Details

Time bar (total: 5.8s)

sample53.0ms

Algorithm
intervals
Results
12.0ms41×body2560valid
9.0ms172×body80valid
8.0ms34×body1280valid
5.0ms98×body80nan
2.0ms13×body640valid
1.0ms4×body5120valid
1.0ms8×body320valid
0.0ms3×body160valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0299
1659
21219
31519
41609
51649
61649

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: 32.3b

Counts
2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b
(- (* b b) (* 4.0 (* a c)))
1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 157
Calls
4 calls:
15.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
4.0ms
(- (* b b) (* 4.0 (* a c)))
10.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series298.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
45.0ms
(- (* b b) (* 4.0 (* a c)))
80.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify83.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05903305
121012212
250022128

prune327.0ms

Filtered
169 candidates to 89 candidates (52.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New15910169
Fresh000
Picked101
Done000
Total16010170

Merged error: 3.4b

Counts
170 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.4b
(- (* b b) (* 4.0 (* a c)))
1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
89×add-sqr-sqrt
88×*-un-lft-identity
68×add-cube-cbrt
67×times-frac
61×prod-diff
38×sqrt-prod
26×distribute-rgt-neg-in
25×add-exp-log
21×distribute-lft-neg-in
13×associate-/r* add-cbrt-cube
12×div-exp
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
9×associate-/r/
7×neg-mul-1 flip3-- flip--
6×pow1
5×cbrt-undiv div-inv
4×expm1-log1p-u log1p-expm1-u
3×rec-exp diff-log 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 205
Calls
4 calls:
17.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
10.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series323.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
51.0ms
(- (* b b) (* 4.0 (* a c)))
83.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify107.0ms

Algorithm
egg-herbie
Counts
217 → 217
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
07184221
130992976
250012863

prune349.0ms

Filtered
217 candidates to 98 candidates (45.2%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2125217
Fresh459
Picked011
Done000
Total21611227

Merged error: 3.3b

Counts
227 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 (* 2.0 a)) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.4b
(- (* b b) (* 4.0 (* a c)))
1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
441×times-frac
291×add-sqr-sqrt
290×*-un-lft-identity
190×add-cube-cbrt
87×add-exp-log
61×prod-diff
58×div-exp sqrt-prod
50×distribute-lft-out-- difference-of-squares
46×distribute-rgt-neg-in
37×div-inv
27×associate-/r*
25×add-cbrt-cube
21×distribute-lft-neg-in
17×associate-/r/
15×rec-exp 1-exp
13×cbrt-undiv
12×prod-exp
11×flip3-- fma-neg flip--
10×add-log-exp
7×neg-mul-1 associate-/l*
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×diff-log
2×sub-neg sqrt-div cbrt-unprod
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/l/
Counts
4 → 394
Calls
4 calls:
21.0ms
(/ (/ 1 (* 2.0 a)) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
10.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series320.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ (/ 1 (* 2.0 a)) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
51.0ms
(- (* b b) (* 4.0 (* a c)))
83.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify102.0ms

Algorithm
egg-herbie
Counts
406 → 406
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
014168437
150026798

prune566.0ms

Filtered
406 candidates to 157 candidates (38.7%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New4042406
Fresh279
Picked011
Done101
Total40710417

Merged error: 3.3b

Counts
417 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (/ 1 (* 2.0 a)))
0.5b
(* (cbrt (/ 1 (* 2.0 a))) (cbrt (/ 1 (* 2.0 a))))
1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
73×add-sqr-sqrt
66×*-un-lft-identity
60×add-cube-cbrt prod-diff
43×cbrt-prod
34×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
15×times-frac
12×pow1 swap-sqr
10×fma-neg associate-*r* associate-*l*
8×add-log-exp
7×neg-mul-1 pow1/3 div-inv
6×add-exp-log
5×cbrt-div
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u unswap-sqr
2×flip3-- sqrt-div diff-log pow-prod-down pow-sqr pow-prod-up flip-- distribute-lft-out-- difference-of-squares
1×associate--l- pow2 neg-sub0 frac-times sub-neg rem-sqrt-square sqrt-pow1 pow-plus pow1/2 associate-*r/ neg-log associate-*l/ prod-exp *-commutative cbrt-unprod
Counts
4 → 184
Calls
4 calls:
3.0ms
(cbrt (/ 1 (* 2.0 a)))
9.0ms
(* (cbrt (/ 1 (* 2.0 a))) (cbrt (/ 1 (* 2.0 a))))
10.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series606.0ms

Counts
4 → 12
Calls
4 calls:
202.0ms
(cbrt (/ 1 (* 2.0 a)))
246.0ms
(* (cbrt (/ 1 (* 2.0 a))) (cbrt (/ 1 (* 2.0 a))))
82.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
76.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify83.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05243350
118432237
250012113

prune412.0ms

Filtered
196 candidates to 102 candidates (52.0%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1942196
Fresh178
Picked011
Done011
Total19511206

Merged error: 3.2b

Counts
206 → 11

regimes253.0ms

Accuracy

87% (3.5b remaining)

Error of 9.3b against oracle of 5.8b and baseline of 32.9b

bsearch193.0ms

Steps
ItersRangePoint
9
1.537663903506608e+146
1.524085477896404e+154
5.336285016730311e+150
8
-3.02535277249636e-96
-5.709024195993626e-101
-7.272022142268576e-101
6
-0.04325046342239626
-0.004915430213868263
-0.04248736169027556

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04940
15140
25140

end0.0ms

sample1.4s

Algorithm
intervals
Results
307.0ms5861×body80valid
302.0ms1016×body2560valid
213.0ms898×body1280valid
146.0ms2937×body80nan
85.0ms447×body640valid
42.0ms119×body5120valid
36.0ms256×body320valid
12.0ms127×body160valid