Details

Time bar (total: 5.0s)

sample43.0ms

Algorithm
intervals
Results
9.0ms34×body1280valid
7.0ms189×body80valid
6.0ms28×body2560valid
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 (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: 35.5b

localize11.0ms

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)))

rewrite61.0ms

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:
38.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
13.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series296.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(- (* b b) (* (* 4.0 a) c))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify49.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0438854
11702750
25001735

prune314.0ms

Filtered
102 candidates to 82 candidates (80.4%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.9b

localize16.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* (* 4.0 a) c))
2.3b
(/ (/ (+ 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)))))
25.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff flip-+
Counts
4 → 158
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
43.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
31.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series429.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* 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)))

simplify125.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (100.0ms)

IterNodesCost
06742663
134622412
250012406

prune490.0ms

Filtered
170 candidates to 117 candidates (68.8%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.8b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(- (* b b) (* (* 4.0 a) c))
16.5b
(/ (* 2.0 a) (* 4.0 (* a c)))
25.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite38.0ms

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 log1p-expm1-u
3×flip3-- diff-log flip--
2×sub-neg sqrt-div 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 → 150
Calls
4 calls:
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
7.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series203.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify96.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
06103042
130781945
250021857

prune326.0ms

Filtered
162 candidates to 79 candidates (48.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
1.2b
(- (- 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)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
113×add-exp-log
61×prod-diff
53×add-sqr-sqrt
52×*-un-lft-identity
51×prod-exp
48×add-cube-cbrt
44×div-exp
34×sqrt-prod
29×add-cbrt-cube
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
16×rec-exp 1-exp
14×associate-/r/
11×pow1 frac-times fma-neg
10×cbrt-undiv add-log-exp
9×cbrt-unprod
8×flip3-- flip--
7×neg-mul-1 associate-*l/
5×associate-*r/
4×expm1-log1p-u log1p-expm1-u
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 frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/r* div-inv inv-pow
Counts
4 → 196
Calls
4 calls:
65.0ms
(/ 1 (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series369.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(/ 1 (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(- (* b b) (* (* 4.0 a) c))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify113.0ms

Algorithm
egg-herbie
Counts
208 → 208
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
09213920
139652595
250012555

prune365.0ms

Filtered
208 candidates to 96 candidates (46.2%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.8b

regimes146.0ms

Accuracy

95.7% (1.0b remaining)

Error of 6.8b against oracle of 5.7b and baseline of 29.8b

bsearch188.0ms

Steps
ItersRangePoint
5
1.1874868645648804e+84
3.824179182553312e+84
3.347196852696382e+84
11
1.7635143872496245e-284
6.841012161467506e-264
1.7859783972070086e-284
8
-3.734333779790662e+128
-2.2987999557012895e+125
-5.238946631357967e+127

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04731
14731

end0.0ms

sample1.1s

Algorithm
intervals
Results
242.0ms1050×body2560valid
227.0ms5875×body80valid
171.0ms905×body1280valid
107.0ms2863×body80nan
69.0ms457×body640valid
30.0ms99×body5120valid
23.0ms212×body320valid
9.0ms128×body160valid