Details

Time bar (total: 13.7s)

sample67.0ms

Algorithm
intervals
Results
18.0ms42×body2560valid
13.0ms181×body80valid
12.0ms41×body1280valid
5.0ms79×body80nan
3.0ms12×body640valid
1.0ms3×body5120valid
1.0ms3×body320valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b
(- (* b b) (* (* 4.0 a) c))
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite58.0ms

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:
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
37.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series298.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
107.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
44.0ms
(- (* b b) (* (* 4.0 a) c))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify50.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0438854
11702750
25001735

prune289.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.4b

localize15.0ms

Local error

Found 4 expressions with local error:

2.3b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite104.0ms

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:
18.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms
(/ (/ (+ 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)))))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series472.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
144.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
181.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify140.0ms

Algorithm
egg-herbie
Counts
244 → 244
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
08295119
137633863
250013860

prune559.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize19.0ms

Local error

Found 4 expressions with local error:

2.3b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b
(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))) (* 2.0 a))
10.6b
(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
609×times-frac
301×add-sqr-sqrt
300×*-un-lft-identity
200×add-cube-cbrt
154×add-exp-log
117×associate-/l*
94×div-exp
72×add-cbrt-cube
60×prod-diff
58×sqrt-prod
50×distribute-lft-out-- difference-of-squares
46×distribute-rgt-neg-in
40×cbrt-undiv
30×prod-exp
21×distribute-lft-neg-in
18×div-inv
12×cbrt-unprod
10×rec-exp fma-neg 1-exp
8×add-log-exp
7×neg-mul-1
5×pow1
4×expm1-log1p-u log1p-expm1-u
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 → 422
Calls
4 calls:
16.0ms
(- (- 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))
38.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series392.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
124.0ms
(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))) (* 2.0 a))
107.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))
84.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify101.0ms

Algorithm
egg-herbie
Counts
434 → 434
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
019548568
150026995

prune870.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.3b

localize16.0ms

Local error

Found 4 expressions with local error:

2.0b
(/ (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) a) c)
2.3b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b
(/ (/ 1 (/ (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) a) c)) (* 2.0 a))
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite580.0ms

Algorithm
rewrite-expression-head
Rules
6869×times-frac
3185×add-sqr-sqrt
3184×*-un-lft-identity
2388×add-cube-cbrt
807×associate-/l*
398×distribute-lft-out-- difference-of-squares
232×sqrt-prod
220×distribute-rgt-neg-in
122×add-exp-log
98×div-inv
84×div-exp
60×prod-diff
58×add-cbrt-cube
36×cbrt-undiv
21×distribute-lft-neg-in
13×prod-exp
10×fma-neg
8×rec-exp 1-exp add-log-exp
7×neg-mul-1
5×pow1 cbrt-unprod
4×expm1-log1p-u associate-/r* log1p-expm1-u
3×div-sub
2×flip3-- frac-2neg sqrt-div diff-log clear-num associate-/r/ flip-- associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 1952
Calls
4 calls:
58.0ms
(/ (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) a) c)
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
235.0ms
(/ (/ 1 (/ (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) a) c)) (* 2.0 a))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series411.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(/ (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) a) c)
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
133.0ms
(/ (/ 1 (/ (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) a) c)) (* 2.0 a))
81.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify405.0ms

Algorithm
egg-herbie
Counts
1964 → 1964
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
0500244920

prune6.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 5.3b

regimes143.0ms

Accuracy

87.7% (3.3b remaining)

Error of 8.9b against oracle of 5.6b and baseline of 32.6b

bsearch166.0ms

Steps
ItersRangePoint
7
1.0320989087612647e-20
5.408012210248103e-19
1.1689690778247071e-19
5
-9.237006875632357e-258
-4.348398702340512e-258
-6.63395785424786e-258
7
-1.5320971041566743e+27
-3.280360895118841e+25
-1.5052990324106084e+27

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04729
14729

end0.0ms

sample1.8s

Algorithm
intervals
Results
419.0ms5822×body80valid
402.0ms1083×body2560valid
282.0ms903×body1280valid
196.0ms2984×body80nan
113.0ms452×body640valid
49.0ms113×body5120valid
43.0ms218×body320valid
14.0ms108×body160valid