Details

Time bar (total: 5.1s)

sample45.0ms

Algorithm
intervals
Results
9.0ms34×body2560valid
8.0ms179×body80valid
6.0ms29×body1280valid
4.0ms85×body80nan
3.0ms17×body640valid
2.0ms5×body5120valid
1.0ms8×body320valid
0.0ms3×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0229
1439
2839
31109
41189
51189

prune2.0ms

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: 36.0b

Counts
2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.0b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b
(- (* b b) (* (* 3.0 a) c))
23.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite33.0ms

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) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series300.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
48.0ms
(- (* b b) (* (* 3.0 a) c))
67.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify51.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0433855
11670751
25001736

prune275.0ms

Filtered
102 candidates to 82 candidates (80.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New939102
Fresh000
Picked101
Done000
Total949103

Merged error: 5.0b

Counts
103 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

2.8b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.3b
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
11.1b
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
23.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite56.0ms

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:
10.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
16.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
12.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series471.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
148.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
179.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
67.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify146.0ms

Algorithm
egg-herbie
Counts
244 → 244
Iterations

Useful iterations: 2 (104.0ms)

IterNodesCost
08255119
137383863
250013860

prune460.0ms

Filtered
244 candidates to 141 candidates (57.8%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New2404244
Fresh178
Picked011
Done000
Total24112253

Merged error: 4.8b

Counts
253 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 3.0 a) c))
2.8b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
16.0b
(/ (* 3.0 a) (* 3.0 (* a c)))
23.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite34.0ms

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:
7.0ms
(- (* b b) (* (* 3.0 a) c))
10.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
7.0ms
(/ (* 3.0 a) (* 3.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series247.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(- (* b b) (* (* 3.0 a) c))
94.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
16.0ms
(/ (* 3.0 a) (* 3.0 (* a c)))
65.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify115.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
05983041
130531925
250021816

prune259.0ms

Filtered
162 candidates to 79 candidates (48.8%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1602162
Fresh2810
Picked101
Done011
Total16311174

Merged error: 4.8b

Counts
174 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (* (/ 1.0 c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
1.0b
(- (* b b) (* (* 3.0 a) c))
2.8b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite37.0ms

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:
13.0ms
(/ 1 (* (/ 1.0 c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms
(- (* b b) (* (* 3.0 a) c))
10.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series397.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(/ 1 (* (/ 1.0 c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
43.0ms
(- (* b b) (* (* 3.0 a) c))
98.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
83.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify89.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06143343
123772171
250012121

prune249.0ms

Filtered
174 candidates to 87 candidates (50.0%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1722174
Fresh279
Picked011
Done011
Total17411185

Merged error: 4.8b

Counts
185 → 11

regimes282.0ms

Accuracy

92.2% (1.9b remaining)

Error of 7.3b against oracle of 5.4b and baseline of 29.8b

bsearch171.0ms

Steps
ItersRangePoint
9
14028.172733867412
3007116902181.375
2947728123750.7354
8
-4.654091770266614e-259
-1.1349992526466847e-263
-1.3969863832568379e-263
8
-3.346688072492859e+118
-7.406473594041322e+115
-1.0306858894842368e+117

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04626
14626

end0.0ms

sample1.3s

Algorithm
intervals
Results
296.0ms1099×body2560valid
282.0ms5799×body80valid
199.0ms888×body1280valid
139.0ms2953×body80nan
85.0ms468×body640valid
41.0ms118×body5120valid
28.0ms214×body320valid
12.0ms111×body160valid