Details

Time bar (total: 6.5s)

sample70.0ms

Algorithm
intervals
Results
19.0ms42×body2560valid
14.0ms181×body80valid
13.0ms41×body1280valid
6.0ms79×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

localize12.0ms

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))))

rewrite64.0ms

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:
16.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
38.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series300.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
105.0ms
(/ (+ (- 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
11658750
25001735

prune301.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.4b

localize14.0ms

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))))

rewrite111.0ms

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:
18.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
49.0ms
(/ (/ (+ 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))))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series485.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
152.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
182.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify131.0ms

Algorithm
egg-herbie
Counts
244 → 244
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
08185119
135603863
250013860

prune522.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize19.0ms

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))))

rewrite104.0ms

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:
18.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
26.0ms
(/ (* 1 (/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* a c)))) (* 2.0 a))
46.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* a c))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series585.0ms

Counts
4 → 12
Calls
4 calls:
290.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
122.0ms
(/ (* 1 (/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* a c)))) (* 2.0 a))
100.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* a c))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify126.0ms

Algorithm
egg-herbie
Counts
197 → 197
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
09524084
145732692
250012691

prune335.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.3b

localize16.0ms

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))))

rewrite119.0ms

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:
41.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a) c)
20.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
37.0ms
(/ (* 1 (/ 4.0 (/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a) c))) (* 2.0 a))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series369.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a) c)
73.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
130.0ms
(/ (* 1 (/ 4.0 (/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a) c))) (* 2.0 a))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify67.0ms

Algorithm
egg-herbie
Counts
284 → 284
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
012275730
150014425

prune539.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 5.3b

regimes143.0ms

Accuracy

87.7% (3.3b remaining)

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

bsearch166.0ms

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
465.0ms5822×body80valid
402.0ms1083×body2560valid
280.0ms903×body1280valid
215.0ms2984×body80nan
115.0ms452×body640valid
50.0ms113×body5120valid
40.0ms218×body320valid
15.0ms108×body160valid