Details

Time bar (total: 5.4s)

sample45.0ms

Algorithm
intervals
Results
7.0ms33×body2560valid
7.0ms186×body80valid
5.0ms28×body1280valid
3.0ms86×body80nan
2.0ms15×body640valid
1.0ms5×body5120valid
1.0ms7×body320valid
0.0ms6×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.6b
(- (* b b) (* (* 4.0 a) c))
1.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite112.0ms

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:
65.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
9.0ms
(- (* b b) (* (* 4.0 a) c))
24.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series300.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
44.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify49.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0438854
11702750
25001735

prune287.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.2b

localize17.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.1b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite195.0ms

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:
30.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
84.0ms
(/ (/ (+ 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)))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series480.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
149.0ms
(/ (/ (+ 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)))))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify142.0ms

Algorithm
egg-herbie
Counts
244 → 244
Iterations

Useful iterations: 2 (105.0ms)

IterNodesCost
08295119
137633863
250013860

prune526.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0b
(/ (* 2.0 a) (* 4.0 (* a c)))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite79.0ms

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 log1p-expm1-u
3×flip3-- diff-log flip--
2×sub-neg sqrt-div 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 → 150
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
30.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series209.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify90.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
06103042
130781945
250021857

prune293.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (* (/ 2.0 (/ (* c 4.0) 1)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.6b
(- (* b b) (* (* 4.0 a) c))
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
77×add-exp-log
61×prod-diff
53×add-sqr-sqrt
52×*-un-lft-identity
48×add-cube-cbrt
41×div-exp
34×sqrt-prod
24×prod-exp add-cbrt-cube
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
13×1-exp
11×fma-neg
10×cbrt-undiv add-log-exp
8×pow1
7×neg-mul-1 rec-exp
5×flip3-- associate-/r/ flip-- cbrt-unprod
4×expm1-log1p-u log1p-expm1-u
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 frac-2neg sqrt-pow1 pow1/2 pow-prod-down neg-log associate-*l/ clear-num associate-/r* div-inv inv-pow
Counts
4 → 176
Calls
4 calls:
77.0ms
(/ 1 (* (/ 2.0 (/ (* c 4.0) 1)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
9.0ms
(- (* 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)))

series374.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(/ 1 (* (/ 2.0 (/ (* c 4.0) 1)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
49.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify91.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
07923640
131892381
250022334

prune301.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.1b

regimes187.0ms

Accuracy

95.7% (1.0b remaining)

Error of 6.7b against oracle of 5.7b and baseline of 29.5b

bsearch157.0ms

Steps
ItersRangePoint
7
1.2310742480127578e+144
1.3446930168628618e+146
1.458057835821772e+144
8
-4.3329860630795565e-185
-1.209307133318773e-187
-3.3193805664383666e-186
7
-2.3419197238566892e+109
-5.519096697972622e+107
-2.2237630570465103e+109

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04836
14836

end0.0ms

sample1.2s

Algorithm
intervals
Results
232.0ms1052×body2560valid
229.0ms5865×body80valid
173.0ms932×body1280valid
106.0ms2817×body80nan
64.0ms453×body640valid
31.0ms113×body5120valid
30.0ms235×body320valid
9.0ms120×body160valid