Details

Time bar (total: 13.2s)

sample48.0ms

Algorithm
intervals
Results
31.0ms620×body80valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
01829
15327
215226
340726
4103026
5262526
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)
0.7b
(* (* 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)
13.0ms
(* (* b b) (+ 3.0 a))

series271.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0))
46.0ms
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
107.0ms
(pow (fma a a (* b b)) 2.0)
36.0ms
(* (* b b) (+ 3.0 a))

simplify1.2s

Counts
77 → 77
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01361157
13241101
21216970
done5000966

prune253.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* b (+ 3.0 a))
0.1b
(fma (* a a) (- 1.0 a) (* b (* b (+ 3.0 a))))
0.2b
(* b (* b (+ 3.0 a)))
0.3b
(pow (fma a a (* b b)) 2.0)

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1 add-exp-log
11×add-sqr-sqrt *-un-lft-identity add-cbrt-cube
9×add-cube-cbrt
6×associate-*r/ associate-*l*
5×distribute-rgt-in distribute-lft-in associate-*r*
4×expm1-log1p-u pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow
2×flip3-+ *-commutative flip-+
1×pow-to-exp pow-pow pow-exp fma-udef distribute-lft-out unswap-sqr sqr-pow
Counts
4 → 80
Calls
4 calls:
9.0ms
(* b (+ 3.0 a))
0.0ms
(fma (* a a) (- 1.0 a) (* b (* b (+ 3.0 a))))
11.0ms
(* b (* b (+ 3.0 a)))
1.0ms
(pow (fma a a (* b b)) 2.0)

series226.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* b (+ 3.0 a))
43.0ms
(fma (* a a) (- 1.0 a) (* b (* b (+ 3.0 a))))
37.0ms
(* b (* b (+ 3.0 a)))
110.0ms
(pow (fma a a (* b b)) 2.0)

simplify1.8s

Counts
92 → 92
Iterations

Useful iterations: 3 (582.0ms)

IterNodesCost
0138990
1323942
21004833
33584829
done5000829

prune302.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (* b b) (+ 3.0 a))
10.2b
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
10.2b
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
10.2b
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×pow1 add-exp-log cbrt-prod add-sqr-sqrt add-cbrt-cube
8×add-cube-cbrt
4×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
3×pow1/3 pow-prod-down prod-exp cbrt-unprod
2×associate-*r/
1×distribute-rgt-in distribute-lft-in flip3-+ associate-*l* *-commutative flip-+ distribute-lft-out unswap-sqr
Counts
4 → 65
Calls
4 calls:
16.0ms
(* (* b b) (+ 3.0 a))
0.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
0.0ms
(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)))

series746.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* (* b b) (+ 3.0 a))
242.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
239.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
231.0ms
(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
77 → 77
Iterations

Useful iterations: 3 (1.2s)

IterNodesCost
01242134
13102094
210911866
347021710
done50001710

prune335.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite3.0ms

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 (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)))
0.0ms
(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)))

series844.0ms

Counts
4 → 12
Calls
4 calls:
191.0ms
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
194.0ms
(sqrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
232.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))
226.0ms
(cbrt (fma (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)))

simplify684.0ms

Counts
68 → 68
Iterations

Useful iterations: done (682.0ms)

IterNodesCost
01162294
12562156
26441972
319201858
done50011850

prune335.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes157.0ms

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 (0.0ms)

IterNodesCost
01726
12026
done2026

end0.0ms

sample1.3s

Algorithm
intervals
Results
994.0ms20313×body80valid