Details

Time bar (total: 2.5m)

sample76.0ms

Algorithm
intervals
Results
16.0ms136×body160valid
14.0ms528×pre80true
13.0ms272×body80nan
5.0ms120×body80valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune5.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.3b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
28.2b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite28.0ms

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:
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
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))))

series65.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(- (* b b) (* (* 4.0 a) c))
25.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
17.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify44.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0396773
11550683
25001673

prune342.0ms

Filtered
82 candidates to 63 candidates (23.2%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New78482
Fresh000
Picked011
Done000
Total78583

Merged error: 0.3b

Counts
83 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.4b
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
82×add-sqr-sqrt *-un-lft-identity
38×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
11×distribute-rgt-neg-in sqrt-prod
10×add-log-exp
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 div-inv
3×diff-log associate-/l/
2×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 151
Calls
4 calls:
8.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series126.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
45.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
57.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify111.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
06432666
132102408
250012396

prune1.1s

Filtered
163 candidates to 106 candidates (35.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New15310163
Fresh303
Picked101
Done101
Total15810168

Merged error: 0.0b

Counts
168 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.3b
(/ (* 2.0 a) (* 4.0 (* a c)))
0.3b
(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
152×add-exp-log
92×add-cbrt-cube
73×prod-exp
46×div-exp
41×cbrt-unprod
26×cbrt-undiv
14×add-sqr-sqrt
12×*-un-lft-identity
9×pow1
8×add-cube-cbrt rec-exp 1-exp
7×associate-*r*
6×add-log-exp
5×flip3-- times-frac associate-*l* associate-/r/ flip--
4×frac-times associate-*r/ associate-/l*
3×sub-neg div-inv
2×distribute-rgt-in pow-flip frac-2neg distribute-lft-in pow-prod-down associate-*l/ clear-num associate-/r* distribute-lft-out-- difference-of-squares
1×distribute-rgt-neg-in diff-log sqrt-prod *-commutative inv-pow unswap-sqr
Counts
4 → 139
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
7.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
20.0ms
(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series83.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
46.0ms
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
2.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
26.0ms
(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify40.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08162127
150011586

prune497.0ms

Filtered
151 candidates to 72 candidates (52.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1501151
Fresh279
Picked011
Done000
Total1529161

Merged error: 0.0b

Counts
161 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite952.0ms

Algorithm
rewrite-expression-head
Rules
20548×times-frac
9815×add-sqr-sqrt *-un-lft-identity
7499×add-cube-cbrt
1158×distribute-lft-out-- difference-of-squares
879×div-inv
621×associate-/l*
579×distribute-rgt-neg-in sqrt-prod
200×add-exp-log
169×div-exp
129×associate-/r/
54×add-cbrt-cube
37×cbrt-undiv
30×rec-exp 1-exp
20×associate-/r*
10×add-log-exp
4×pow1
3×flip3-- diff-log flip--
2×sub-neg frac-2neg clear-num associate-/l/
1×associate--l- neg-sub0 neg-log
Counts
4 → 5377
Calls
4 calls:
24.0ms
(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))
182.0ms
(/ (/ (/ 1 (/ 2.0 4.0)) (/ 1 c)) (- (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))

series82.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))
48.0ms
(/ (/ (/ 1 (/ 2.0 4.0)) (/ 1 c)) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
15.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(- (* b b) (* (* 4.0 a) c))

simplify1.3s

Algorithm
egg-herbie
Counts
5389 → 5389
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
05494146352

prune2.4m

Filtered
5389 candidates to 2864 candidates (46.9%)

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