Details

Time bar (total: 2.3s)

sample49.0ms

Algorithm
intervals
Results
11.0ms39×body2560valid
9.0ms175×body80valid
6.0ms27×body1280valid
5.0ms100×body80nan
3.0ms15×body640valid
1.0ms8×body320valid
1.0ms2×body5120valid
0.0ms1×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune3.0ms

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

localize16.0ms

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))))

rewrite31.0ms

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:
13.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series309.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
82.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms
(- (* b b) (* 4.0 (* a c)))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify51.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0403780
11514685
25002674

prune218.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New73982
Fresh000
Picked101
Done000
Total74983

Merged error: 7.4b

Counts
83 → 9

localize13.0ms

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))))

rewrite39.0ms

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:
18.0ms
(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
8.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series338.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
81.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
49.0ms
(- (* b b) (* 4.0 (* a c)))
68.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify75.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
05211586
125221373
250021306

prune227.0ms

Filtered
126 candidates to 70 candidates (55.6%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1242126
Fresh268
Picked011
Done000
Total1269135

Merged error: 7.3b

Counts
135 → 9

localize15.0ms

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))))

rewrite17.0ms

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))))

series235.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b b) (* 4.0 (* a c)))
48.0ms
(- (* b b) (* 4.0 (* a c)))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify79.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 3 (71.0ms)

IterNodesCost
0145478
1528446
22232444
35002440

prune212.0ms

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

localize3.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify2.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune0.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New000
Fresh066
Picked011
Done022
Total099

Merged error: 7.3b

Counts
9 → 9

regimes333.0ms

bsearch3.0ms

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