Details

Time bar (total: 6.2s)

sample36.0ms

Algorithm
intervals
Results
14.0ms274×body80valid
5.0ms99×body80nan

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03918
18018
214318
317718
418918
519318
619318

prune4.0ms

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: 20.5b

Counts
2 → 1

localize117.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
53×add-sqr-sqrt
51×*-un-lft-identity
47×add-cube-cbrt
37×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
7×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
3×diff-log
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 neg-log
Counts
4 → 140
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series273.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify66.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04062988
114311956
250021869

prune393.0ms

Filtered
152 candidates to 80 candidates (52.6%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1448152
Fresh000
Picked101
Done000
Total1458153

Merged error: 8.5b

Counts
153 → 8

localize119.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.4b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
6.3b
(/ (* a c) b)
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
62×*-un-lft-identity
60×prod-diff
55×add-sqr-sqrt
50×add-cube-cbrt
34×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
14×add-exp-log add-cbrt-cube
10×fma-neg
8×times-frac associate-/r* add-log-exp
7×neg-mul-1
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u distribute-lft-out
2×flip3-- frac-2neg sqrt-div diff-log prod-exp clear-num associate-/r/ flip-- cbrt-unprod div-inv associate-/l* distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 159
Calls
4 calls:
11.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
5.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series351.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
179.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
19.0ms
(/ (* a c) b)
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify83.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
06103137
125642048
250011968

prune440.0ms

Filtered
171 candidates to 88 candidates (51.5%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1647171
Fresh347
Picked101
Done000
Total16811179

Merged error: 7.6b

Counts
179 → 11

localize120.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.4b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ a (/ b c))) b)))
4.9b
(/ a (/ b c))
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
102×*-un-lft-identity
95×add-sqr-sqrt
90×add-cube-cbrt
80×times-frac
60×prod-diff
34×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
18×associate-/r*
14×add-exp-log add-cbrt-cube
10×fma-neg
8×add-log-exp
7×neg-mul-1
6×div-inv
5×pow1 cbrt-undiv div-exp
4×expm1-log1p-u log1p-expm1-u distribute-lft-out associate-/l*
3×associate-/r/
2×flip3-- frac-2neg sqrt-div diff-log clear-num flip-- distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log prod-exp cbrt-unprod flip-+
Counts
4 → 208
Calls
4 calls:
15.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ a (/ b c))) b)))
6.0ms
(/ a (/ b c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series359.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
183.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ a (/ b c))) b)))
27.0ms
(/ a (/ b c))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify102.0ms

Algorithm
egg-herbie
Counts
220 → 220
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
08333504
135072369
250022332

prune655.0ms

Filtered
220 candidates to 133 candidates (60.5%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2191220
Fresh01010
Picked101
Done000
Total22011231

Merged error: 7.6b

Counts
231 → 11

localize132.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.9b
(/ (* (cbrt a) (cbrt a)) (/ (* (cbrt b) (cbrt b)) (* (cbrt c) (cbrt c))))
4.4b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ (* (cbrt a) (cbrt a)) (/ (* (cbrt b) (cbrt b)) (* (cbrt c) (cbrt c)))) (/ (cbrt a) (/ (cbrt b) (cbrt c))))) b)))
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
62×*-un-lft-identity
60×prod-diff
55×add-sqr-sqrt
50×add-exp-log add-cube-cbrt
34×sqrt-prod
24×distribute-rgt-neg-in add-cbrt-cube
21×distribute-lft-neg-in
20×cbrt-undiv div-exp
14×prod-exp cbrt-unprod
12×times-frac
10×fma-neg associate-/r*
8×add-log-exp
7×neg-mul-1
5×pow1
4×expm1-log1p-u log1p-expm1-u div-inv distribute-lft-out
3×associate-/r/
2×flip3-- frac-2neg sqrt-div diff-log clear-num flip-- associate-/l* distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 180
Calls
4 calls:
10.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms
(/ (* (cbrt a) (cbrt a)) (/ (* (cbrt b) (cbrt b)) (* (cbrt c) (cbrt c))))
45.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ (* (cbrt a) (cbrt a)) (/ (* (cbrt b) (cbrt b)) (* (cbrt c) (cbrt c)))) (/ (cbrt a) (/ (cbrt b) (cbrt c))))) b)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series505.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
133.0ms
(/ (* (cbrt a) (cbrt a)) (/ (* (cbrt b) (cbrt b)) (* (cbrt c) (cbrt c))))
217.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ (* (cbrt a) (cbrt a)) (/ (* (cbrt b) (cbrt b)) (* (cbrt c) (cbrt c)))) (/ (cbrt a) (/ (cbrt b) (cbrt c))))) b)))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify111.0ms

Algorithm
egg-herbie
Counts
192 → 192
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
09164302
140082966
250012954

prune730.0ms

Filtered
192 candidates to 110 candidates (57.3%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1911192
Fresh01010
Picked101
Done000
Total19211203

Merged error: 7.6b

Counts
203 → 11

regimes257.0ms

Accuracy

91.2% (1.3b remaining)

Error of 7.9b against oracle of 6.6b and baseline of 20.9b

bsearch221.0ms

Steps
ItersRangePoint
8
3.6696373663460875e+72
1.716395662560696e+75
1.700743369447203e+75
10
-3.3972521543541393e+93
-2.6938476684742574e+82
-1.4465906485348473e+93

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
070101
170101

end0.0ms

sample887.0ms

Algorithm
intervals
Results
469.0ms8743×body80valid
156.0ms2961×body80nan