Details

Time bar (total: 5.3s)

sample54.0ms

Algorithm
intervals
Results
10.0ms145×body160valid
10.0ms530×pre80true
9.0ms274×body80nan
5.0ms50×body320valid
2.0ms61×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 (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
37.9b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite57.0ms

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))
37.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series309.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
48.0ms
(- (* b b) (* (* 4.0 a) c))
108.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify46.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0405779
11563685
25002674

prune198.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(- (- b) (sqrt (- (* 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)))))

rewrite102.0ms

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:
3.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
32.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series460.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
146.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
186.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify115.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
06422664
131752400
250032388

prune431.0ms

Filtered
163 candidates to 106 candidates (65.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
27×add-exp-log add-cbrt-cube
16×add-sqr-sqrt
14×*-un-lft-identity
10×prod-exp cbrt-unprod add-log-exp
7×associate-*r*
6×pow1 cbrt-undiv add-cube-cbrt div-exp
4×sub-neg flip3-- associate-*r/ flip-- distribute-lft-out-- difference-of-squares
3×diff-log associate-*l*
2×distribute-rgt-in distribute-rgt-neg-in distribute-lft-in sqrt-prod associate-/r/
1×associate--l- neg-sub0 frac-2neg times-frac pow-prod-down neg-log clear-num associate-/r* *-commutative div-inv associate-/l* unswap-sqr
Counts
4 → 85
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
19.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series386.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* (* 4.0 a) c))
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
107.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
150.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify89.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
05121105
13243867
25001860

prune243.0ms

Filtered
97 candidates to 62 candidates (63.9%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(/ (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c)
0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b
(/ 1 (/ (/ (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c) 4.0))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
198×times-frac
92×add-sqr-sqrt *-un-lft-identity
88×add-cube-cbrt
55×add-exp-log
34×div-exp
28×associate-/r*
23×add-cbrt-cube
18×div-inv
11×cbrt-undiv
10×add-log-exp
9×1-exp
8×prod-exp
5×pow1 rec-exp
4×associate-/l*
3×flip3-- diff-log flip--
2×sub-neg frac-2neg associate-*r/ clear-num cbrt-unprod associate-/l/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 pow-flip distribute-rgt-neg-in neg-log sqrt-prod associate-/r/ inv-pow
Counts
4 → 189
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(/ (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c)
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
32.0ms
(/ 1 (/ (/ (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c) 4.0))

series343.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* b b) (* (* 4.0 a) c))
89.0ms
(/ (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c)
73.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
130.0ms
(/ 1 (/ (/ (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c) 4.0))

simplify111.0ms

Algorithm
egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
010042983
146292602
250012579

prune479.0ms

Filtered
201 candidates to 126 candidates (62.7%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes94.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02312
12312

end0.0ms

sample1.5s

Algorithm
intervals
Results
345.0ms4927×body160valid
309.0ms16554×pre80true
289.0ms8554×body80nan
138.0ms1296×body320valid
68.0ms1777×body80valid