Details

Time bar (total: 5.1s)

sample44.0ms

Algorithm
intervals
Results
7.0ms33×body2560valid
7.0ms186×body80valid
5.0ms86×body80nan
5.0ms28×body1280valid
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
0249
1459
2799
3979
41059
51059

prune3.0ms

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)))

rewrite104.0ms

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:
64.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
7.0ms
(- (* b b) (* (* 4.0 a) c))
22.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series318.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
50.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0405779
11563685
25001674

prune229.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.2b

localize16.0ms

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)))

rewrite180.0ms

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:
22.0ms
(- (- 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))
58.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series506.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
157.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
193.0ms
(/ (+ 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 (90.0ms)

IterNodesCost
06512694
131392439
250022426

prune424.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize16.0ms

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)))

rewrite62.0ms

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:
7.0ms
(- (* b b) (* (* 4.0 a) c))
22.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series215.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* b b) (* (* 4.0 a) c))
82.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify63.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
0429637
12471542
25003534

prune219.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- 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)))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
295×add-exp-log
166×div-exp
119×prod-exp
64×1-exp
60×add-cbrt-cube
34×rec-exp
31×times-frac
26×cbrt-undiv
24×add-sqr-sqrt
23×*-un-lft-identity
19×add-cube-cbrt
18×cbrt-unprod
14×associate-/r/
13×associate-/l*
11×frac-times
10×add-log-exp
8×flip3-- flip--
7×associate-*l/
5×pow1 associate-*r/
4×sqrt-prod
3×diff-log un-div-inv div-inv
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* associate-/l/
Counts
4 → 179
Calls
4 calls:
67.0ms
(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
7.0ms
(- (* b b) (* (* 4.0 a) c))
22.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series397.0ms

Counts
4 → 12
Calls
4 calls:
192.0ms
(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
47.0ms
(- (* b b) (* (* 4.0 a) c))
83.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify49.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
011722503
150012016

prune287.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.1b

regimes205.0ms

Accuracy

95.7% (1.0b remaining)

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

bsearch168.0ms

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

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04736
14736

end0.0ms

sample1.3s

Algorithm
intervals
Results
240.0ms1052×body2560valid
239.0ms5865×body80valid
174.0ms932×body1280valid
108.0ms2817×body80nan
71.0ms453×body640valid
33.0ms113×body5120valid
25.0ms235×body320valid
9.0ms120×body160valid