Details

Time bar (total: 3.5s)

analyze146.0ms (4.2%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
25%74.9%0.1%5
25%68.7%6.3%6
25%56.2%18.8%7
25%48.4%26.6%8
25%35.1%39.9%9
28.1%18.3%53.6%10
31.6%12.3%56.1%11
33.4%5.9%60.8%12
35.2%3.8%61%13
36.1%2.9%61%14

sample25.0ms (0.7%)

Algorithm
1×intervals
Results
17.0ms256×body80valid

simplify86.0ms (2.5%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (84.0ms)

IterNodesCost
0490631
1490631

prune7.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 0.2b

Counts
2 → 1

localize17.0ms (0.5%)

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)))

rewrite33.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
10×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt
7×associate-*r*
6×pow-prod-down prod-exp cbrt-unprod add-log-exp
4×associate-*r/
3×distribute-rgt-in unpow-prod-down pow-unpow distribute-lft-in
2×sub-neg associate-+r+ flip3-+ associate-*l* *-commutative flip-+ unswap-sqr
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out sqr-pow
Counts
4 → 77
Calls

4 calls:

10.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
8.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
8.0ms
(* (* a a) (+ 1.0 a))
5.0ms
(pow (+ (* a a) (* b b)) 2.0)

series57.0ms (1.7%)

Counts
4 → 12
Calls

4 calls:

24.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
21.0ms
(pow (+ (* a a) (* b b)) 2.0)
7.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
5.0ms
(* (* a a) (+ 1.0 a))

simplify31.0ms (0.9%)

Algorithm
1×egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
058811271

prune218.0ms (6.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New83689
Fresh000
Picked101
Done000
Total84690

Merged error: 0b

Counts
90 → 6

localize24.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (* b (* b (- 1.0 (* 3.0 a))))) (cbrt (* b (* b (- 1.0 (* 3.0 a))))))
24.3b
(cbrt (* b (* b (- 1.0 (* 3.0 a)))))
24.3b
(cbrt (* b (* b (- 1.0 (* 3.0 a)))))
24.3b
(cbrt (* b (* b (- 1.0 (* 3.0 a)))))

rewrite26.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Rules
38×associate-*r/
18×cbrt-div
11×pow1
10×add-sqr-sqrt
9×flip3-- pow1/3 flip--
8×add-cube-cbrt *-un-lft-identity
7×cbrt-prod
6×add-exp-log
4×frac-times swap-sqr associate-*r* associate-*l* add-cbrt-cube add-log-exp
2×pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 72
Calls

4 calls:

7.0ms
(* (cbrt (* b (* b (- 1.0 (* 3.0 a))))) (cbrt (* b (* b (- 1.0 (* 3.0 a))))))
6.0ms
(cbrt (* b (* b (- 1.0 (* 3.0 a)))))
5.0ms
(cbrt (* b (* b (- 1.0 (* 3.0 a)))))
5.0ms
(cbrt (* b (* b (- 1.0 (* 3.0 a)))))

series84.0ms (2.4%)

Counts
4 → 12
Calls

4 calls:

23.0ms
(* (cbrt (* b (* b (- 1.0 (* 3.0 a))))) (cbrt (* b (* b (- 1.0 (* 3.0 a))))))
22.0ms
(cbrt (* b (* b (- 1.0 (* 3.0 a)))))
20.0ms
(cbrt (* b (* b (- 1.0 (* 3.0 a)))))
19.0ms
(cbrt (* b (* b (- 1.0 (* 3.0 a)))))

simplify47.0ms (1.4%)

Algorithm
1×egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
050191763

prune357.0ms (10.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New84084
Fresh055
Picked011
Done000
Total84690

Merged error: 0b

Counts
90 → 6

localize31.0ms (0.9%)

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a))))))) (cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a))))))))
11.0b
(cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))
11.0b
(cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))
11.0b
(cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))

rewrite40.0ms (1.2%)

Algorithm
1×rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×flip3-+ pow1/3 flip-+
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 87
Calls

4 calls:

17.0ms
(* (cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a))))))) (cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a))))))))
7.0ms
(cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))
7.0ms
(cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))
7.0ms
(cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))

series207.0ms (6%)

Counts
4 → 12
Calls

4 calls:

59.0ms
(* (cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a))))))) (cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a))))))))
50.0ms
(cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))
50.0ms
(cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))
48.0ms
(cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))

simplify60.0ms (1.7%)

Algorithm
1×egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
050824803

prune644.0ms (18.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New99099
Fresh044
Picked011
Done011
Total996105

Merged error: 0b

Counts
105 → 6

localize26.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ (* b b) (* a a))) (cbrt (+ (* b b) (* a a))))
11.1b
(cbrt (+ (* b b) (* a a)))
11.1b
(cbrt (+ (* b b) (* a a)))
11.1b
(cbrt (+ (* b b) (* a a)))

rewrite26.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×flip3-+ pow1/3 flip-+
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 87
Calls

4 calls:

12.0ms
(* (cbrt (+ (* b b) (* a a))) (cbrt (+ (* b b) (* a a))))
4.0ms
(cbrt (+ (* b b) (* a a)))
4.0ms
(cbrt (+ (* b b) (* a a)))
4.0ms
(cbrt (+ (* b b) (* a a)))

series87.0ms (2.5%)

Counts
4 → 12
Calls

4 calls:

25.0ms
(* (cbrt (+ (* b b) (* a a))) (cbrt (+ (* b b) (* a a))))
21.0ms
(cbrt (+ (* b b) (* a a)))
21.0ms
(cbrt (+ (* b b) (* a a)))
21.0ms
(cbrt (+ (* b b) (* a a)))

simplify60.0ms (1.7%)

Algorithm
1×egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
048721309
148721309

prune245.0ms (7.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New99099
Fresh033
Picked011
Done022
Total996105

Merged error: 0b

Counts
105 → 6

regimes173.0ms (5%)

Accuracy

Total 0.2b remaining (91.2%)

Threshold costs 0.2b (91.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06754
16754

end0.0ms (0%)

sample692.0ms (20.1%)

Algorithm
1×intervals
Results
548.0ms8000×body80valid
0.0ms6×body80invalid

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