Details

Time bar (total: 5.0s)

sample44.0ms

Algorithm
intervals
Results
8.0ms32×body2560valid
7.0ms179×body80valid
7.0ms36×body1280valid
6.0ms110×body80nan
1.0ms10×body640valid
1.0ms12×body320valid
1.0ms3×body5120valid
0.0ms2×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: 36.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.2b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b
(- (* b b) (* 4.0 (* a c)))
25.8b
(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:
11.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
7.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series293.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
74.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
46.0ms
(- (* b b) (* 4.0 (* a c)))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0403779
11514685
25002674

prune227.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.5b

localize14.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* 4.0 (* a c)))
4.1b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
13.5b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
25.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite45.0ms

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:
4.0ms
(- (* b b) (* 4.0 (* a c)))
19.0ms
(/ (/ (+ 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))))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series435.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* b b) (* 4.0 (* a c)))
140.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
180.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
68.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify99.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
06282579
129542333
250012320

prune401.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
1.2b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b
(- (* b b) (* 4.0 (* a c)))
25.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
53×times-frac
45×*-un-lft-identity
26×add-sqr-sqrt
25×add-exp-log add-cube-cbrt
13×add-cbrt-cube
12×div-exp
11×associate-/r*
10×distribute-lft-out add-log-exp
9×associate-/r/
6×pow1
5×cbrt-undiv distribute-rgt-neg-in flip3-+ flip-+ div-inv
3×rec-exp 1-exp prod-exp sqrt-prod associate-/l*
2×flip3-- sqrt-div sum-log flip--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 diff-log neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 114
Calls
4 calls:
13.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
7.0ms
(+ (- 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))))

series329.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
77.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
46.0ms
(- (* b b) (* 4.0 (* a c)))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify65.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05211588
125221375
250021308

prune254.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.5b

localize17.0ms

Local error

Found 4 expressions with local error:

13.5b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
13.5b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
25.8b
(sqrt (- (* b b) (* 4.0 (* a c))))
25.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
62×*-un-lft-identity
42×times-frac
30×add-cube-cbrt
16×distribute-lft-out-- difference-of-squares
14×associate-/r* sqrt-prod
8×add-exp-log distribute-rgt-neg-in add-cbrt-cube
6×pow1 associate-/l*
4×flip3-- sqrt-div associate-/r/ flip-- associate-/l/ add-log-exp
2×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 div-exp clear-num flip-+ div-inv
Counts
4 → 124
Calls
4 calls:
12.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
12.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (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))))

series493.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
177.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
68.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify70.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
03351978
115541834
250011818

prune460.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 7.5b

regimes228.0ms

Accuracy

87.2% (3.4b remaining)

Error of 9.1b against oracle of 5.6b and baseline of 32.3b

bsearch128.0ms

Steps
ItersRangePoint
6
389373804.8346531
2491217878.346211
2114787851.2472425
3
2.4536482440551318e-264
3.391651544154436e-264
2.98127510036099e-264
9
-3.2701742958179892e+66
-3.862137329617324e+60
-1.0461303908572575e+65

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04832
14832

end0.0ms

sample1.2s

Algorithm
intervals
Results
258.0ms1095×body2560valid
232.0ms5839×body80valid
183.0ms934×body1280valid
115.0ms2928×body80nan
66.0ms449×body640valid
29.0ms101×body5120valid
27.0ms235×body320valid
10.0ms101×body160valid