Details

Time bar (total: 18.3s)

sample136.0ms

Algorithm
intervals
Results
114.0ms630×body80valid

simplify634.0ms

Counts
1 → 1

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

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))

rewrite53.0ms

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
51.0ms
(* (+ (* -12 a) 4) b)
1.0ms
(fma (fma b b (* a a)) (fma b b (* a a)) -1)
1.0ms
(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))

series386.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
117.0ms
(fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))
106.0ms
(fma (fma b b (* a a)) (fma b b (* a a)) -1)
103.0ms
(fma (* a a) a (* a a))
60.0ms
(* (+ (* -12 a) 4) b)

simplify1.0s

Counts
68 → 68

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize44.0ms

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)))))

rewrite237.0ms

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
127.0ms
(* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))
50.0ms
(* (* b b) (- 1 (* 3 a)))
42.0ms
(* (* a a) (+ 1 a))
16.0ms
(pow (+ (* a a) (* b b)) 2)

series258.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
82.0ms
(* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))
70.0ms
(* (* a a) (+ 1 a))
64.0ms
(* (* b b) (- 1 (* 3 a)))
41.0ms
(pow (+ (* a a) (* b b)) 2)

simplify361.0ms

Counts
140 → 123

prune1.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize70.0ms

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)))

rewrite22.0ms

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
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))))
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)))

series922.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
297.0ms
(* (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))))
214.0ms
(cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
209.0ms
(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)))

simplify690.0ms

Counts
111 → 97

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize128.0ms

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 (* (* (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)))) (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 (* (* (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)))) (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)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
27×cbrt-prod
17×add-cube-cbrt
16×*-un-lft-identity
13×pow1
12×associate-*r*
10×pow1/3 associate-*l*
8×add-exp-log
7×swap-sqr
6×unswap-sqr
4×expm1-log1p-u add-cbrt-cube pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
2×prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod
1×pow2 pow-plus pow3 rem-cbrt-cube
Counts
4 → 98
Calls
4 calls:
Slowest
27.0ms
(* (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))))
24.0ms
(* (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)))) (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))))
18.0ms
(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)))) (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)))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
309.0ms
(* (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)))) (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))))
291.0ms
(* (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))))
221.0ms
(cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
215.0ms
(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)))) (cbrt (fma (fma (* a a) a (* a a)) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))))

simplify605.0ms

Counts
121 → 110

prune1.9s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes717.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample4.5s

Algorithm
intervals
Results
4.1s20659×body80valid