Details

Time bar (total: 28.2s)

sample161.0ms

Algorithm
intervals
Results
86.0ms684×body80valid

simplify3.9s

Counts
1 → 1
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
01829
15327
217226
355426
4211326
done500126

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize51.0ms

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
(* (* b b) (+ 3.0 a))
0.4b
(pow (fma a a (* b b)) 2.0)

rewrite90.0ms

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:
1.0ms
(fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0))
1.0ms
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
79.0ms
(* (* b b) (+ 3.0 a))
6.0ms
(pow (fma a a (* b b)) 2.0)

series548.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0))
89.0ms
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
66.0ms
(* (* b b) (+ 3.0 a))
221.0ms
(pow (fma a a (* b b)) 2.0)

simplify3.9s

Counts
77 → 77
Iterations

Useful iterations: done (3.9s)

IterNodesCost
01361157
13641101
22156971
done5001969

prune708.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize79.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0))) (cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0))))
7.8b
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
7.8b
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
7.8b
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
23.0ms
(* (cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0))) (cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0))))
2.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
2.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
2.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

series1.8s

Counts
4 → 12
Calls
4 calls:
474.0ms
(* (cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0))) (cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0))))
434.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
437.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
441.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

simplify1.5s

Counts
93 → 93
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01504505
13444244
211043844
done50003219

prune1.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize109.0ms

Local error

Found 4 expressions with local error:

7.2b
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
7.2b
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
7.8b
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
7.8b
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

rewrite12.0ms

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:
3.0ms
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
3.0ms
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
2.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
2.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

series1.5s

Counts
4 → 12
Calls
4 calls:
357.0ms
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
326.0ms
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
384.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
389.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

simplify2.5s

Counts
68 → 68
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01162294
12572156
27451972
332331906
done50001904

prune874.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize86.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (fma a a (* b b)) 2.0)
0.9b
(pow (sqrt (cbrt (fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (pow (fma a a (* b b)) 2.0)))) (+ 3 1))
7.8b
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
7.8b
(cbrt (fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (pow (fma a a (* b b)) 2.0)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×add-sqr-sqrt add-cube-cbrt unpow-prod-down
9×cbrt-prod
7×pow1 pow-unpow
6×add-exp-log sqrt-prod
5×pow-pow
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
2×pow-to-exp sqrt-pow1 pow-exp sqr-pow
1×unpow-prod-up pow1/2 sqrt-pow2 distribute-lft-out
Counts
4 → 76
Calls
4 calls:
4.0ms
(pow (fma a a (* b b)) 2.0)
16.0ms
(pow (sqrt (cbrt (fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (pow (fma a a (* b b)) 2.0)))) (+ 3 1))
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 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (pow (fma a a (* b b)) 2.0)))

series1.5s

Counts
4 → 12
Calls
4 calls:
203.0ms
(pow (fma a a (* b b)) 2.0)
551.0ms
(pow (sqrt (cbrt (fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (pow (fma a a (* b b)) 2.0)))) (+ 3 1))
393.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
397.0ms
(cbrt (fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (pow (fma a a (* b b)) 2.0)))

simplify1.2s

Counts
88 → 88
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02172902
15552698
216212419
done50012241

prune1.2s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes490.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01626
11826
done1826

end0.0ms

sample4.8s

Algorithm
intervals
Results
3.8s20353×body80valid