Details

Time bar (total: 3.8s)

sample42.0ms

Algorithm
intervals
Results
20.0ms286×body80valid
6.0ms94×body80nan

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03518
16618
211618
314418
415918
516118
616118

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: 19.8b

Counts
2 → 1

localize115.0ms

Local error

Found 4 expressions with local error:

0.8b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite29.0ms

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:
7.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series295.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
77.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
65.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify115.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (107.0ms)

IterNodesCost
0246646
1890606
23700588
35001584

prune261.0ms

Filtered
75 candidates to 60 candidates (80.0%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New70575
Fresh000
Picked101
Done000
Total71576

Merged error: 8.7b

Counts
76 → 5

localize118.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.4b
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
7.2b
(/ (* a c) b)
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-sqr-sqrt add-cbrt-cube
13×*-un-lft-identity
9×add-cube-cbrt
8×add-log-exp
6×times-frac
5×pow1
4×cbrt-undiv div-exp associate-/r* sqrt-prod associate-/l*
3×flip3-- flip--
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod div-inv associate-/l/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 div-sub neg-log
Counts
4 → 78
Calls
4 calls:
8.0ms
(- (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)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
81.0ms
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
19.0ms
(/ (* a c) b)
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify57.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0478706
12176625
25001623

prune296.0ms

Filtered
90 candidates to 66 candidates (73.3%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New86490
Fresh134
Picked101
Done000
Total88795

Merged error: 6.8b

Counts
95 → 7

localize114.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2.0 c) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.6b
(- (* b b) (* (* 4.0 a) c))
1.0b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/r*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/r/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
11.0ms
(/ (* 2.0 c) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series370.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(/ (* 2.0 c) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
47.0ms
(- (* b b) (* (* 4.0 a) c))
77.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0362863
11529768
25001759

prune278.0ms

Filtered
88 candidates to 63 candidates (71.6%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New83588
Fresh156
Picked101
Done000
Total851095

Merged error: 6.6b

Counts
95 → 10

localize126.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.4b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.4b
(/ (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)) (* 2.0 a))
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
31×times-frac
30×add-exp-log
26×*-un-lft-identity
23×add-cbrt-cube
22×add-cube-cbrt associate-*r*
11×cbrt-prod
9×cbrt-undiv div-exp prod-exp cbrt-unprod
8×add-log-exp
7×pow1 associate-*l*
6×unswap-sqr
4×sqrt-prod
3×flip3-- flip-- div-inv associate-/l*
2×sqrt-div diff-log associate-/l/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 frac-times sub-neg rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 div-sub associate-*r/ pow-prod-down neg-log associate-*l/ clear-num associate-/r* *-commutative
Counts
4 → 116
Calls
4 calls:
8.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
15.0ms
(/ (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)) (* 2.0 a))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series302.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
52.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
100.0ms
(/ (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)) (* 2.0 a))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify92.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
07751399
136841220
250021172

prune478.0ms

Filtered
128 candidates to 95 candidates (74.2%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1253128
Fresh099
Picked101
Done000
Total12612138

Merged error: 6.6b

Counts
138 → 12

regimes260.0ms

bsearch6.0ms

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