Details

Time bar (total: 4.9s)

sample45.0ms

Algorithm
intervals
Results
10.0ms35×body2560valid
7.0ms181×body80valid
6.0ms33×body1280valid
3.0ms92×body80nan
2.0ms17×body640valid
2.0ms6×body5120valid
1.0ms6×body320valid
0.0ms2×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize11.0ms

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))))

rewrite33.0ms

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:
13.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
4.0ms
(- (* b b) (* 4.0 (* a c)))
10.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series295.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
45.0ms
(- (* b b) (* 4.0 (* a c)))
77.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify48.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0438854
11658750
25001735

prune293.0ms

Filtered
102 candidates to 82 candidates (80.4%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.0b

localize14.0ms

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))))

rewrite62.0ms

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))))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series461.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
142.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
174.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify128.0ms

Algorithm
egg-herbie
Counts
244 → 244
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
08185119
135603863
250013860

prune533.0ms

Filtered
244 candidates to 141 candidates (57.8%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.9b

localize14.0ms

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))))

rewrite45.0ms

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)))
11.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series331.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* b b) (* 4.0 (* a c)))
75.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
139.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify100.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
06553361
132672163
250022073

prune314.0ms

Filtered
164 candidates to 82 candidates (50.0%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) 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
61×prod-diff
53×add-sqr-sqrt
52×*-un-lft-identity
48×add-cube-cbrt
34×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×add-exp-log fma-neg
10×add-log-exp
9×add-cbrt-cube
7×neg-mul-1
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×times-frac diff-log div-exp associate-/r*
2×cbrt-undiv sub-neg sqrt-div associate-*r/ prod-exp associate-/l/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 1-exp neg-log clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 149
Calls
4 calls:
21.0ms
(/ (* 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) c)
5.0ms
(- (* b b) (* 4.0 (* a c)))
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series271.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(/ (* 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) c)
42.0ms
(- (* b b) (* 4.0 (* a c)))
74.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify77.0ms

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05703168
120932044
250022000

prune322.0ms

Filtered
161 candidates to 86 candidates (53.4%)
Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.9b

regimes173.0ms

Accuracy

95.5% (1.1b remaining)

Error of 6.8b against oracle of 5.7b and baseline of 30.2b

bsearch70.0ms

Steps
ItersRangePoint
3
5.062782482725967e+112
6.853081242536654e+112
5.398463500190471e+112
2
-9.893319725742429e-275
-9.099256253469455e-275
-9.198514187503577e-275
5
-2.2693772293991552e+117
-7.333494566860601e+116
-1.5277916383184032e+117

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04929
15129
25129

end0.0ms

sample1.2s

Algorithm
intervals
Results
255.0ms1057×body2560valid
235.0ms5837×body80valid
165.0ms876×body1280valid
108.0ms2892×body80nan
70.0ms459×body640valid
39.0ms137×body5120valid
27.0ms245×body320valid
7.0ms95×body160valid