Details

Time bar (total: 5.2s)

sample41.0ms

Algorithm
intervals
Results
8.0ms209×body80valid
8.0ms34×body2560valid
5.0ms79×body80nan
4.0ms22×body1280valid
3.0ms18×body640valid
0.0ms3×body320valid
0.0ms4×body160valid

simplify11.0ms

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: 34.9b

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) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
23.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite59.0ms

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:
37.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series291.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
77.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(- (* b b) (* (* 4.0 a) c))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify71.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
0438854
11702750
25001735

prune301.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.7b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
4.4b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.6b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite87.0ms

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))
45.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
27.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series438.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b b) (* (* 4.0 a) c))
146.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
179.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
69.0ms
(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

prune467.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
14.1b
(/ (* 2.0 a) (* 4.0 (* a c)))
23.5b
(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))
8.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series201.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(- (- 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)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify99.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
06103042
130781945
250021857

prune328.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (/ 1 1) (* (/ 2.0 (/ (* c 4.0) 1)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.8b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
23.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
200×add-exp-log
140×div-exp
65×add-sqr-sqrt
64×*-un-lft-identity
61×prod-diff
60×add-cube-cbrt
56×prod-exp
49×1-exp add-cbrt-cube
34×sqrt-prod
31×times-frac
25×cbrt-undiv
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
14×rec-exp
13×associate-/l*
11×fma-neg
10×cbrt-unprod add-log-exp
7×neg-mul-1
5×pow1 flip3-- associate-/r/ flip--
4×expm1-log1p-u log1p-expm1-u
3×diff-log div-inv
2×frac-times sub-neg sqrt-div associate-*r/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log associate-*l/ clear-num associate-/r* associate-/l/
Counts
4 → 227
Calls
4 calls:
26.0ms
(/ (/ 1 1) (* (/ 2.0 (/ (* c 4.0) 1)) (- (- 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))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series370.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(/ (/ 1 1) (* (/ 2.0 (/ (* c 4.0) 1)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms
(- (* b b) (* (* 4.0 a) c))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify128.0ms

Algorithm
egg-herbie
Counts
239 → 239
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
011264440
149133023
250013021

prune370.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.6b

regimes251.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.5b against oracle of 5.3b and baseline of 29.3b

bsearch197.0ms

Steps
ItersRangePoint
8
1.9559514031553493e+101
2.0413668072230428e+104
9.373511171447418e+103
9
1.0311906074547519e-259
1.091011630730822e-254
1.0417939395900796e-259
9
-2.3467190644739184e+107
-3.2019781887028674e+101
-1.7431685240570133e+102

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05233
15233

end0.0ms

sample1.2s

Algorithm
intervals
Results
259.0ms1070×body2560valid
234.0ms5839×body80valid
171.0ms884×body1280valid
110.0ms2849×body80nan
74.0ms496×body640valid
29.0ms102×body5120valid
27.0ms220×body320valid
8.0ms103×body160valid