Details

Time bar (total: 3.1s)

sample47.0ms

Algorithm
intervals
Results
9.0ms193×body80valid
8.0ms28×body2560valid
7.0ms32×body1280valid
5.0ms109×body80nan
2.0ms13×body640valid
1.0ms10×body320valid
0.0ms1×body5120valid
0.0ms2×body160valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0289
1649
21149
31359
41449
51489
61489

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: 35.5b

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))
0.9b
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
23.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

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-/l*
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-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 77
Calls
4 calls:
13.0ms
(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms
(- (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))))

series292.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
78.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms
(- (* b b) (* 4.0 (* a c)))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0404890
11481801
25001796

prune237.0ms

Filtered
89 candidates to 65 candidates (73.0%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New781189
Fresh000
Picked101
Done000
Total791190

Merged error: 7.9b

Counts
90 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
1.2b
(- (* b b) (* 4.0 (* a c)))
3.9b
(- (/ (neg b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
23.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
12×add-sqr-sqrt
10×times-frac
9×add-exp-log add-cube-cbrt sqrt-prod add-cbrt-cube
8×add-log-exp
6×associate-/l*
5×pow1
4×flip3-- sqrt-div flip--
3×div-inv distribute-lft-out--
2×cbrt-undiv sub-neg diff-log div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-out-- distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* frac-sub cbrt-unprod sub-div difference-of-squares
Counts
4 → 76
Calls
4 calls:
7.0ms
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
4.0ms
(- (* b b) (* 4.0 (* a c)))
20.0ms
(- (/ (neg b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series353.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
43.0ms
(- (* b b) (* 4.0 (* a c)))
112.0ms
(- (/ (neg b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
68.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0419882
11458817
25001806

prune220.0ms

Filtered
88 candidates to 68 candidates (77.3%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New85388
Fresh4610
Picked011
Done000
Total891099

Merged error: 7.9b

Counts
99 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.9b
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
23.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
19×add-sqr-sqrt
16×*-un-lft-identity
13×add-cbrt-cube
10×prod-exp add-log-exp
8×add-cube-cbrt
7×pow1 associate-*r* associate-*l*
5×flip3-- sqrt-prod flip--
4×div-exp cbrt-unprod distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv frac-times sub-neg rec-exp distribute-rgt-neg-in sqrt-div 1-exp associate-*l/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 85
Calls
4 calls:
20.0ms
(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
9.0ms
(- (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))))

series291.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
79.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms
(- (* b b) (* 4.0 (* a c)))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify58.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0469991
12048866
25002857

prune207.0ms

Filtered
97 candidates to 65 candidates (67.0%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New95297
Fresh358
Picked011
Done011
Total989107

Merged error: 7.9b

Counts
107 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* 4.0 (* a c)))
4.3b
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
13.5b
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
72×add-sqr-sqrt
61×*-un-lft-identity
52×times-frac
51×add-exp-log
30×add-cube-cbrt associate-*l*
27×add-cbrt-cube
20×prod-exp
18×difference-of-squares
16×div-exp
13×distribute-lft-out
12×sqrt-prod
9×distribute-lft-out--
8×cbrt-undiv cbrt-unprod
7×pow1 associate-*r*
6×associate-/r* add-log-exp
4×rec-exp flip3-- 1-exp associate-/r/ flip-- associate-/l*
3×div-inv
2×sqrt-div associate-/l/ unswap-sqr
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 149
Calls
4 calls:
4.0ms
(- (* b b) (* 4.0 (* a c)))
22.0ms
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
12.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series488.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* 4.0 (* a c)))
165.0ms
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
202.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify119.0ms

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 2 (98.0ms)

IterNodesCost
07602359
136892008
250011985

prune332.0ms

Filtered
161 candidates to 102 candidates (63.4%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1574161
Fresh426
Picked101
Done112
Total1637170

Merged error: 7.8b

Counts
170 → 7

regimes162.0ms

bsearch3.0ms

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