Details

Time bar (total: 5.7s)

sample47.0ms

Algorithm
intervals
Results
8.0ms35×body2560valid
7.0ms181×body80valid
6.0ms33×body1280valid
6.0ms17×body640valid
4.0ms92×body80nan
2.0ms6×body5120valid
1.0ms6×body320valid
0.0ms2×body160valid

simplify13.0ms

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: 37.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b
(- (* b b) (* (* 4.0 a) c))
1.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

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))
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)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
47.0ms
(- (* b b) (* (* 4.0 a) c))
89.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
80.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify53.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0438854
11702750
25001735

prune335.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.0b

localize16.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.7b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
124×*-un-lft-identity
90×times-frac
80×add-cube-cbrt
60×prod-diff
44×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
10×fma-neg
8×associate-/r* add-log-exp
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u 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 → 232
Calls
4 calls:
11.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
17.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series551.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
174.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
205.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
82.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify152.0ms

Algorithm
egg-herbie
Counts
244 → 244
Iterations

Useful iterations: 2 (115.0ms)

IterNodesCost
08295119
137633863
250013860

prune630.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.4b
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
51×add-sqr-sqrt
50×*-un-lft-identity
46×add-cube-cbrt
34×sqrt-prod
25×add-exp-log add-cbrt-cube
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×prod-exp cbrt-unprod
7×neg-mul-1
6×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×sub-neg sqrt-div associate-*r/ associate-/r/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 152
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
10.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series384.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* (* 4.0 a) c))
90.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
168.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
78.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify119.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
06683371
134822161
250012072

prune358.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (* c 4.0) 1) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.8b
(- (* b b) (* (* 4.0 a) c))
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
107×add-sqr-sqrt
106×*-un-lft-identity
73×times-frac
70×add-cube-cbrt
61×prod-diff
42×sqrt-prod
30×distribute-rgt-neg-in
21×distribute-lft-neg-in
18×add-exp-log distribute-lft-out-- difference-of-squares
13×add-cbrt-cube
11×fma-neg
10×add-log-exp
9×div-exp div-inv
7×neg-mul-1 associate-/r* associate-/l*
5×pow1 cbrt-undiv
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×sub-neg sqrt-div 1-exp prod-exp associate-/r/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num cbrt-unprod associate-/l/
Counts
4 → 209
Calls
4 calls:
15.0ms
(/ (/ (* c 4.0) 1) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series400.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(/ (/ (* c 4.0) 1) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
48.0ms
(- (* b b) (* (* 4.0 a) c))
86.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
80.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify109.0ms

Algorithm
egg-herbie
Counts
221 → 221
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
07574277
132393087
250033006

prune437.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.9b

regimes187.0ms

Accuracy

95.9% (1.0b remaining)

Error of 6.7b against oracle of 5.7b and baseline of 30.1b

bsearch136.0ms

Steps
ItersRangePoint
3
5.062782482725967e+112
6.853081242536654e+112
6.7411875700484855e+112
8
-6.840002653067741e-267
-6.65450989691572e-271
-6.312755445441822e-270
5
-2.2693772293991552e+117
-7.333494566860601e+116
-1.5277916383184032e+117

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04828
14828

end0.0ms

sample1.2s

Algorithm
intervals
Results
254.0ms1057×body2560valid
231.0ms5837×body80valid
167.0ms876×body1280valid
104.0ms2892×body80nan
67.0ms459×body640valid
41.0ms137×body5120valid
32.0ms245×body320valid
7.0ms95×body160valid