Details

Time bar (total: 5.7s)

sample55.0ms

Algorithm
intervals
Results
14.0ms194×body80valid
8.0ms30×body2560valid
7.0ms100×body80nan
7.0ms28×body1280valid
3.0ms14×body640valid
1.0ms8×body320valid
1.0ms2×body5120valid
1.0ms6×body160valid

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: 33.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.2b
(- (* b b) (* 4.0 (* a c)))
1.9b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite60.0ms

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:
35.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
15.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series301.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
44.0ms
(- (* b b) (* 4.0 (* a c)))
79.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify54.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0438854
11658750
25001735

prune312.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.6b

localize14.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.8b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
9.7b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
23.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite105.0ms

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)))))
43.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
30.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series481.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
146.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
184.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify134.0ms

Algorithm
egg-herbie
Counts
244 → 244
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
08185119
135603863
250013860

prune745.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.5b

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* 4.0 (* a c)))
1.4b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.9b
(/ (* 2.0 a) (* 4.0 (* a c)))
23.0b
(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:
3.0ms
(- (* b b) (* 4.0 (* a c)))
16.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series206.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* b b) (* 4.0 (* a c)))
77.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify89.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
05973032
128321946
250021857

prune300.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
1.2b
(- (* b b) (* 4.0 (* a c)))
1.4b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
53×add-sqr-sqrt
52×*-un-lft-identity
48×add-cube-cbrt
34×sqrt-prod
25×add-exp-log
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
13×add-cbrt-cube
11×fma-neg
10×add-log-exp
9×div-exp
8×pow1
7×neg-mul-1
6×prod-exp
5×flip3-- associate-/r/ flip--
4×cbrt-undiv expm1-log1p-u log1p-expm1-u
3×rec-exp times-frac diff-log 1-exp associate-/l*
2×frac-times sub-neg pow-flip sqrt-div associate-*r/ cbrt-unprod distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down neg-log associate-*l/ clear-num associate-/r* div-inv inv-pow
Counts
4 → 162
Calls
4 calls:
28.0ms
(/ 1 (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
20.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series367.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(/ 1 (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
44.0ms
(- (* b b) (* 4.0 (* a c)))
77.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify83.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
06143343
123312171
250022121

prune302.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.5b

regimes127.0ms

Accuracy

95.4% (1.1b remaining)

Error of 6.9b against oracle of 5.8b and baseline of 29.8b

bsearch171.0ms

Steps
ItersRangePoint
5
3.0336165705843857e+124
7.533619617198572e+124
3.0781255133678807e+124
7
-3.9106408528448323e-240
-1.785276478006513e-242
-1.8135608595479747e-242
9
-8.769455893714235e+71
-3.4877376356874454e+65
-5.42705832741983e+68

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04424
14624
24624

end0.0ms

sample1.6s

Algorithm
intervals
Results
436.0ms5937×body80valid
294.0ms1019×body2560valid
213.0ms879×body1280valid
205.0ms2907×body80nan
87.0ms438×body640valid
40.0ms116×body5120valid
38.0ms250×body320valid
12.0ms106×body160valid