Details

Time bar (total: 6.3s)

sample68.0ms

Algorithm
intervals
Results
19.0ms42×body2560valid
14.0ms181×body80valid
12.0ms41×body1280valid
5.0ms79×body80nan
3.0ms12×body640valid
1.0ms3×body5120valid
1.0ms3×body320valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b
(- (* b b) (* (* 4.0 a) c))
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite57.0ms

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:
14.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
34.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series297.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
104.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
47.0ms
(- (* b b) (* (* 4.0 a) c))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify49.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0438854
11702750
25001735

prune290.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.4b

localize16.0ms

Local error

Found 4 expressions with local error:

2.3b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite104.0ms

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:
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
29.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series475.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
148.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
181.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify144.0ms

Algorithm
egg-herbie
Counts
244 → 244
Iterations

Useful iterations: 2 (104.0ms)

IterNodesCost
08295119
137633863
250013860

prune569.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize16.0ms

Local error

Found 4 expressions with local error:

2.3b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b
(/ (* 1 (/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (* 2.0 a))
10.6b
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
86×add-exp-log
61×add-sqr-sqrt
60×*-un-lft-identity prod-diff
54×add-cbrt-cube
48×add-cube-cbrt
40×div-exp
36×sqrt-prod
30×prod-exp
24×distribute-rgt-neg-in
22×cbrt-undiv
21×distribute-lft-neg-in
16×cbrt-unprod
10×fma-neg
8×times-frac 1-exp associate-/l* add-log-exp
7×neg-mul-1
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×flip3-- flip-- associate-/l/
2×frac-2neg sqrt-div diff-log clear-num associate-/r* div-inv
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 div-sub associate-*r/ neg-log
Counts
4 → 185
Calls
4 calls:
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.0ms
(/ (* 1 (/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (* 2.0 a))
45.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series386.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
126.0ms
(/ (* 1 (/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (* 2.0 a))
110.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify115.0ms

Algorithm
egg-herbie
Counts
197 → 197
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
09544084
145792692
250012690

prune373.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.3b

localize21.0ms

Local error

Found 4 expressions with local error:

2.0b
(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a) c)
2.3b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b
(/ (* 1 (/ 4.0 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a) c))) (* 2.0 a))
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
169×add-sqr-sqrt
168×*-un-lft-identity
160×times-frac
116×add-cube-cbrt
86×add-exp-log
60×prod-diff
54×add-cbrt-cube
46×sqrt-prod
45×div-exp
34×distribute-rgt-neg-in
26×associate-/l* distribute-lft-out-- difference-of-squares
25×cbrt-undiv prod-exp
21×distribute-lft-neg-in
13×cbrt-unprod
10×fma-neg
8×1-exp add-log-exp
7×neg-mul-1
6×div-inv
5×pow1
4×expm1-log1p-u associate-/r* log1p-expm1-u
2×flip3-- frac-2neg sqrt-div diff-log div-sub clear-num flip-- associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ neg-log
Counts
4 → 272
Calls
4 calls:
40.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a) c)
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
34.0ms
(/ (* 1 (/ 4.0 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a) c))) (* 2.0 a))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series385.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a) c)
74.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
129.0ms
(/ (* 1 (/ 4.0 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a) c))) (* 2.0 a))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify68.0ms

Algorithm
egg-herbie
Counts
284 → 284
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012285741
150014425

prune581.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 5.3b

regimes140.0ms

Accuracy

87.7% (3.3b remaining)

Error of 8.9b against oracle of 5.6b and baseline of 32.6b

bsearch160.0ms

Steps
ItersRangePoint
7
1.0320989087612647e-20
5.408012210248103e-19
1.1689690778247071e-19
5
-9.237006875632357e-258
-4.348398702340512e-258
-6.63395785424786e-258
7
-1.5320971041566743e+27
-3.280360895118841e+25
-1.5052990324106084e+27

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04829
15029
25029

end0.0ms

sample1.8s

Algorithm
intervals
Results
427.0ms5822×body80valid
413.0ms1083×body2560valid
273.0ms903×body1280valid
204.0ms2984×body80nan
113.0ms452×body640valid
51.0ms113×body5120valid
40.0ms218×body320valid
14.0ms108×body160valid