Details

Time bar (total: 13.4s)

sample59.0ms

Algorithm
intervals
Results
13.0ms279×body80nan
11.0ms156×body160valid
10.0ms535×pre80true
5.0ms48×body320valid
2.0ms52×body80valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
39.2b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-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 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
36.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series300.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
43.0ms
(- (* b b) (* (* 4.0 a) c))
105.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify45.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0405779
11563685
25002674

prune199.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
82×add-sqr-sqrt *-un-lft-identity
38×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
11×distribute-rgt-neg-in sqrt-prod
10×add-log-exp
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 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 → 151
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
44.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
26.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series456.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(- (* b b) (* (* 4.0 a) c))
150.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
184.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify110.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
06422664
131752400
250032388

prune420.0ms

Filtered
163 candidates to 106 candidates (65.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
880×times-frac
380×add-sqr-sqrt *-un-lft-identity
236×add-cube-cbrt
198×add-exp-log
122×div-exp
120×associate-/l*
90×add-cbrt-cube
72×distribute-lft-out-- difference-of-squares
51×cbrt-undiv
36×distribute-rgt-neg-in prod-exp sqrt-prod
31×associate-/r*
27×div-inv
15×rec-exp 1-exp
14×cbrt-unprod
6×add-log-exp
5×pow1
3×frac-2neg clear-num associate-/r/
2×div-sub associate-/l/
1×sub-neg flip3-- pow-flip diff-log flip-- inv-pow
Counts
4 → 475
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
62.0ms
(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))) (* 2.0 a))
35.0ms
(/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c)))
37.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))

series445.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* (* 4.0 a) c))
128.0ms
(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))) (* 2.0 a))
160.0ms
(/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c)))
114.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))

simplify104.0ms

Algorithm
egg-herbie
Counts
487 → 487
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
017558758
150027862

prune969.0ms

Filtered
487 candidates to 242 candidates (49.7%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite687.0ms

Algorithm
rewrite-expression-head
Rules
6798×times-frac
3505×add-sqr-sqrt *-un-lft-identity
2605×add-cube-cbrt
730×associate-*r*
450×distribute-lft-out-- difference-of-squares
332×add-exp-log
245×associate-/l*
225×distribute-rgt-neg-in sqrt-prod
187×div-exp
110×div-inv
102×add-cbrt-cube
99×prod-exp
82×associate-/r*
51×cbrt-undiv
32×rec-exp 1-exp
25×cbrt-unprod
10×pow1
8×associate-/r/
6×add-log-exp
3×pow-prod-down associate-*l/
2×frac-2neg clear-num
1×frac-times sub-neg flip3-- pow-flip diff-log associate-*r/ associate-*l* *-commutative flip-- associate-/l/ inv-pow
Counts
4 → 2166
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
104.0ms
(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) c)) a)
38.0ms
(/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) c))
240.0ms
(* (* (/ 1 2.0) a) (/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) c)) a))

series628.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* (* 4.0 a) c))
156.0ms
(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) c)) a)
273.0ms
(/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) c))
156.0ms
(* (* (/ 1 2.0) a) (/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) c)) a))

simplify398.0ms

Algorithm
egg-herbie
Counts
2178 → 2178
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
0500146136

prune6.5s

Filtered
2178 candidates to 1308 candidates (60.1%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes125.0ms

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
02614
12614

end0.0ms

sample1.5s

Algorithm
intervals
Results
352.0ms4850×body160valid
306.0ms16117×pre80true
279.0ms8117×body80nan
148.0ms1343×body320valid
67.0ms1807×body80valid