Details

Time bar (total: 4.7s)

sample41.0ms

Algorithm
intervals
Results
19.0ms274×body80valid
6.0ms89×body80nan

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03818
17918
213618
316118
417318
517718
617718

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: 19.2b

Counts
2 → 1

localize117.0ms

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))))
23.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite26.0ms

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))))
9.0ms
(- (neg b) (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)))

series298.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
77.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify116.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (108.0ms)

IterNodesCost
0246646
1890606
23700588
35001584

prune266.0ms

Filtered
75 candidates to 60 candidates (80.0%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New69675
Fresh000
Picked101
Done000
Total70676

Merged error: 8.4b

Counts
76 → 6

localize117.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.1b
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
7.0b
(/ (* a c) b)
23.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

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 associate-/r*
5×pow1
4×cbrt-undiv div-exp sqrt-prod
3×flip3-- flip--
2×frac-2neg sqrt-div diff-log prod-exp clear-num associate-/r/ 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 neg-log
Counts
4 → 77
Calls
4 calls:
9.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
5.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series241.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
19.0ms
(/ (* a c) b)
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify55.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0450688
12176609
25001606

prune283.0ms

Filtered
89 candidates to 65 candidates (73.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New85489
Fresh235
Picked101
Done000
Total88795

Merged error: 6.6b

Counts
95 → 7

localize122.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.1b
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
3.2b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
23.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite53.0ms

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-- associate-/r* flip-- div-inv
2×sqrt-div diff-log associate-/r/ 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 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 115
Calls
4 calls:
9.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
16.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series301.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
101.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
53.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify92.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
07461376
137511199
250021152

prune493.0ms

Filtered
127 candidates to 91 candidates (71.7%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1216127
Fresh156
Picked101
Done000
Total12311134

Merged error: 6.6b

Counts
134 → 11

localize137.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b))))) (/ (cbrt c) (cbrt (cbrt b))))
1.6b
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))))
3.1b
(/ (* 2.0 c) (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b))))) (/ (cbrt c) (cbrt (cbrt b))))) (* 2 b)))
23.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
266×add-exp-log
132×add-cbrt-cube
129×prod-exp cbrt-unprod
84×cbrt-undiv div-exp
81×cbrt-prod
65×times-frac
63×associate-*r*
54×add-sqr-sqrt
47×add-cube-cbrt *-un-lft-identity
12×pow1
8×associate-*l*
6×frac-times associate-*l/
4×associate-*r/ pow-prod-down div-inv add-log-exp unswap-sqr
3×associate-/r* sqrt-prod
2×flip3-- sqrt-div associate-/r/ *-commutative flip--
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l*
Counts
4 → 236
Calls
4 calls:
54.0ms
(* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b))))) (/ (cbrt c) (cbrt (cbrt b))))
18.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))))
30.0ms
(/ (* 2.0 c) (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b))))) (/ (cbrt c) (cbrt (cbrt b))))) (* 2 b)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series374.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b))))) (/ (cbrt c) (cbrt (cbrt b))))
213.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))))
67.0ms
(/ (* 2.0 c) (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b))))) (/ (cbrt c) (cbrt (cbrt b))))) (* 2 b)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify69.0ms

Algorithm
egg-herbie
Counts
248 → 248
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
015405663
150014366

prune1.0s

Filtered
248 candidates to 159 candidates (64.1%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New2462248
Fresh2810
Picked101
Done000
Total24910259

Merged error: 6.6b

Counts
259 → 10

regimes267.0ms

bsearch7.0ms

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