Details

Time bar (total: 19.9s)

sample167.0ms

Algorithm
intervals
Results
140.0ms630×body80valid

simplify758.0ms

Counts
1 → 1

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.1b
(fma (* a a) a (* a a))
0.1b
(* (+ (* -12 a) 4) b)
0.0b
(fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* associate-*l* fma-udef
2×associate-*l/
1×flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 56
Calls
4 calls:
Slowest
20.0ms
(* (+ (* -12 a) 4) b)
0.0ms
(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.0ms
(fma (* a a) a (* a a))
0.0ms
(fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))

series384.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
146.0ms
(fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))
97.0ms
(fma (fma b b (* a a)) (fma b b (* a a)) -1)
94.0ms
(fma (* a a) a (* a a))
46.0ms
(* (+ (* -12 a) 4) b)

simplify1.1s

Counts
68 → 68

prune821.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (* b b) (- 1 (* 3 a)))
0.3b
(pow (+ (* a a) (* b b)) 2)
0.1b
(* (* a a) (+ 1 a))
0.0b
(* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
18×associate-*r/
17×pow1 add-exp-log
16×add-sqr-sqrt add-cbrt-cube
14×*-un-lft-identity
12×add-cube-cbrt
10×associate-*r*
7×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp cbrt-unprod
6×prod-diff
5×associate-*l*
4×expm1-log1p-u flip3-+ frac-add flip-+ insert-posit16 log1p-expm1-u add-log-exp
3×pow-unpow unpow-prod-down flip3-- *-commutative flip-- unswap-sqr
2×sub-neg
1×pow-to-exp pow-pow pow-exp distribute-lft-out unpow2 sqr-pow
Counts
4 → 111
Calls
4 calls:
Slowest
90.0ms
(* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))
36.0ms
(* (* a a) (+ 1 a))
30.0ms
(* (* b b) (- 1 (* 3 a)))
14.0ms
(pow (+ (* a a) (* b b)) 2)

series224.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
61.0ms
(* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))
57.0ms
(* (* b b) (- 1 (* 3 a)))
56.0ms
(* (* a a) (+ 1 a))
50.0ms
(pow (+ (* a a) (* b b)) 2)

simplify308.0ms

Counts
140 → 123

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
0.2b
(cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
0.2b
(cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
0.2b
(cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 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 → 85
Calls
4 calls:
Slowest
8.0ms
(* (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
1.0ms
(cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
1.0ms
(cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
1.0ms
(cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))

series916.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
298.0ms
(* (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
215.0ms
(cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
202.0ms
(cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
201.0ms
(cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))

simplify760.0ms

Counts
111 → 97

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize86.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
0.2b
(cbrt (* (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))))
0.2b
(* (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
0.2b
(* (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
42×cbrt-prod
38×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
18×pow1
14×pow1/3
12×swap-sqr associate-*r* associate-*l*
8×add-exp-log unswap-sqr
4×expm1-log1p-u add-cbrt-cube pow-prod-down pow-sqr pow-prod-up insert-posit16 log1p-expm1-u add-log-exp
2×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 115
Calls
4 calls:
Slowest
28.0ms
(* (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
16.0ms
(* (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
8.0ms
(cbrt (* (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))))
2.0ms
(cbrt (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
283.0ms
(cbrt (* (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))))
276.0ms
(* (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
273.0ms
(* (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
246.0ms
(cbrt (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))

simplify620.0ms

Counts
148 → 127

prune2.4s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes808.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch4.0ms

end0.0ms

sample5.9s

Algorithm
intervals
Results
5.4s20659×body80valid