Details

Time bar (total: 6.7s)

sample72.0ms

Algorithm
intervals
Results
19.0ms152×body160valid
15.0ms535×pre80true
13.0ms279×body80nan
5.0ms104×body80valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

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: 30.0b

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) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b
(- (* b b) (* (* 4.0 a) c))
29.9b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-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 neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
4.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series322.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
110.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
51.0ms
(- (* b b) (* (* 4.0 a) c))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify53.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0438854
11702750
25001735

prune257.0ms

Filtered
102 candidates to 82 candidates (80.4%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New957102
Fresh000
Picked101
Done000
Total967103

Merged error: 0.4b

Counts
103 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
123×add-sqr-sqrt *-un-lft-identity
90×times-frac
79×add-cube-cbrt
61×prod-diff
41×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
11×fma-neg
10×add-log-exp
8×associate-/r*
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 expm1-log1p-u log1p-expm1-u 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 → 231
Calls
4 calls:
10.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series478.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
50.0ms
(- (* b b) (* (* 4.0 a) c))
152.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
193.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify161.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (121.0ms)

IterNodesCost
08325099
139673830
250013828

prune574.0ms

Filtered
243 candidates to 137 candidates (56.4%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New23211243
Fresh516
Picked101
Done000
Total23812250

Merged error: 0.0b

Counts
250 → 12

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c)))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c))))))
0.4b
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c)))
0.4b
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
130×add-sqr-sqrt times-frac
118×pow1
92×*-un-lft-identity
66×pow-prod-down
56×add-exp-log add-cbrt-cube
52×add-cube-cbrt
42×difference-of-squares
39×associate-/l*
29×prod-exp cbrt-unprod
20×sqrt-prod distribute-lft-out--
12×associate-/r*
10×distribute-rgt-neg-in
9×pow-sqr pow-prod-up
8×cbrt-undiv div-exp
6×associate-/r/
5×div-inv associate-/l/
4×expm1-log1p-u unpow-prod-down flip3-- flip-- log1p-expm1-u add-log-exp sqr-pow
3×frac-2neg pow-plus clear-num
1×pow2 flip3-+ div-sub swap-sqr associate-*r* associate-*l* *-commutative flip-+
Counts
4 → 241
Calls
4 calls:
27.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c)))))) (* 2.0 a))
27.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c))))))
8.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c)))
12.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series588.0ms

Counts
4 → 12
Calls
4 calls:
196.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c)))))) (* 2.0 a))
243.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c))))))
104.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c)))
44.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify77.0ms

Algorithm
egg-herbie
Counts
253 → 253
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09565104
150004587

prune697.0ms

Filtered
253 candidates to 150 candidates (59.3%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New2530253
Fresh01111
Picked011
Done000
Total25312265

Merged error: 0.0b

Counts
265 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (fma b b (- 0 (* 4.0 (* a c)))))
0.2b
(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
0.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
124×*-un-lft-identity
90×times-frac
80×add-cube-cbrt
60×prod-diff
44×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
10×fma-neg
8×associate-/r* add-log-exp
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 230
Calls
4 calls:
2.0ms
(sqrt (fma b b (- 0 (* 4.0 (* a c)))))
9.0ms
(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
15.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
10.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))

series533.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(sqrt (fma b b (- 0 (* 4.0 (* a c)))))
92.0ms
(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
161.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
196.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))

simplify128.0ms

Algorithm
egg-herbie
Counts
242 → 242
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
07675082
131663826
250013733

prune456.0ms

Filtered
242 candidates to 132 candidates (54.5%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New2420242
Fresh01010
Picked011
Done011
Total24212254

Merged error: 0.0b

Counts
254 → 12

regimes173.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02920
13220
23220

end0.0ms

sample1.9s

Algorithm
intervals
Results
459.0ms16895×pre80true
437.0ms4515×body160valid
416.0ms8895×body80nan
169.0ms3485×body80valid