Details

Time bar (total: 2.8s)

sample50.0ms

Algorithm
intervals
Results
11.0ms39×body2560valid
9.0ms175×body80valid
7.0ms100×body80nan
6.0ms27×body1280valid
3.0ms15×body640valid
1.0ms8×body320valid
1.0ms2×body5120valid
0.0ms1×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 35.9b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b
(- (* b b) (* (* 4.0 a) c))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
11.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series291.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
76.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(- (* b b) (* (* 4.0 a) c))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify44.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0405779
11563685
25001674

prune202.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New74882
Fresh000
Picked101
Done000
Total75883

Merged error: 7.4b

Counts
83 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.2b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b
(- (* b b) (* (* 4.0 a) c))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
53×times-frac
45×*-un-lft-identity
26×add-sqr-sqrt
25×add-exp-log add-cube-cbrt
13×add-cbrt-cube
12×div-exp
11×associate-/r*
10×distribute-lft-out add-log-exp
9×associate-/r/
6×pow1
5×cbrt-undiv distribute-rgt-neg-in flip3-+ flip-+ div-inv
3×rec-exp 1-exp prod-exp sqrt-prod associate-/l*
2×flip3-- sqrt-div sum-log flip--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 diff-log neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 114
Calls
4 calls:
13.0ms
(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
10.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series327.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
77.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(- (* b b) (* (* 4.0 a) c))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify66.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05251586
125701373
250011306

prune216.0ms

Filtered
126 candidates to 70 candidates (55.6%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1233126
Fresh257
Picked011
Done000
Total1259134

Merged error: 7.3b

Counts
134 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
1.0b
(- (* b b) (* (* 4.0 a) c))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 54
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series227.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* (* 4.0 a) c))
48.0ms
(- (* b b) (* (* 4.0 a) c))
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify80.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 3 (73.0ms)

IterNodesCost
0149476
1576446
22486444
35001440

prune207.0ms

Filtered
66 candidates to 50 candidates (75.8%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New66066
Fresh077
Picked011
Done011
Total66975

Merged error: 7.3b

Counts
75 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
12.7b
(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log sqrt-div add-cbrt-cube
3×flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 sum-log
1×+-commutative neg-sub0 associate-+l- sub-neg flip3-+ diff-log neg-log flip-+
Counts
4 → 55
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (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)))

series261.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* (* 4.0 a) c))
79.0ms
(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify135.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 3 (127.0ms)

IterNodesCost
0251648
11020537
24512523
35002521

prune196.0ms

Filtered
67 candidates to 54 candidates (80.6%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New67067
Fresh066
Picked011
Done022
Total67976

Merged error: 7.3b

Counts
76 → 9

regimes324.0ms

bsearch7.0ms

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