Details

Time bar (total: 27.1s)

sample97.0ms

Algorithm
intervals
Results
66.0ms709×body80valid

simplify4.7s

Counts
1 → 1
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
01829
15327
217226
350926
4149726
5357326
done500026

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize44.0ms

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)
0.4b
(* (* b b) (+ 3.0 a))

rewrite67.0ms

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)))
4.0ms
(pow (fma a a (* b b)) 2.0)
59.0ms
(* (* b b) (+ 3.0 a))

series480.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0))
74.0ms
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
207.0ms
(pow (fma a a (* b b)) 2.0)
71.0ms
(* (* b b) (+ 3.0 a))

simplify3.7s

Counts
77 → 77
Iterations

Useful iterations: 3 (2.2s)

IterNodesCost
01361157
13201101
21101970
34265962
done5000962

prune451.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (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))))
11.4b
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
11.4b
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
11.4b
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

rewrite16.0ms

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:
11.0ms
(* (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))))
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)))
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)))

series1.4s

Counts
4 → 12
Calls
4 calls:
376.0ms
(* (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))))
335.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
357.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
319.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

simplify1.7s

Counts
93 → 93
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01504505
13214244
27763844
320063080
done50013009

prune612.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

10.8b
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
10.8b
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
11.4b
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
11.4b
(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
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:
2.0ms
(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
(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)))

series1.2s

Counts
4 → 12
Calls
4 calls:
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)))
291.0ms
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
323.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
275.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

simplify3.1s

Counts
68 → 68
Iterations

Useful iterations: 4 (2.2s)

IterNodesCost
01162294
12562156
26111972
316601860
446401826
done50001826

prune418.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* b b) (+ 3.0 a))
0.8b
(pow (sqrt (cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))) 4)
11.4b
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
11.4b
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×add-sqr-sqrt
11×pow1 add-cube-cbrt
10×add-exp-log
9×cbrt-prod unpow-prod-down add-cbrt-cube
6×sqrt-prod
4×expm1-log1p-u pow-pow associate-*r* log1p-expm1-u add-log-exp
3×pow-unpow pow1/3 pow-prod-down prod-exp cbrt-unprod
2×sqrt-pow1 associate-*r/
1×distribute-rgt-in pow-to-exp distribute-lft-in flip3-+ pow1/2 associate-*l* pow-exp *-commutative sqrt-pow2 flip-+ distribute-lft-out unswap-sqr sqr-pow
Counts
4 → 81
Calls
4 calls:
36.0ms
(* (* b b) (+ 3.0 a))
5.0ms
(pow (sqrt (cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))) 4)
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)))

series1.2s

Counts
4 → 12
Calls
4 calls:
59.0ms
(* (* b b) (+ 3.0 a))
510.0ms
(pow (sqrt (cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))) 4)
266.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
338.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

simplify3.5s

Counts
93 → 93
Iterations

Useful iterations: 3 (2.1s)

IterNodesCost
02112776
14982653
214692329
349282093
done50002093

prune629.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes207.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01626
11826
done1826

end0.0ms

sample3.4s

Algorithm
intervals
Results
2.7s20340×body80valid