Details

Time bar (total: 3.0s)

analyze1.1s

Algorithm
search
sampling

Space saved by range analysis: 0.146413%

Space saved by search: 25.557761%

Guaranteed chance to sample good point: 84.788571%

sample36.0ms

Algorithm
intervals
Results
22.0ms256×body80valid
1.0ms16×body80invalid
1.0ms16×body80nan

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03818
17918
213618
316118
417318
517718
617718

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 21.0b

Counts
2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.1b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×add-sqr-sqrt add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log sqrt-div add-cbrt-cube
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 diff-log neg-log sum-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative associate--l- associate-+l- sub-neg flip3-+ flip-+
Counts
4 → 63
Calls
4 calls:
8.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series66.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify116.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (106.0ms)

IterNodesCost
0248644
1898606
23865590
35001586

prune182.0ms

Filtered
60 candidates to 75 candidates (-25.0%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New70575
Fresh000
Picked101
Done000
Total71576

Merged error: 7.9b

Counts
76 → 5

localize29.0ms

Local error

Found 4 expressions with local error:

7.5b
(+ (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
23.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0b
(cbrt (- (* b b) (* (* 4.0 a) c)))
24.0b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
7×add-cube-cbrt *-un-lft-identity
6×cbrt-prod
5×pow1
4×add-exp-log cbrt-div add-cbrt-cube
3×flip3-- sqrt-prod flip--
2×pow1/3 sqrt-div sum-log
1×+-commutative neg-sub0 associate-+l- rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 54
Calls
4 calls:
4.0ms
(+ (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series99.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
26.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify44.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0382835
11434761
25002721

prune221.0ms

Filtered
60 candidates to 66 candidates (-10.0%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New66066
Fresh044
Picked011
Done000
Total66571

Merged error: 7.9b

Counts
71 → 5

localize27.0ms

Local error

Found 4 expressions with local error:

23.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- add-log-exp
Counts
4 → 60
Calls
4 calls:
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series55.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify66.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (60.0ms)

IterNodesCost
0127536
1460520
21957516
35001512

prune243.0ms

Filtered
60 candidates to 72 candidates (-20.0%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New72072
Fresh033
Picked011
Done011
Total72577

Merged error: 7.9b

Counts
77 → 5

localize28.0ms

Local error

Found 4 expressions with local error:

1.1b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.7b
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
6.0b
(/ (* a c) b)
23.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
13×*-un-lft-identity
10×add-sqr-sqrt
9×add-cube-cbrt
8×add-log-exp
6×times-frac
5×pow1
4×cbrt-undiv div-exp associate-/r* associate-/l*
3×sqrt-prod
2×flip3-- frac-2neg sqrt-div prod-exp clear-num sum-log flip-- cbrt-unprod div-inv associate-/l/ distribute-lft-out
1×+-commutative neg-sub0 associate-+l- rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 div-sub neg-log flip-+
Counts
4 → 75
Calls
4 calls:
7.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
4.0ms
(/ (* a c) b)
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series47.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
5.0ms
(/ (* a c) b)
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify56.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0483657
12202575
25002570

prune145.0ms

Filtered
66 candidates to 87 candidates (-31.8%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New85287
Fresh022
Picked101
Done022
Total86692

Merged error: 6.8b

Counts
92 → 6

regimes244.0ms

bsearch2.0ms

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