Details

Time bar (total: 6.1s)

sample47.0ms

Algorithm
intervals
Results
7.0ms191×body80valid
7.0ms33×body2560valid
7.0ms37×body1280valid
3.0ms96×body80nan
2.0ms12×body640valid
1.0ms4×body5120valid
1.0ms8×body320valid
0.0ms3×body160valid

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b
(- (* b b) (* (* 4.0 a) c))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
27.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-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 neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
68.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(- (* b b) (* (* 4.0 a) c))
26.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series308.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
45.0ms
(- (* b b) (* (* 4.0 a) c))
82.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify56.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0438855
11702750
25001735

prune340.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.8b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.6b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
27.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
124×*-un-lft-identity
90×times-frac
80×add-cube-cbrt
60×prod-diff
44×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
10×fma-neg
8×associate-/r* add-log-exp
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u 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 → 232
Calls
4 calls:
32.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
86.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
60.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series544.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
169.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
207.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
82.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify164.0ms

Algorithm
egg-herbie
Counts
244 → 244
Iterations

Useful iterations: 2 (124.0ms)

IterNodesCost
08295119
137633863
250013860

prune646.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
0.9b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.7b
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
27.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
51×add-sqr-sqrt
50×*-un-lft-identity
46×add-cube-cbrt
34×sqrt-prod
25×add-exp-log add-cbrt-cube
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×prod-exp cbrt-unprod
7×neg-mul-1
6×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×sub-neg sqrt-div associate-*r/ associate-/r/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 152
Calls
4 calls:
11.0ms
(- (* b b) (* (* 4.0 a) c))
30.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series375.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* b b) (* (* 4.0 a) c))
87.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
160.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
78.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify123.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
06683371
134822161
250012072

prune357.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (* c 4.0) 1) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.8b
(- (* b b) (* (* 4.0 a) c))
0.9b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
27.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
107×add-sqr-sqrt
106×*-un-lft-identity
73×times-frac
70×add-cube-cbrt
61×prod-diff
42×sqrt-prod
30×distribute-rgt-neg-in
21×distribute-lft-neg-in
18×add-exp-log distribute-lft-out-- difference-of-squares
13×add-cbrt-cube
11×fma-neg
10×add-log-exp
9×div-exp div-inv
7×neg-mul-1 associate-/r* associate-/l*
5×pow1 cbrt-undiv
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×sub-neg sqrt-div 1-exp prod-exp associate-/r/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num cbrt-unprod associate-/l/
Counts
4 → 209
Calls
4 calls:
45.0ms
(/ (/ (* c 4.0) 1) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
31.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series360.0ms

Counts
4 → 12
Calls
4 calls:
169.0ms
(/ (/ (* c 4.0) 1) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
48.0ms
(- (* b b) (* (* 4.0 a) c))
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify109.0ms

Algorithm
egg-herbie
Counts
221 → 221
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
07574277
132393087
250033006

prune429.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 8.5b

regimes182.0ms

Accuracy

96% (1.0b remaining)

Error of 6.6b against oracle of 5.7b and baseline of 29.2b

bsearch221.0ms

Steps
ItersRangePoint
10
1.0940858654514709e+88
1.774287867247786e+103
6.156280749566888e+102
9
-7.604767348394258e-257
-1.5878992896022604e-264
-1.9415295134599817e-260
9
-4.3398659734944224e+136
-6.188138656270848e+129
-4.2975228517561493e+130

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04928
14928

end0.0ms

sample1.2s

Algorithm
intervals
Results
241.0ms1090×body2560valid
226.0ms5831×body80valid
155.0ms909×body1280valid
101.0ms2813×body80nan
70.0ms471×body640valid
28.0ms109×body5120valid
24.0ms231×body320valid
9.0ms128×body160valid