Details

Time bar (total: 13.9s)

sample148.0ms

Algorithm
intervals
Results
110.0ms678×body80valid

simplify5.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
018656
151656
2153656
3422656
41269656
53070656
done5000656

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize33.0ms

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) (+ 3.0 a)))))
0.1b
(* (* a a) (- 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
1.3b
(* (* b b) (+ 3.0 a))

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
12×add-sqr-sqrt *-un-lft-identity
9×associate-*r*
8×add-cube-cbrt
6×pow-prod-down prod-exp cbrt-unprod add-log-exp
4×distribute-rgt-in distribute-lft-in associate-*r/
3×pow-unpow unpow-prod-down
2×associate-+r+ sub-neg flip3-+ associate-*l* *-commutative flip-+ unswap-sqr
1×pow-to-exp +-commutative sum-log pow-pow flip3-- pow-exp flip-- distribute-lft-out distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 81
Calls
4 calls:
69.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
46.0ms
(* (* a a) (- 1.0 a))
14.0ms
(pow (+ (* a a) (* b b)) 2.0)
50.0ms
(* (* b b) (+ 3.0 a))

series403.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
64.0ms
(* (* a a) (- 1.0 a))
164.0ms
(pow (+ (* a a) (* b b)) 2.0)
46.0ms
(* (* b b) (+ 3.0 a))

simplify1.7s

Counts
93 → 93
Iterations

Useful iterations: 2 (523.0ms)

IterNodesCost
017933677
153727542
2196027062
done500927062

prune425.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize51.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (* b b) (+ 3.0 a))
24.7b
(cbrt (* (* b b) (+ 3.0 a)))
24.7b
(cbrt (* (* b b) (+ 3.0 a)))
24.7b
(cbrt (* (* b b) (+ 3.0 a)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-cbrt-cube add-exp-log
8×associate-*r/
7×*-un-lft-identity
6×add-sqr-sqrt cbrt-div
5×add-cube-cbrt
4×flip3-+ associate-*r* flip-+ add-log-exp
3×cbrt-prod pow1/3 pow-prod-down prod-exp cbrt-unprod
1×distribute-rgt-in distribute-lft-in associate-*l* *-commutative distribute-lft-out unswap-sqr
Counts
4 → 57
Calls
4 calls:
26.0ms
(* (* b b) (+ 3.0 a))
15.0ms
(cbrt (* (* b b) (+ 3.0 a)))
18.0ms
(cbrt (* (* b b) (+ 3.0 a)))
16.0ms
(cbrt (* (* b b) (+ 3.0 a)))

series415.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (* b b) (+ 3.0 a))
124.0ms
(cbrt (* (* b b) (+ 3.0 a)))
126.0ms
(cbrt (* (* b b) (+ 3.0 a)))
129.0ms
(cbrt (* (* b b) (+ 3.0 a)))

simplify1.4s

Counts
69 → 69
Iterations

Useful iterations: done (1.4s)

IterNodesCost
012224980
133420875
2118120475
done500119305

prune445.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize85.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (* b b) (+ 3.0 a))
11.0b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
11.0b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
11.0b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite326.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×cbrt-prod add-sqr-sqrt pow1 add-cbrt-cube add-exp-log
8×add-cube-cbrt
6×cbrt-div
4×flip3-+ associate-*r* flip-+ add-log-exp
3×pow1/3 pow-prod-down prod-exp cbrt-unprod
2×associate-*r/
1×distribute-rgt-in distribute-lft-in associate-*l* *-commutative distribute-lft-out unswap-sqr
Counts
4 → 63
Calls
4 calls:
25.0ms
(* (* b b) (+ 3.0 a))
24.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
25.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
250.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series597.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (* b b) (+ 3.0 a))
187.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
187.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
188.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify1.1s

Counts
75 → 75
Iterations

Useful iterations: done (1.1s)

IterNodesCost
012253165
134647131
2130346971
done500346371

prune452.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.1b

localize102.0ms

Local error

Found 4 expressions with local error:

10.5b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
10.5b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
11.0b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
11.0b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-prod pow1 sqrt-prod
4×cbrt-div flip3-+ add-cbrt-cube sqrt-div add-exp-log flip-+ add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 56
Calls
4 calls:
47.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
47.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
24.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
25.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series734.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
177.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
190.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
191.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify71.0ms

Iterations

Useful iterations: 0 (15.0ms)

IterNodesCost
011459592