Details

Time bar (total: 4.5s)

sample38.0ms

Algorithm
intervals
Results
8.0ms209×body80valid
8.0ms34×body2560valid
4.0ms22×body1280valid
3.0ms79×body80nan
3.0ms18×body640valid
0.0ms3×body320valid
0.0ms4×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
23.5b
(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:
33.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
14.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series302.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
80.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms
(- (* b b) (* 4.0 (* a c)))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify51.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0403780
11514685
25002674

prune231.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.7b

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* 4.0 (* a c)))
4.4b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
10.6b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
23.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 148
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
43.0ms
(/ (/ (+ 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))))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series446.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* 4.0 (* a c)))
149.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
182.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify99.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
06282579
129542333
250012320

prune423.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
14.1b
(/ (* 2.0 a) (* 4.0 (* a c)))
23.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
10×add-sqr-sqrt add-log-exp
9×*-un-lft-identity prod-exp cbrt-unprod
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×sqrt-prod
3×flip3-- diff-log flip--
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 70
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
7.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
8.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series204.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms
(- (* b b) (* 4.0 (* a c)))
11.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify57.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0413628
12231543
25001535

prune208.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.8b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
23.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
13×add-cbrt-cube
12×add-sqr-sqrt
11×*-un-lft-identity
10×add-log-exp
9×div-exp
8×pow1
7×add-cube-cbrt
6×prod-exp
5×flip3-- associate-/r/ flip--
4×cbrt-undiv sqrt-prod
3×rec-exp times-frac diff-log 1-exp associate-/l*
2×frac-times sub-neg pow-flip sqrt-div associate-*r/ cbrt-unprod distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 pow-prod-down neg-log associate-*l/ clear-num associate-/r* div-inv inv-pow
Counts
4 → 82
Calls
4 calls:
30.0ms
(/ 1 (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
11.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series364.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(/ 1 (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
48.0ms
(- (* b b) (* 4.0 (* a c)))
66.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify48.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0428926
11779797
25002784

prune204.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.6b

regimes250.0ms

Accuracy

95.2% (1.2b remaining)

Error of 6.4b against oracle of 5.3b and baseline of 29.3b

bsearch180.0ms

Steps
ItersRangePoint
8
1.9559514031553493e+101
2.0413668072230428e+104
9.373511171447418e+103
9
1.0311906074547519e-259
1.091011630730822e-254
1.0417939395900796e-259
9
-2.3467190644739184e+107
-3.2019781887028674e+101
-1.7431685240570133e+102

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04625
14625

end0.0ms

sample1.1s

Algorithm
intervals
Results
238.0ms1070×body2560valid
228.0ms5839×body80valid
169.0ms884×body1280valid
106.0ms2849×body80nan
73.0ms496×body640valid
28.0ms102×body5120valid
24.0ms220×body320valid
9.0ms103×body160valid