Details

Time bar (total: 5.5s)

sample59.0ms

Algorithm
intervals
Results
11.0ms145×body160valid
11.0ms540×pre80true
11.0ms284×body80nan
5.0ms44×body320valid
3.0ms67×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: 42.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.1b
(- (* b b) (* (* 4.0 a) c))
36.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite27.0ms

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:
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series304.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
111.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
43.0ms
(- (* b b) (* (* 4.0 a) c))
82.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify50.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0405779
11563685
25002674

prune209.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

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))
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series456.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
145.0ms
(/ (/ (+ 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 (88.0ms)

IterNodesCost
06422664
131752400
250032388

prune456.0ms

Filtered
163 candidates to 106 candidates (65.0%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

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:
11.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series381.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
48.0ms
(- (* b b) (* (* 4.0 a) c))
74.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
152.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify88.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
05121105
13243867
25001860

prune273.0ms

Filtered
97 candidates to 62 candidates (63.9%)
Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(- (- b) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1)))
0.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1)))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1))))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
121×add-sqr-sqrt
114×times-frac
88×*-un-lft-identity
44×add-cube-cbrt difference-of-squares
36×associate-/l*
33×sqrt-prod
22×distribute-lft-out--
18×add-exp-log add-cbrt-cube
11×unpow-prod-down distribute-rgt-neg-in sqr-pow
10×associate-/r* add-log-exp
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 → 173
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(- (- b) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1)))
19.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1)))) (* 2.0 a))
15.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1))))

series454.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(- (- b) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1)))
145.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1)))) (* 2.0 a))
183.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1))))

simplify121.0ms

Algorithm
egg-herbie
Counts
185 → 185
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
07303400
135253069
250013042

prune493.0ms

Filtered
185 candidates to 115 candidates (62.2%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes153.0ms

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

sample1.6s

Algorithm
intervals
Results
362.0ms4773×body160valid
339.0ms16539×pre80true
312.0ms8539×body80nan
164.0ms1436×body320valid
69.0ms1791×body80valid