt-cube add-exp-log
8×add-log-exp
5×pow1 associate-*r*
4×fma-def associate-*r/
3×expm1-log1p-u associate-/r* sum-log times-frac associate-*l* insert-posit16 log1p-expm1-u
2×cbrt-undiv sub-neg flip3-+ flip3-- div-exp prod-exp associate-/r/ cbrt-unprod flip-+ flip-- associate-/l/
1×+-commutative associate-+l+ clear-num frac-2neg pow-prod-down *-commutative div-inv distribute-lft-out associate-/l* distribute-lft-out-- difference-of-squares unswap-sqr
Counts
3 → 95
Calls
3 calls:
16.0ms
(* 6.0 (- x 1.0))
21.0ms
(+ (+ x 1.0) (* 4.0 (sqrt x)))
33.0ms
(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

series169.0ms

Counts
3 → 9
Calls
3 calls:
49.0ms
(* 6.0 (- x 1.0))
37.0ms
(+ (+ x 1.0) (* 4.0 (sqrt x)))
83.0ms
(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

simplify978.0ms

Counts
104 → 104
Iterations
IterNodes
done5002
21549
1511
0191

prune245.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes58.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done22
122
017

end0.0ms

sample946.0ms

Algorithm
intervals
Results
426.0ms8000×body80valid
357.0ms7851×body80nan