Details

Time bar (total: 4.5s)

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

localize16.0ms

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))))

rewrite29.0ms

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:
12.0ms
(/ (+ (- 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))))

series300.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
78.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms
(- (* b b) (* 4.0 (* a c)))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0403779
11514685
25002674

prune232.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.0b

localize14.0ms

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))))

rewrite49.0ms

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:
8.0ms
(- (- 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))
13.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series475.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
147.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
179.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify98.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
06402692
129442439
250012426

prune414.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize16.0ms

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))))

rewrite28.0ms

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)))
11.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series203.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* b b) (* 4.0 (* a c)))
74.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
68.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify56.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0413627
12231543
25001535

prune220.0ms

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))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log
19×add-sqr-sqrt
18×add-cbrt-cube
16×*-un-lft-identity
10×add-log-exp
8×add-cube-cbrt associate-*l* prod-exp
7×pow1 associate-*r*
6×div-exp cbrt-unprod
5×flip3-- sqrt-prod flip--
4×cbrt-undiv sub-neg distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×distribute-rgt-in frac-times distribute-rgt-neg-in distribute-lft-in sqrt-div associate-*r/ associate-*l/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 1-exp pow-prod-down neg-log associate-/r/ *-commutative div-inv unswap-sqr
Counts
4 → 88
Calls
4 calls:
17.0ms
(* (/ 2.0 (* (/ 4.0 1) c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
9.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series301.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(* (/ 2.0 (* (/ 4.0 1) c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
44.0ms
(- (* b b) (* 4.0 (* a c)))
76.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify67.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
05451088
12651932
25001932

prune260.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.9b

regimes185.0ms

Accuracy

94.8% (1.3b remaining)

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

bsearch204.0ms

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
04928
15128
25128

end0.0ms

sample1.2s

Algorithm
intervals
Results
270.0ms1102×body2560valid
250.0ms5879×body80valid
174.0ms882×body1280valid
113.0ms2998×body80nan
64.0ms418×body640valid
37.0ms118×body5120valid
32.0ms236×body320valid
10.0ms124×body160valid