Details

Time bar (total: 4.7s)

sample44.0ms

Algorithm
intervals
Results
8.0ms33×body2560valid
8.0ms189×body80valid
6.0ms31×body1280valid
4.0ms104×body80nan
2.0ms14×body640valid
1.0ms3×body5120valid
1.0ms7×body320valid
0.0ms3×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: 33.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b
(- (* b b) (* 4.0 (* a c)))
20.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

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:
15.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series311.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
83.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
49.0ms
(- (* b b) (* 4.0 (* a c)))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0403779
11514685
25002674

prune234.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.0b

localize15.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.7b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
11.1b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
20.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite52.0ms

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:
9.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
16.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series490.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
152.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
187.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
76.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify106.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
06402692
129442439
250012426

prune442.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* 4.0 (* a c)))
1.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.6b
(/ (* 2.0 a) (* 4.0 (* a c)))
20.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
10×add-sqr-sqrt add-log-exp
9×*-un-lft-identity prod-exp cbrt-unprod
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×sqrt-prod
3×flip3-- diff-log flip--
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 70
Calls
4 calls:
4.0ms
(- (* b b) (* 4.0 (* a c)))
8.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
7.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series219.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(- (* b b) (* 4.0 (* a c)))
82.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify57.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0413627
12231543
25001535

prune219.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
36×add-exp-log
22×add-cbrt-cube
17×prod-exp
15×add-sqr-sqrt
14×*-un-lft-identity
11×frac-times
10×pow1 add-log-exp
9×cbrt-unprod
8×flip3-- div-exp flip--
7×associate-*r* associate-*l/
6×add-cube-cbrt
5×associate-*r/ sqrt-prod
4×cbrt-undiv sub-neg distribute-lft-out-- difference-of-squares
3×diff-log pow-prod-down un-div-inv
2×distribute-rgt-in rec-exp distribute-rgt-neg-in distribute-lft-in sqrt-div 1-exp
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* neg-log *-commutative
Counts
4 → 95
Calls
4 calls:
18.0ms
(* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
13.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series321.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
52.0ms
(- (* b b) (* 4.0 (* a c)))
76.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
76.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify75.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
06141244
130041057
250021056

prune262.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.9b

regimes184.0ms

Accuracy

94.9% (1.2b remaining)

Error of 6.9b against oracle of 5.6b and baseline of 29.8b

bsearch217.0ms

Steps
ItersRangePoint
9
1.846147638884188e+104
1.7844061428947563e+109
1.55563303224959e+106
9
-2.9188174999700146e-273
-1.0308405028667604e-278
-2.3730540219645598e-278
9
-3.3506371122085595e+158
-5.17073721832495e+150
-5.585435738628103e+150

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04828
14828

end0.0ms

sample1.2s

Algorithm
intervals
Results
275.0ms1102×body2560valid
246.0ms5879×body80valid
173.0ms882×body1280valid
113.0ms2998×body80nan
73.0ms418×body640valid
35.0ms118×body5120valid
27.0ms236×body320valid
10.0ms124×body160valid