Details

Time bar (total: 11.1s)

sample51.0ms

Algorithm
intervals
Results
33.0ms620×body80valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
01931
15529
215828
344628
4122728
5353928
done500028

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
0.1b
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
0.3b
(pow (fma a a (* b b)) 2.0)
0.6b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-exp-log add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg associate-*r/ fma-udef
1×pow-to-exp flip3-- pow-pow associate-*l* pow-exp *-commutative flip-- unswap-sqr sqr-pow
Counts
4 → 72
Calls
4 calls:
0.0ms
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
3.0ms
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
1.0ms
(pow (fma a a (* b b)) 2.0)
13.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series353.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
106.0ms
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
129.0ms
(pow (fma a a (* b b)) 2.0)
56.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify791.0ms

Counts
84 → 84
Iterations

Useful iterations: 2 (131.0ms)

IterNodesCost
01601452
13881423
215981221
done50011221

prune312.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (* b b) (- 1.0 (* 3.0 a)))
10.2b
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))
10.2b
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))
10.2b
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow1 add-exp-log cbrt-prod add-cbrt-cube
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3 associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 72
Calls
4 calls:
15.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
1.0ms
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))
1.0ms
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))
1.0ms
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))

series537.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
157.0ms
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))
161.0ms
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))
159.0ms
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))

simplify571.0ms

Counts
84 → 84
Iterations

Useful iterations: 2 (108.0ms)

IterNodesCost
01281811
13241794
212171563
done50011563

prune396.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (* b b) (- 1.0 (* 3.0 a)))
10.2b
(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
10.2b
(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
10.2b
(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow1 add-exp-log cbrt-prod add-cbrt-cube
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3 associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 72
Calls
4 calls:
13.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
1.0ms
(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
1.0ms
(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
1.0ms
(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

series873.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
272.0ms
(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
271.0ms
(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
275.0ms
(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

simplify605.0ms

Counts
84 → 84
Iterations

Useful iterations: 2 (119.0ms)

IterNodesCost
01442483
13582463
213332202
done50002202

prune417.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

9.6b
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
9.6b
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
10.2b
(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
10.2b
(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 56
Calls
4 calls:
1.0ms
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
1.0ms
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
1.0ms
(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
1.0ms
(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

series1.0s

Counts
4 → 12
Calls
4 calls:
237.0ms
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
231.0ms
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
279.0ms
(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
268.0ms
(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

simplify1.1s

Counts
68 → 68
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01162438
12522296
26872112
323101994
done50001990

prune377.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes163.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02065
12465
done2465

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.1s20313×body80valid