Details

Time bar (total: 4.4s)

sample40.0ms

Algorithm
intervals
Results
7.0ms189×body80valid
6.0ms28×body2560valid
6.0ms34×body1280valid
3.0ms92×body80nan
2.0ms16×body640valid
2.0ms7×body5120valid
0.0ms4×body160valid
0.0ms2×body320valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.1b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(- (* b b) (* (* 4.0 a) c))
25.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

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)))) (* 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)))

series299.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(- (* b b) (* (* 4.0 a) c))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify57.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0438855
11702750
25001735

prune305.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 2.0) a)
1.1b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(- (* b b) (* (* 4.0 a) c))
25.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
117×times-frac
116×*-un-lft-identity
65×add-sqr-sqrt
64×add-cube-cbrt
26×distribute-lft-out
19×associate-/l*
16×distribute-rgt-neg-in
10×fma-def add-log-exp
9×add-exp-log add-cbrt-cube
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv distribute-lft-neg-in div-exp associate-/r* sqrt-prod
2×neg-sub0 associate-+l- flip3-- sqrt-div div-sub sum-log flip--
1×+-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff neg-log clear-num flip-+ associate-/l/
Counts
4 → 157
Calls
4 calls:
16.0ms
(/ (/ (+ (- 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:
104.0ms
(/ (/ (+ (- 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))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify72.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
06462036
124951928
250011904

prune426.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (* (/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)) 2.0))
1.1b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.4b
(- (* b b) (* (* 4.0 a) c))
25.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
25×add-exp-log
23×*-un-lft-identity
21×add-cube-cbrt
19×prod-diff
16×sqrt-prod
13×add-cbrt-cube
9×div-exp
8×pow1 add-log-exp
7×fma-neg
6×prod-exp
4×cbrt-undiv expm1-log1p-u log1p-expm1-u
3×rec-exp flip3-- times-frac 1-exp flip-- associate-/l*
2×sub-neg pow-flip sqrt-div diff-log cbrt-unprod difference-of-squares
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*l/ clear-num associate-/r* associate-/r/ div-inv distribute-lft-out-- inv-pow
Counts
4 → 109
Calls
4 calls:
13.0ms
(/ 1 (* (/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)) 2.0))
8.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series342.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(/ 1 (* (/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)) 2.0))
76.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
48.0ms
(- (* b b) (* (* 4.0 a) c))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify63.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
04811250
11985982
25001949

prune267.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.8b

localize14.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (* b b) (* (* 4.0 a) c))
25.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 66
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series241.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* (* 4.0 a) c))
45.0ms
(- (* b b) (* (* 4.0 a) c))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify90.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
0170540
1665506
22925502
35002490

prune280.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.8b

regimes235.0ms

Accuracy

85.4% (4.1b remaining)

Error of 10.0b against oracle of 5.8b and baseline of 34.2b

bsearch105.0ms

Steps
ItersRangePoint
7
1.9426594712364374e-87
2.1051237392284573e-85
1.667046824505827e-85
8
-3.734333779790662e+128
-2.2987999557012895e+125
-5.238946631357967e+127

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03215
13215

end0.0ms

sample1.1s

Algorithm
intervals
Results
247.0ms1050×body2560valid
225.0ms5875×body80valid
164.0ms905×body1280valid
100.0ms2863×body80nan
69.0ms457×body640valid
27.0ms99×body5120valid
22.0ms212×body320valid
9.0ms128×body160valid