Details

Time bar (total: 13.3s)

sample52.0ms

Algorithm
intervals
Results
34.0ms622×body80valid

simplify3.0s

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
01829
15327
215226
340726
4103026
5262426
done500026

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

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))

rewrite17.0ms

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))

series267.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0))
42.0ms
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
107.0ms
(pow (fma a a (* b b)) 2.0)
35.0ms
(* (* b b) (+ 3.0 a))

simplify1.6s

Counts
77 → 77
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01361157
13241101
21216970
done5001966

prune250.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

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)))
8.0ms
(* (pow (hypot a b) 2.0) (pow (hypot a b) 2.0))
14.0ms
(* (* b b) (+ 3.0 a))

series343.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(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)))
44.0ms
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
160.0ms
(* (pow (hypot a b) 2.0) (pow (hypot a b) 2.0))
31.0ms
(* (* b b) (+ 3.0 a))

simplify861.0ms

Counts
112 → 112
Iterations

Useful iterations: 2 (218.0ms)

IterNodesCost
01711881
13851544
214841376
done50001376

prune316.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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 1 2.0) (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 (* (pow 1 2.0) (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))

rewrite19.0ms

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 (* (pow 1 2.0) (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 (* (pow 1 2.0) (pow (hypot a b) (+ 2.0 2.0))))
0.0ms
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
14.0ms
(* (* b b) (+ 3.0 a))

series281.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(- (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (* (pow 1 2.0) (pow (hypot a b) (+ 2.0 2.0)))) 1.0)
107.0ms
(fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (* (pow 1 2.0) (pow (hypot a b) (+ 2.0 2.0))))
43.0ms
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
31.0ms
(* (* b b) (+ 3.0 a))

simplify833.0ms

Counts
87 → 87
Iterations

Useful iterations: done (830.0ms)

IterNodesCost
01502381
13582104
212561756
done50001725

prune281.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

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 (* (pow 1 2.0) (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 (* (pow 1 2.0) (pow (hypot a b) (+ 2.0 2.0)))))

rewrite34.0ms

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))
16.0ms
(* (* b b) (+ 3.0 a))
1.0ms
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (* (pow 1 2.0) (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 (* (pow 1 2.0) (pow (hypot a b) (+ 2.0 2.0)))))

series492.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (* b b) (+ 3.0 a))
32.0ms
(* (* b b) (+ 3.0 a))
215.0ms
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (* (pow 1 2.0) (pow (hypot a b) (+ 2.0 2.0)))))
211.0ms
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (* (pow 1 2.0) (pow (hypot a b) (+ 2.0 2.0)))))

simplify2.7s

Counts
94 → 94
Iterations

Useful iterations: done (2.7s)

IterNodesCost
01111774
12841536
210381330
344741320
done50011316

prune377.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes50.0ms

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: 0 (0.0ms)

IterNodesCost
02029
12529
done2529

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.0s20276×body80valid