Details

Time bar (total: 21.8s)

sample87.0ms

Algorithm
intervals
Results
58.0ms655×body80valid

simplify3.3s

Counts
1 → 1
Iterations
IterNodes
done5000
42195
3588
2179
155
019

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize38.0ms

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)
0.7b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite167.0ms

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/ 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 → 100
Calls
4 calls:
84.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
34.0ms
(* (* a a) (+ 1.0 a))
16.0ms
(pow (+ (* a a) (* b b)) 2.0)
31.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series430.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
65.0ms
(* (* a a) (+ 1.0 a))
143.0ms
(pow (+ (* a a) (* b b)) 2.0)
64.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify2.7s

Counts
112 → 112
Iterations
IterNodes
done5000
24499
1620
0201

prune611.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (* b b) (- 1.0 (* 3.0 a)))
0.7b
(* (* b b) (- 1.0 (* 3.0 a)))
7.6b
(sqrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma b b (pow a 2)) 2.0)))
7.6b
(sqrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma b b (pow a 2)) 2.0)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt pow1
14×add-cbrt-cube add-exp-log
12×*-un-lft-identity prod-diff add-cube-cbrt
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 sqrt-pow1 flip3-- pow1/2 associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 96
Calls
4 calls:
51.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
41.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
1.0ms
(sqrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma b b (pow a 2)) 2.0)))
1.0ms
(sqrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma b b (pow a 2)) 2.0)))

series704.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
82.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
296.0ms
(sqrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma b b (pow a 2)) 2.0)))
269.0ms
(sqrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma b b (pow a 2)) 2.0)))

simplify1.6s

Counts
108 → 108
Iterations
IterNodes
done5001
22022
1350
0130

prune913.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize110.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (* b b) (- 1.0 (* 3.0 a)))
7.6b
(sqrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma b b (pow a 2)) 2.0)))
7.6b
(sqrt (fma (fma (* (fma a (- 3.0) 1.0) b) b (* (+ a 1.0) (* a a))) 4.0 (pow (fma b b (* a a)) 2.0)))
7.6b
(sqrt (fma (fma (* (fma a (- 3.0) 1.0) b) b (* (+ a 1.0) (* a a))) 4.0 (pow (fma b b (* a a)) 2.0)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×pow1
10×*-un-lft-identity add-cube-cbrt
9×add-cbrt-cube add-exp-log sqrt-prod
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 78
Calls
4 calls:
33.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
1.0ms
(sqrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma b b (pow a 2)) 2.0)))
1.0ms
(sqrt (fma (fma (* (fma a (- 3.0) 1.0) b) b (* (+ a 1.0) (* a a))) 4.0 (pow (fma b b (* a a)) 2.0)))
2.0ms
(sqrt (fma (fma (* (fma a (- 3.0) 1.0) b) b (* (+ a 1.0) (* a a))) 4.0 (pow (fma b b (* a a)) 2.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
97.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
320.0ms
(sqrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma b b (pow a 2)) 2.0)))
319.0ms
(sqrt (fma (fma (* (fma a (- 3.0) 1.0) b) b (* (+ a 1.0) (* a a))) 4.0 (pow (fma b b (* a a)) 2.0)))
314.0ms
(sqrt (fma (fma (* (fma a (- 3.0) 1.0) b) b (* (+ a 1.0) (* a a))) 4.0 (pow (fma b b (* a a)) 2.0)))

simplify1.8s

Counts
90 → 90
Iterations
IterNodes
done5001
22123
1387
0154

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize82.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (* b b) (- 1.0 (* 3.0 a)))
20.2b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
20.2b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
20.2b
(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite70.0ms

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 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 → 84
Calls
4 calls:
26.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
13.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
12.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
16.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

series844.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
241.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
273.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
232.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify1.5s

Counts
96 → 96
Iterations
IterNodes
done5001
21975
1334
0132

prune748.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes219.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done39
239
138
033

end0.0ms

sample3.6s

Algorithm
intervals
Results
2.9s20671×body80valid