Details

Time bar (total: 5.3s)

sample45.0ms

Algorithm
intervals
Results
10.0ms183×body80valid
6.0ms28×body2560valid
5.0ms29×body1280valid
3.0ms89×body80nan
3.0ms22×body640valid
1.0ms5×body5120valid
0.0ms7×body160valid
0.0ms1×body320valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b
(- (* b b) (* (* 4.0 a) c))
1.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite111.0ms

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:
68.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
10.0ms
(- (* b b) (* (* 4.0 a) c))
22.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series381.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
65.0ms
(- (* b b) (* (* 4.0 a) c))
114.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify47.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0405779
11563685
25001674

prune240.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.5b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.9b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
25.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite324.0ms

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:
24.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
222.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
62.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series509.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
153.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
202.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
77.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify115.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
06512692
131392439
250022426

prune437.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.5b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
1.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.5b
(/ (* 2.0 a) (* 4.0 (* a c)))
25.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite66.0ms

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:
8.0ms
(- (* b b) (* (* 4.0 a) c))
23.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series210.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* b b) (* (* 4.0 a) c))
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify62.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
0429637
12471542
25003534

prune205.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
1.0b
(- (* b b) (* (* 4.0 a) c))
1.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
113×add-exp-log
51×prod-exp
44×div-exp
29×add-cbrt-cube
16×rec-exp 1-exp
14×associate-/r/
12×add-sqr-sqrt
11×pow1 frac-times *-un-lft-identity
10×cbrt-undiv add-log-exp
9×cbrt-unprod
8×flip3-- flip--
7×add-cube-cbrt associate-*l/
5×associate-*r/
4×sqrt-prod
3×pow-flip times-frac diff-log pow-prod-down un-div-inv associate-/l*
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 pow1/2 neg-log clear-num associate-/r* div-inv inv-pow
Counts
4 → 116
Calls
4 calls:
123.0ms
(/ 1 (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
25.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series393.0ms

Counts
4 → 12
Calls
4 calls:
188.0ms
(/ 1 (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
50.0ms
(- (* b b) (* (* 4.0 a) c))
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify82.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
07391499
134181216
250011210

prune240.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.5b

regimes172.0ms

Accuracy

95% (1.2b remaining)

Error of 6.7b against oracle of 5.5b and baseline of 30.1b

bsearch208.0ms

Steps
ItersRangePoint
8
3.1248942757642245e+89
1.1714167766929137e+92
6.09240124692818e+90
12
-2.833440705943036e-251
-4.668939852252329e-295
-2.1023086245622604e-293
10
-7.651517840437919e+135
-3.890563902308465e+123
-4.739386840053889e+131

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04928
14928

end0.0ms

sample1.3s

Algorithm
intervals
Results
237.0ms1058×body2560valid
230.0ms5792×body80valid
165.0ms935×body1280valid
112.0ms2915×body80nan
63.0ms453×body640valid
29.0ms101×body5120valid
24.0ms225×body320valid
8.0ms113×body160valid