Details

Time bar (total: 5.5s)

sample44.0ms

Algorithm
intervals
Results
10.0ms40×body2560valid
8.0ms28×body1280valid
8.0ms194×body80valid
3.0ms76×body80nan
2.0ms10×body640valid
1.0ms2×body5120valid
0.0ms3×body320valid
0.0ms1×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: 34.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(* (* 4.0 a) c)
0.4b
(- (* b b) (* (* 4.0 a) c))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 *-un-lft-identity add-log-exp
9×add-exp-log add-cbrt-cube
7×add-sqr-sqrt
6×add-cube-cbrt
3×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×flip3-- sqrt-div sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 diff-log associate-*l* neg-log *-commutative flip-+
Counts
4 → 60
Calls
4 calls:
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
6.0ms
(* (* 4.0 a) c)
2.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series216.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms
(* (* 4.0 a) c)
48.0ms
(- (* b b) (* (* 4.0 a) c))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify44.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0307469
11303428
25001417

prune192.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b b) (* (* 4.0 a) c))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div add-log-exp
4×add-exp-log flip3-- add-cbrt-cube flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg diff-log
Counts
4 → 57
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series255.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* b b) (* (* 4.0 a) c))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify83.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 3 (77.0ms)

IterNodesCost
0149508
1576483
22486480
35001474

prune259.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 10.7b

localize16.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.5b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.4b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.7b
(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:
13.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
41.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
29.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series485.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
147.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
192.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify113.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
06512692
131392439
250022426

prune475.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 10.4b

localize18.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.5b
(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))) (* 2.0 a))
10.9b
(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
609×times-frac
260×add-sqr-sqrt
259×*-un-lft-identity
159×add-cube-cbrt
154×add-exp-log
117×associate-/l*
94×div-exp
72×add-cbrt-cube
50×distribute-lft-out-- difference-of-squares
40×cbrt-undiv
30×prod-exp
28×sqrt-prod
25×distribute-rgt-neg-in
18×div-inv
12×cbrt-unprod
10×rec-exp 1-exp
8×add-log-exp
5×pow1
2×flip3-- frac-2neg sqrt-div diff-log div-sub clear-num associate-/r* associate-/r/ flip-- associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 344
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
65.0ms
(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))) (* 2.0 a))
42.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series400.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
129.0ms
(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))) (* 2.0 a))
116.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))
77.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify90.0ms

Algorithm
egg-herbie
Counts
356 → 356
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
017776143
150025522

prune800.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.6b

regimes294.0ms

Accuracy

91.7% (2.4b remaining)

Error of 8.1b against oracle of 5.8b and baseline of 34.2b

bsearch223.0ms

Steps
ItersRangePoint
8
10920358539895.18
4.2009936632527795e+17
26039420339585284.0
10
9.410701402418836e-271
4.7345175229648096e-260
9.52089004516142e-271
11
-1.829086240692416e+154
-2.187052964502477e+134
-8.555281377770497e+140

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04528
14528

end0.0ms

sample1.2s

Algorithm
intervals
Results
269.0ms1104×body2560valid
235.0ms5868×body80valid
177.0ms910×body1280valid
109.0ms2861×body80nan
63.0ms422×body640valid
27.0ms96×body5120valid
24.0ms212×body320valid
11.0ms120×body160valid