Details

Time bar (total: 31.4s)

sample89.0ms

Algorithm
intervals
Results
65.0ms656×body80valid

simplify6.5s

Counts
1 → 1
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
01931
15529
217828
354528
4167228
5479728
done500028

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
0.1b
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
0.3b
(pow (fma a a (* b b)) 2.0)
0.4b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite72.0ms

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:
1.0ms
(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
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
6.0ms
(pow (fma a a (* b b)) 2.0)
61.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series510.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
95.0ms
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
192.0ms
(pow (fma a a (* b b)) 2.0)
73.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify3.6s

Counts
84 → 84
Iterations

Useful iterations: 3 (1.9s)

IterNodesCost
01601452
13771411
211451221
342491207
done50001207

prune462.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (* (* b b) (- 1.0 (* 3.0 a)))) (cbrt (* (* b b) (- 1.0 (* 3.0 a)))))
23.7b
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))
23.7b
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))
23.7b
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
20×associate-*r/
18×cbrt-div
11×pow1
10×add-sqr-sqrt
9×flip3-- pow1/3 flip--
8×add-cube-cbrt *-un-lft-identity
7×cbrt-prod
6×add-exp-log
4×expm1-log1p-u frac-times swap-sqr associate-*r* associate-*l* add-cbrt-cube log1p-expm1-u add-log-exp
2×pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 80
Calls
4 calls:
63.0ms
(* (cbrt (* (* b b) (- 1.0 (* 3.0 a)))) (cbrt (* (* b b) (- 1.0 (* 3.0 a)))))
27.0ms
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))
27.0ms
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))
26.0ms
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))

series1.1s

Counts
4 → 12
Calls
4 calls:
349.0ms
(* (cbrt (* (* b b) (- 1.0 (* 3.0 a)))) (cbrt (* (* b b) (- 1.0 (* 3.0 a)))))
217.0ms
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))
250.0ms
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))
263.0ms
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))

simplify2.9s

Counts
92 → 92
Iterations

Useful iterations: done (2.9s)

IterNodesCost
01992658
14812451
214332240
349461858
done50001849

prune830.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* b b) (- 1.0 (* 3.0 a)))
0.4b
(* (* b b) (- 1.0 (* 3.0 a)))
8.9b
(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)))
8.9b
(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)))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1 add-sqr-sqrt
14×add-exp-log add-cbrt-cube
12×add-cube-cbrt *-un-lft-identity prod-diff
10×distribute-rgt-in distribute-lft-in
6×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×expm1-log1p-u sub-neg associate-*r/ log1p-expm1-u add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 96
Calls
4 calls:
43.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
60.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
4.0ms
(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)))
3.0ms
(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)))

series820.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
96.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
348.0ms
(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)))
309.0ms
(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)))

simplify3.9s

Counts
108 → 108
Iterations

Useful iterations: done (3.9s)

IterNodesCost
01302220
13212078
29591844
334121820
done50011748

prune700.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* b b) (- 1.0 (* 3.0 a)))
8.9b
(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)))
9.5b
(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)))
9.5b
(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)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity
9×add-exp-log add-cbrt-cube
6×cbrt-prod prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×sub-neg pow1/3 associate-*r/
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 74
Calls
4 calls:
46.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
3.0ms
(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)))
2.0ms
(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)))
2.0ms
(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)))

series1.1s

Counts
4 → 12
Calls
4 calls:
83.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
264.0ms
(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)))
386.0ms
(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)))
324.0ms
(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)))

simplify3.6s

Counts
86 → 86
Iterations

Useful iterations: done (3.6s)

IterNodesCost
01812406
14352325
212712090
343671968
done50001964

prune662.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes287.0ms

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
01957
12257
done2257

end0.0ms

sample3.8s

Algorithm
intervals
Results
3.3s20728×body80valid