Details

Time bar (total: 11.5s)

sample58.0ms

Algorithm
intervals
Results
14.0ms314×body80nan
11.0ms570×pre80true
10.0ms142×body160valid
4.0ms114×body80valid

simplify11.0ms

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 (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 27.2b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.3b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.3b
(- (* b b) (* (* 4.0 a) c))
27.2b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
139×add-sqr-sqrt
116×*-un-lft-identity
60×times-frac
42×unswap-sqr
36×add-cube-cbrt associate-*l*
30×difference-of-squares
28×distribute-lft-out
24×sqrt-prod
18×associate-*r*
14×distribute-rgt-neg-in
12×associate-/r* *-commutative distribute-lft-out--
10×add-log-exp
9×add-exp-log add-cbrt-cube
6×swap-sqr
5×pow1 associate-/l*
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 cbrt-unprod div-inv
Counts
4 → 178
Calls
4 calls:
25.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
42.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
25.0ms
(- (* b b) (* (* 4.0 a) c))
35.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series334.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
116.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
51.0ms
(- (* b b) (* (* 4.0 a) c))
87.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify78.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
06212253
124432157
250022140

prune280.0ms

Filtered
190 candidates to 109 candidates (42.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1837190
Fresh000
Picked101
Done000
Total1847191

Merged error: 0.4b

Counts
191 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite354.0ms

Algorithm
rewrite-expression-head
Rules
1801×*-un-lft-identity
1346×times-frac
946×add-sqr-sqrt
408×distribute-lft-out--
400×distribute-lft-out
385×add-cube-cbrt
377×associate-*l*
217×difference-of-squares
168×associate-*r*
101×distribute-rgt-neg-in sqrt-prod
74×unswap-sqr
69×associate-/l*
59×*-commutative
28×associate-/r/
26×associate-/r*
23×associate-/l/
18×add-exp-log add-cbrt-cube
16×flip3-- flip--
15×div-inv
10×add-log-exp
7×cbrt-undiv div-exp
4×pow1
3×frac-2neg diff-log div-sub swap-sqr clear-num
2×associate-+l- sub-neg flip3-+ prod-exp cbrt-unprod flip-+
1×associate--l- neg-sub0 neg-log
Counts
4 → 896
Calls
4 calls:
35.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
114.0ms
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
26.0ms
(- (* b b) (* (* 4.0 a) c))
88.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series457.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
139.0ms
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
49.0ms
(- (* b b) (* (* 4.0 a) c))
184.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify260.0ms

Algorithm
egg-herbie
Counts
908 → 908
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
0173224064
1500122943

prune1.3s

Filtered
908 candidates to 285 candidates (68.6%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New89810908
Fresh606
Picked101
Done000
Total90510915

Merged error: 0b

Counts
915 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.4b
(* (* 4.0 (* a c)) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a)))

rewrite397.0ms

Algorithm
rewrite-expression-head
Rules
1245×times-frac
1076×add-sqr-sqrt
836×*-un-lft-identity
511×associate-*r*
480×add-cube-cbrt
205×associate-*l*
183×difference-of-squares
174×distribute-lft-out--
153×add-exp-log
129×unswap-sqr
87×add-cbrt-cube
84×distribute-rgt-neg-in sqrt-prod
70×prod-exp
66×associate-/l*
62×*-commutative
55×associate-*r/
54×associate-/r/
50×div-exp
45×associate-/r*
38×cbrt-unprod
30×div-inv
29×associate-/l/
28×flip3-- flip--
25×cbrt-undiv
14×pow1
9×rec-exp 1-exp
7×clear-num
6×pow-prod-down un-div-inv add-log-exp
5×frac-2neg
3×swap-sqr
1×sub-neg pow-flip diff-log inv-pow
Counts
4 → 965
Calls
4 calls:
40.0ms
(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
27.0ms
(- (* b b) (* (* 4.0 a) c))
58.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
196.0ms
(* (* 4.0 (* a c)) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a)))

series463.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
51.0ms
(- (* b b) (* (* 4.0 a) c))
135.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
169.0ms
(* (* 4.0 (* a c)) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a)))

simplify217.0ms

Algorithm
egg-herbie
Counts
977 → 977
Iterations

Useful iterations: 1 (61.0ms)

IterNodesCost
0316716442
1500115610

prune1.6s

Filtered
977 candidates to 450 candidates (53.9%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New9743977
Fresh459
Picked011
Done000
Total9789987

Merged error: 0b

Counts
987 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite560.0ms

Algorithm
rewrite-expression-head
Rules
1831×times-frac
1520×add-sqr-sqrt
1254×associate-*r*
1203×*-un-lft-identity
699×add-cube-cbrt
282×associate-*l*
255×difference-of-squares
246×distribute-lft-out--
171×associate-*r/
167×unswap-sqr
154×add-exp-log
120×distribute-rgt-neg-in sqrt-prod
96×associate-/l*
91×*-commutative
90×add-cbrt-cube
78×associate-/r/
73×prod-exp
57×associate-/r*
48×div-exp
45×associate-/l/
44×div-inv
41×cbrt-unprod
40×flip3-- flip--
24×cbrt-undiv
18×pow1
12×un-div-inv
10×clear-num
9×pow-prod-down
8×rec-exp 1-exp
6×frac-2neg add-log-exp
3×swap-sqr
1×sub-neg diff-log
Counts
4 → 1329
Calls
4 calls:
228.0ms
(* (* 4.0 c) (* a (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))))
123.0ms
(* a (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a)))
24.0ms
(- (* b b) (* (* 4.0 a) c))
58.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series537.0ms

Counts
4 → 12
Calls
4 calls:
190.0ms
(* (* 4.0 c) (* a (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))))
163.0ms
(* a (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a)))
47.0ms
(- (* b b) (* (* 4.0 a) c))
137.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify279.0ms

Algorithm
egg-herbie
Counts
1341 → 1341
Iterations

Useful iterations: 1 (73.0ms)

IterNodesCost
0382620408
1500219593

prune2.6s

Filtered
1341 candidates to 657 candidates (51.0%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New134011341
Fresh257
Picked011
Done011
Total134281350

Merged error: 0b

Counts
1350 → 8

regimes129.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02713
12713

end0.0ms

sample1.4s

Algorithm
intervals
Results
322.0ms16745×pre80true
308.0ms4411×body160valid
296.0ms8745×body80nan
134.0ms3589×body80valid