Details

Time bar (total: 48.7s)

sample122.0ms

Algorithm
intervals
Results
82.0ms631×body80valid

simplify5.9s

Counts
1 → 1
Iterations
IterNodes
done5000
41809
3551
2177
155
019

prune48.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize222.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 4.0 (fma (* a a) (+ a 1.0) (* (* b b) (- 1.0 (* 3.0 a)))) (- (pow (fma b b (* a a)) 2.0) 1.0))
0.1b
(fma (* a a) (+ a 1.0) (* (* b b) (- 1.0 (* 3.0 a))))
0.3b
(pow (fma b b (* a a)) 2.0)
0.5b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt pow1 add-exp-log
9×*-un-lft-identity add-cbrt-cube add-cube-cbrt
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow-unpow unpow-prod-down associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg associate-*r/ fma-udef
1×pow-to-exp pow-pow flip3-- associate-*l* pow-exp *-commutative flip-- unswap-sqr sqr-pow
Counts
4 → 76
Calls
4 calls:
3.0ms
(fma 4.0 (fma (* a a) (+ a 1.0) (* (* b b) (- 1.0 (* 3.0 a)))) (- (pow (fma b b (* a a)) 2.0) 1.0))
3.0ms
(fma (* a a) (+ a 1.0) (* (* b b) (- 1.0 (* 3.0 a))))
13.0ms
(pow (fma b b (* a a)) 2.0)
133.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series710.0ms

Counts
4 → 12
Calls
4 calls:
197.0ms
(fma 4.0 (fma (* a a) (+ a 1.0) (* (* b b) (- 1.0 (* 3.0 a)))) (- (pow (fma b b (* a a)) 2.0) 1.0))
114.0ms
(fma (* a a) (+ a 1.0) (* (* b b) (- 1.0 (* 3.0 a))))
310.0ms
(pow (fma b b (* a a)) 2.0)
89.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify3.8s

Counts
88 → 88
Iterations
IterNodes
done5000
21308
1413
0163

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize181.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b
(* (* a a) (+ 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.5b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite517.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-sqr-sqrt *-un-lft-identity add-cbrt-cube
12×add-cube-cbrt
7×distribute-rgt-in fma-def distribute-lft-in associate-*r*
6×unpow-prod-down prod-diff pow-prod-down prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u associate-*r/ insert-posit16 log1p-expm1-u
3×pow-unpow
2×associate-+r+ sub-neg flip3-+ associate-*l* *-commutative flip-+ unswap-sqr sqr-pow
1×pow-to-exp +-commutative sum-log pow-pow flip3-- pow-exp flip-- distribute-lft-out
Counts
4 → 104
Calls
4 calls:
239.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
113.0ms
(* (* a a) (+ 1.0 a))
48.0ms
(pow (+ (* a a) (* b b)) 2.0)
104.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series806.0ms

Counts
4 → 12
Calls
4 calls:
305.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
98.0ms
(* (* a a) (+ 1.0 a))
287.0ms
(pow (+ (* a a) (* b b)) 2.0)
116.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify4.9s

Counts
116 → 116
Iterations
IterNodes
done5008
22281
1588
0205

prune1.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize357.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* b b) (- 1.0 (* 3.0 a)))
16.9b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
16.9b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
16.9b
(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite211.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
14×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
9×pow1 unpow-prod-down add-cbrt-cube add-exp-log
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 associate-*r* pow-prod-down prod-exp cbrt-unprod sqr-pow
2×sub-neg associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 88
Calls
4 calls:
93.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
35.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
43.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
33.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
117.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
443.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
490.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
442.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify8.4s

Counts
100 → 100
Iterations
IterNodes
done5000
33733
2973
1324
0134

prune1.7s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize518.0ms

Local error

Found 4 expressions with local error:

9.1b
(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
9.1b
(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
16.9b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
16.9b
(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
34×cbrt-prod
18×unpow-prod-down
14×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×sqrt-prod
4×expm1-log1p-u pow1 add-cbrt-cube pow1/3 add-exp-log insert-posit16 log1p-expm1-u add-log-exp sqr-pow
Counts
4 → 78
Calls
4 calls:
51.0ms
(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
51.0ms
(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
43.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
43.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
454.0ms
(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
497.0ms
(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
390.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
473.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify5.3s

Counts
90 → 90
Iterations
IterNodes
done5000
42268
3816
2342
1178
0103

prune1.6s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes1.7s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify19.0ms

Iterations
IterNodes
done27
127
019

end0.0ms

sample5.1s

Algorithm
intervals
Results
4.3s20836×body80valid