Details

Time bar (total: 22.2s)

sample137.0ms

Algorithm
intervals
Results
93.0ms659×body80valid

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
01931
15529
217928
358828
4219528
done500028

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

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)))

rewrite194.0ms

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:
99.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
47.0ms
(* (* a a) (+ 1.0 a))
8.0ms
(pow (+ (* a a) (* b b)) 2.0)
36.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series477.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
57.0ms
(* (* a a) (+ 1.0 a))
165.0ms
(pow (+ (* a a) (* b b)) 2.0)
81.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify2.7s

Counts
112 → 112
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
02011802
16201629
244991447
done50001447

prune681.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.7b
(* (* b b) (- 1.0 (* 3.0 a)))
8.1b
(sqrt (+ (* a a) (* b b)))
8.1b
(sqrt (+ (* a a) (* b b)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
11×pow1
9×*-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×prod-diff sqrt-prod
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ flip-+ hypot-def
1×flip3-- associate-*l* *-commutative fma-udef flip-- unswap-sqr
Counts
4 → 79
Calls
4 calls:
1.0ms
(fma (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
47.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
7.0ms
(sqrt (+ (* a a) (* b b)))
12.0ms
(sqrt (+ (* a a) (* b b)))

series393.0ms

Counts
4 → 12
Calls
4 calls:
211.0ms
(fma (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
68.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
64.0ms
(sqrt (+ (* a a) (* b b)))
50.0ms
(sqrt (+ (* a a) (* b b)))

simplify3.2s

Counts
91 → 91
Iterations

Useful iterations: done (3.2s)

IterNodesCost
01391569
14061171
22708999
done5000979

prune591.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 1.0 (* 3.0 a))
0.0b
(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b
(* (* a a) (+ 1.0 a))
0.7b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log
12×add-cube-cbrt
9×prod-diff
8×add-log-exp
7×distribute-rgt-in fma-def distribute-lft-in associate-*r*
6×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×sub-neg unpow-prod-down fma-neg
2×associate-+r+ flip3-+ flip3-- associate-*l* *-commutative flip-+ flip-- unswap-sqr
1×+-commutative sum-log diff-log distribute-lft-out sqr-pow
Counts
4 → 101
Calls
4 calls:
5.0ms
(- 1.0 (* 3.0 a))
17.0ms
(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
38.0ms
(* (* a a) (+ 1.0 a))
40.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series371.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(- 1.0 (* 3.0 a))
172.0ms
(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
77.0ms
(* (* a a) (+ 1.0 a))
70.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify1.9s

Counts
113 → 113
Iterations

Useful iterations: 2 (836.0ms)

IterNodesCost
01791682
15571582
242771380
done50001380

prune590.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* a a) (+ 1.0 a))
0.2b
(* (sqrt (fma 4.0 (fma (* (- 1.0 (* a 3.0)) b) b (* (* a a) (+ 1.0 a))) (pow (hypot a b) (* 2 2.0)))) (sqrt (fma 4.0 (fma (* (- 1.0 (* a 3.0)) b) b (* (* a a) (+ 1.0 a))) (pow (hypot a b) (* 2 2.0)))))
8.1b
(sqrt (fma 4.0 (fma (* (- 1.0 (* a 3.0)) b) b (* (* a a) (+ 1.0 a))) (pow (hypot a b) (* 2 2.0))))
8.1b
(sqrt (fma 4.0 (fma (* (- 1.0 (* a 3.0)) b) b (* (* a a) (+ 1.0 a))) (pow (hypot a b) (* 2 2.0))))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
26×pow1
24×sqrt-prod
17×*-un-lft-identity
15×add-cube-cbrt
11×add-cbrt-cube add-exp-log
10×sqrt-pow1 pow1/2 associate-*r*
8×swap-sqr
7×associate-*l*
6×pow-prod-down
5×pow-prod-up unswap-sqr
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×pow-sqr
2×rem-sqrt-square associate-*r/ *-commutative
1×pow2 distribute-rgt-in rem-square-sqrt distribute-lft-in flip3-+ pow-plus sqrt-unprod flip-+ distribute-lft-out
Counts
4 → 107
Calls
4 calls:
38.0ms
(* (* a a) (+ 1.0 a))
11.0ms
(* (sqrt (fma 4.0 (fma (* (- 1.0 (* a 3.0)) b) b (* (* a a) (+ 1.0 a))) (pow (hypot a b) (* 2 2.0)))) (sqrt (fma 4.0 (fma (* (- 1.0 (* a 3.0)) b) b (* (* a a) (+ 1.0 a))) (pow (hypot a b) (* 2 2.0)))))
1.0ms
(sqrt (fma 4.0 (fma (* (- 1.0 (* a 3.0)) b) b (* (* a a) (+ 1.0 a))) (pow (hypot a b) (* 2 2.0))))
1.0ms
(sqrt (fma 4.0 (fma (* (- 1.0 (* a 3.0)) b) b (* (* a a) (+ 1.0 a))) (pow (hypot a b) (* 2 2.0))))

series1.1s

Counts
4 → 12
Calls
4 calls:
76.0ms
(* (* a a) (+ 1.0 a))
141.0ms
(* (sqrt (fma 4.0 (fma (* (- 1.0 (* a 3.0)) b) b (* (* a a) (+ 1.0 a))) (pow (hypot a b) (* 2 2.0)))) (sqrt (fma 4.0 (fma (* (- 1.0 (* a 3.0)) b) b (* (* a a) (+ 1.0 a))) (pow (hypot a b) (* 2 2.0)))))
260.0ms
(sqrt (fma 4.0 (fma (* (- 1.0 (* a 3.0)) b) b (* (* a a) (+ 1.0 a))) (pow (hypot a b) (* 2 2.0))))
606.0ms
(sqrt (fma 4.0 (fma (* (- 1.0 (* a 3.0)) b) b (* (* a a) (+ 1.0 a))) (pow (hypot a b) (* 2 2.0))))

simplify2.1s

Counts
119 → 119
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01534534
14183199
225522822
done50002682

prune649.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes138.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02129
12929
done2929

end0.0ms

sample3.4s

Algorithm
intervals
Results
2.7s20551×body80valid