Details

Time bar (total: 5.9s)

sample44.0ms

Algorithm
intervals
Results
8.0ms34×body2560valid
7.0ms172×body80valid
6.0ms32×body1280valid
3.0ms79×body80nan
3.0ms16×body640valid
3.0ms9×body5120valid
1.0ms9×body320valid
0.0ms3×body160valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 35.6b

Counts
2 → 1

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 b) (* (* 4.0 a) c))
1.2b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite36.0ms

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:
13.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(- (* b b) (* (* 4.0 a) c))
9.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series368.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
59.0ms
(- (* b b) (* (* 4.0 a) c))
97.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
83.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify56.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0438854
11702750
25001735

prune344.0ms

Filtered
102 candidates to 82 candidates (80.4%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New9210102
Fresh000
Picked101
Done000
Total9310103

Merged error: 6.1b

Counts
103 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (- 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))
8.8b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite61.0ms

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:
11.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series543.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
166.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
211.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify159.0ms

Algorithm
egg-herbie
Counts
244 → 244
Iterations

Useful iterations: 2 (114.0ms)

IterNodesCost
08295119
137633863
250013860

prune631.0ms

Filtered
244 candidates to 141 candidates (57.8%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2413244
Fresh459
Picked011
Done000
Total2459254

Merged error: 6.0b

Counts
254 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
0.8b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.5b
(/ (* 2.0 a) (* 4.0 (* a c)))
23.2b
(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:
4.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series237.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(- (* b b) (* (* 4.0 a) c))
84.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify105.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
06103043
130781945
250021857

prune358.0ms

Filtered
162 candidates to 79 candidates (48.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1611162
Fresh167
Picked101
Done011
Total1638171

Merged error: 6.0b

Counts
171 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ 1 1) (* (/ 2.0 (/ (* c 4.0) 1)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.8b
(- (* b b) (* (* 4.0 a) c))
0.8b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite55.0ms

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:
20.0ms
(/ (/ 1 1) (* (/ 2.0 (/ (* c 4.0) 1)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series429.0ms

Counts
4 → 12
Calls
4 calls:
207.0ms
(/ (/ 1 1) (* (/ 2.0 (/ (* c 4.0) 1)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
56.0ms
(- (* b b) (* (* 4.0 a) c))
92.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify141.0ms

Algorithm
egg-herbie
Counts
239 → 239
Iterations

Useful iterations: 2 (107.0ms)

IterNodesCost
011264440
149133023
250013021

prune423.0ms

Filtered
239 candidates to 100 candidates (41.8%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2381239
Fresh246
Picked101
Done011
Total2416247

Merged error: 6.0b

Counts
247 → 6

regimes377.0ms

Accuracy

94.8% (1.2b remaining)

Error of 6.6b against oracle of 5.4b and baseline of 29.3b

bsearch190.0ms

Steps
ItersRangePoint
9
4.546949039871578e+116
7.0067478635952275e+121
2.079077083921404e+119
4
-1.1837570975005782e-173
-6.311599190677229e-174
-8.415357623026543e-174
9
-1.8864815038392082e+94
-1.5243980513895428e+89
-6.875360452843506e+92

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05029
15029

end0.0ms

sample1.2s

Algorithm
intervals
Results
253.0ms1052×body2560valid
241.0ms5820×body80valid
171.0ms891×body1280valid
111.0ms2865×body80nan
74.0ms469×body640valid
32.0ms111×body5120valid
29.0ms235×body320valid
10.0ms122×body160valid