Details

Time bar (total: 8.9s)

sample48.0ms

Algorithm
intervals
Results
31.0ms622×body80valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01829
15327
215226
340726
4103026
5262626
done500026

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0))
0.1b
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
0.3b
(pow (fma a a (* b b)) 2.0)
1.4b
(* (* b b) (+ 3.0 a))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-exp-log
9×*-un-lft-identity add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
4×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow pow-prod-down prod-exp cbrt-unprod
2×associate-*r/ fma-udef
1×distribute-rgt-in pow-to-exp pow-pow distribute-lft-in flip3-+ associate-*l* pow-exp *-commutative flip-+ distribute-lft-out unswap-sqr sqr-pow
Counts
4 → 65
Calls
4 calls:
0.0ms
(fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0))
0.0ms
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
1.0ms
(pow (fma a a (* b b)) 2.0)
14.0ms
(* (* b b) (+ 3.0 a))

series271.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0))
41.0ms
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
108.0ms
(pow (fma a a (* b b)) 2.0)
35.0ms
(* (* b b) (+ 3.0 a))

simplify834.0ms

Counts
77 → 77
Iterations

Useful iterations: 2 (337.0ms)

IterNodesCost
01361157
13241101
21284970
done5000970

prune249.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (* (pow (hypot a b) 2.0) (pow (hypot a b) 2.0)))
0.1b
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
0.3b
(* (pow (hypot a b) 2.0) (pow (hypot a b) 2.0))
1.4b
(* (* b b) (+ 3.0 a))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
21×add-exp-log
18×unpow-prod-down
15×*-un-lft-identity
13×add-cube-cbrt
12×prod-exp
11×associate-*r* add-cbrt-cube
10×unswap-sqr sqr-pow
9×pow1
8×associate-*l*
7×swap-sqr
6×pow-to-exp pow-exp
4×expm1-log1p-u pow-prod-down cbrt-unprod log1p-expm1-u add-log-exp
2×associate-*r/ *-commutative fma-udef
1×pow2 distribute-rgt-in distribute-lft-in flip3-+ pow-sqr pow-prod-up flip-+ distribute-lft-out
Counts
4 → 100
Calls
4 calls:
0.0ms
(fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (* (pow (hypot a b) 2.0) (pow (hypot a b) 2.0)))
0.0ms
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
9.0ms
(* (pow (hypot a b) 2.0) (pow (hypot a b) 2.0))
15.0ms
(* (* b b) (+ 3.0 a))

series356.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (* (pow (hypot a b) 2.0) (pow (hypot a b) 2.0)))
48.0ms
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
163.0ms
(* (pow (hypot a b) 2.0) (pow (hypot a b) 2.0))
31.0ms
(* (* b b) (+ 3.0 a))

simplify668.0ms

Counts
112 → 112
Iterations

Useful iterations: 2 (160.0ms)

IterNodesCost
01711881
13851544
215741376
done50001376

prune321.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (* 1 (pow (hypot a b) (+ 2.0 2.0)))) 1.0)
0.0b
(fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (* 1 (pow (hypot a b) (+ 2.0 2.0))))
0.1b
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
1.4b
(* (* b b) (+ 3.0 a))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
15×add-sqr-sqrt
12×add-cube-cbrt
9×pow1 add-exp-log prod-diff add-cbrt-cube
6×add-log-exp
4×expm1-log1p-u associate-*r* log1p-expm1-u
3×fma-neg pow-prod-down prod-exp cbrt-unprod fma-udef
2×associate-*r/
1×distribute-rgt-in sub-neg flip3-- distribute-lft-in flip3-+ diff-log associate-*l* associate--l+ *-commutative flip-- flip-+ distribute-lft-out distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 75
Calls
4 calls:
3.0ms
(- (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (* 1 (pow (hypot a b) (+ 2.0 2.0)))) 1.0)
0.0ms
(fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (* 1 (pow (hypot a b) (+ 2.0 2.0))))
0.0ms
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
16.0ms
(* (* b b) (+ 3.0 a))

series304.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(- (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (* 1 (pow (hypot a b) (+ 2.0 2.0)))) 1.0)
121.0ms
(fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (* 1 (pow (hypot a b) (+ 2.0 2.0))))
42.0ms
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
38.0ms
(* (* b b) (+ 3.0 a))

simplify625.0ms

Counts
87 → 87
Iterations

Useful iterations: 2 (142.0ms)

IterNodesCost
01492273
13542000
213541747
done50011747

prune278.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (* b b) (+ 3.0 a))
1.4b
(* (* b b) (+ 3.0 a))
8.3b
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (* 1 (pow (hypot a b) (+ 2.0 2.0)))))
8.3b
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (* 1 (pow (hypot a b) (+ 2.0 2.0)))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
14×add-exp-log add-cbrt-cube
12×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt associate-*r*
6×pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×expm1-log1p-u associate-*r/ log1p-expm1-u add-log-exp
2×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 flip3-+ pow1/2 associate-*l* *-commutative flip-+ distribute-lft-out unswap-sqr
Counts
4 → 82
Calls
4 calls:
14.0ms
(* (* b b) (+ 3.0 a))
15.0ms
(* (* b b) (+ 3.0 a))
1.0ms
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (* 1 (pow (hypot a b) (+ 2.0 2.0)))))
1.0ms
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (* 1 (pow (hypot a b) (+ 2.0 2.0)))))

series517.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* (* b b) (+ 3.0 a))
32.0ms
(* (* b b) (+ 3.0 a))
225.0ms
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (* 1 (pow (hypot a b) (+ 2.0 2.0)))))
222.0ms
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (* 1 (pow (hypot a b) (+ 2.0 2.0)))))

simplify1.0s

Counts
94 → 94
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01101702
12801472
210461330
done50001322

prune400.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes60.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01927
12425
done2425

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.0s20276×body80valid