Details

Time bar (total: 23.3s)

sample114.0ms

Algorithm
intervals
Results
78.0ms642×body80valid

simplify3.3s

Counts
1 → 1
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
018656
153646
2172621
3566621
42092621
done5002621

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

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))
0.0b
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
0.3b
(pow (fma a a (* b b)) 2.0)
0.9b
(* (* b b) (+ 3.0 a))

rewrite48.0ms

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×pow-unpow unpow-prod-down 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)))
2.0ms
(pow (fma a a (* b b)) 2.0)
44.0ms
(* (* b b) (+ 3.0 a))

series406.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0))
68.0ms
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
176.0ms
(pow (fma a a (* b b)) 2.0)
43.0ms
(* (* b b) (+ 3.0 a))

simplify3.2s

Counts
77 → 77
Iterations

Useful iterations: done (3.2s)

IterNodesCost
013628482
137023769
2221523174
done500023149

prune517.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (* b b) (+ 3.0 a))
0.9b
(* (* b b) (+ 3.0 a))
6.7b
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
6.7b
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
14×add-cbrt-cube add-exp-log
12×add-sqr-sqrt *-un-lft-identity
8×associate-*r* add-cube-cbrt
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:
35.0ms
(* (* b b) (+ 3.0 a))
39.0ms
(* (* b b) (+ 3.0 a))
1.0ms
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
1.0ms
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

series634.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (* b b) (+ 3.0 a))
44.0ms
(* (* b b) (+ 3.0 a))
279.0ms
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
263.0ms
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

simplify1.9s

Counts
94 → 94
Iterations

Useful iterations: done (1.9s)

IterNodesCost
010834444
130331048
2190030514
done500030414

prune814.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.1b

localize93.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (* b b) (+ 3.0 a))
6.7b
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
7.3b
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
7.3b
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt pow1 *-un-lft-identity
9×add-cbrt-cube add-exp-log
8×add-cube-cbrt
6×cbrt-prod
4×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×pow1/3 associate-*r/
1×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 → 67
Calls
4 calls:
32.0ms
(* (* b b) (+ 3.0 a))
1.0ms
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
1.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
1.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (* b b) (+ 3.0 a))
316.0ms
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
363.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
330.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

simplify2.6s

Counts
79 → 79
Iterations

Useful iterations: done (2.6s)

IterNodesCost
016043158
141839782
2219939417
done500038707

prune895.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.1b

localize135.0ms

Local error

Found 4 expressions with local error:

6.7b
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
6.7b
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
6.7b
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
7.3b
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×*-un-lft-identity add-cube-cbrt
7×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×cbrt-prod rem-sqrt-square sqrt-pow1 pow1/2
1×pow1/3
Counts
4 → 58
Calls
4 calls:
1.0ms
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
1.0ms
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
1.0ms
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
1.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
261.0ms
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
270.0ms
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
260.0ms
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
375.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

simplify1.8s

Counts
70 → 70
Iterations

Useful iterations: done (1.8s)

IterNodesCost
011646391
125743927
276543631
3341442971
done500042946

prune522.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 0.1b

regimes519.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
016621
118621
done18621

end0.0ms

sample3.3s

Algorithm
intervals
Results
2.7s20748×body80valid