Details

Time bar (total: 4.6s)

sample42.0ms

Algorithm
intervals
Results
10.0ms189×body80valid
8.0ms35×body2560valid
5.0ms25×body1280valid
3.0ms87×body80nan
2.0ms12×body640valid
1.0ms8×body320valid
0.0ms5×body160valid
0.0ms1×body5120valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b
(- (* b b) (* (* 4.0 a) c))
1.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite56.0ms

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:
36.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series300.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
48.0ms
(- (* b b) (* (* 4.0 a) c))
75.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0405779
11563685
25001674

prune242.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.2b

localize16.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.5b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-rgt-neg-in
8×associate-/r* add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div 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 → 154
Calls
4 calls:
12.0ms
(- (- 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))
27.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series487.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
151.0ms
(/ (/ (+ 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)))))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify117.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
06512692
131392439
250022426

prune455.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.1b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.2b
(/ (* 2.0 a) (* 4.0 (* a c)))
23.2b
(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:
2.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series206.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* (* 4.0 a) c))
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify61.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
0429637
12471542
25003534

prune218.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (* (/ 2.0 (* (/ 4.0 1) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
1.0b
(- (* b b) (* (* 4.0 a) c))
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
30×div-exp
24×prod-exp add-cbrt-cube
12×add-sqr-sqrt
11×*-un-lft-identity
10×add-log-exp
9×cbrt-undiv 1-exp
8×pow1
7×add-cube-cbrt
6×rec-exp cbrt-unprod
5×flip3-- associate-/r/ flip--
4×sqrt-prod
3×times-frac diff-log associate-/l*
2×frac-times sub-neg pow-flip sqrt-div associate-*r/ 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 → 93
Calls
4 calls:
50.0ms
(/ 1 (* (/ 2.0 (* (/ 4.0 1) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
2.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series379.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(/ 1 (* (/ 2.0 (* (/ 4.0 1) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
45.0ms
(- (* b b) (* (* 4.0 a) c))
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify63.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05961183
12533967
25002960

prune222.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

regimes175.0ms

Accuracy

92.4% (1.9b remaining)

Error of 7.2b against oracle of 5.3b and baseline of 29.8b

bsearch132.0ms

Steps
ItersRangePoint
5
5.10808278574109e+145
1.867402505400959e+146
1.6656334680497556e+146
7
-2.782279184329671e-219
-5.296311981150072e-221
-1.0621980184587312e-219
7
-2.963931757502914e+119
-3.3757792073266624e+117
-3.439785982885987e+117

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04828
14828

end0.0ms

sample1.2s

Algorithm
intervals
Results
252.0ms1073×body2560valid
238.0ms5759×body80valid
175.0ms914×body1280valid
108.0ms2900×body80nan
67.0ms451×body640valid
33.0ms100×body5120valid
27.0ms229×body320valid
10.0ms132×body160valid