Details

Time bar (total: 5.7s)

sample284.0ms

Algorithm
intervals
Results
8.0ms192×body80valid
6.0ms33×body2560valid
4.0ms26×body1280valid
4.0ms113×body80nan
1.0ms10×body640valid
1.0ms4×body5120valid
1.0ms9×body320valid
0.0ms7×body160valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1337
2467
3497
4497

prune4.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 34.4b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b
(- (* b_2 b_2) (* a c))
2.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
587×add-sqr-sqrt
380×prod-diff
326×*-un-lft-identity
210×add-cube-cbrt
192×sqrt-prod
132×associate-*l*
130×difference-of-squares
112×unswap-sqr
84×associate-*r*
68×distribute-rgt-neg-in
63×distribute-lft-neg-in swap-sqr
58×distribute-lft-out--
52×*-commutative
25×fma-neg
21×neg-mul-1 times-frac
10×add-log-exp
7×associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log associate-/r*
2×associate--l- neg-sub0 sub-neg sqrt-div div-sub associate-/l/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp neg-log clear-num div-inv
Counts
4 → 533
Calls
4 calls:
43.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
20.0ms
(- (* b_2 b_2) (* a c))
28.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
42.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series279.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
38.0ms
(- (* b_2 b_2) (* a c))
78.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
75.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify178.0ms

Algorithm
egg-herbie
Counts
545 → 545
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
0115910954
136307708
250017703

prune405.0ms

Filtered
545 candidates to 140 candidates (74.3%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New5369545
Fresh000
Picked101
Done000
Total5379546

Merged error: 5.1b

Counts
546 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.4b
(- (* b_2 b_2) (* a c))
2.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
685×add-sqr-sqrt
425×*-un-lft-identity
380×prod-diff
272×add-cube-cbrt
201×sqrt-prod
165×times-frac
148×difference-of-squares
132×associate-*l*
112×unswap-sqr
84×associate-*r*
77×distribute-rgt-neg-in
76×distribute-lft-out--
63×distribute-lft-neg-in swap-sqr
52×*-commutative
34×associate-/r*
25×fma-neg
21×neg-mul-1 associate-/r/
15×add-exp-log
10×add-log-exp
9×add-cbrt-cube
7×flip3-- div-exp flip-- associate-/l*
6×pow1
5×div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv diff-log clear-num
2×sub-neg rec-exp frac-2neg sqrt-div 1-exp remove-double-div
1×associate--l- neg-sub0 rem-sqrt-square pow-flip sqrt-pow1 pow1/2 neg-log inv-pow
Counts
4 → 632
Calls
4 calls:
32.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
19.0ms
(- (* b_2 b_2) (* a c))
32.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series287.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
35.0ms
(- (* b_2 b_2) (* a c))
75.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
71.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify133.0ms

Algorithm
egg-herbie
Counts
644 → 644
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
0138912500
150019072

prune482.0ms

Filtered
644 candidates to 176 candidates (72.7%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New6395644
Fresh538
Picked011
Done000
Total6449653

Merged error: 5.0b

Counts
653 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b
(- (* b_2 b_2) (* a c))
2.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
587×add-sqr-sqrt
380×prod-diff
326×*-un-lft-identity
210×add-cube-cbrt
192×sqrt-prod
132×associate-*l*
130×difference-of-squares
112×unswap-sqr
84×associate-*r*
68×distribute-rgt-neg-in
63×distribute-lft-neg-in swap-sqr
58×distribute-lft-out--
52×*-commutative
25×fma-neg
21×neg-mul-1 times-frac
10×add-log-exp
7×associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log associate-/r*
2×associate--l- neg-sub0 sub-neg sqrt-div div-sub associate-/l/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp neg-log clear-num div-inv
Counts
4 → 533
Calls
4 calls:
39.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
22.0ms
(- (* b_2 b_2) (* a c))
28.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
28.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series268.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms
(- (* b_2 b_2) (* a c))
75.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
68.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify171.0ms

Algorithm
egg-herbie
Counts
545 → 545
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
0115910955
136207708
250017703

prune343.0ms

Filtered
545 candidates to 136 candidates (75.0%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New5450545
Fresh077
Picked011
Done011
Total5459554

Merged error: 5.0b

Counts
554 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt a)
0.7b
(cbrt a)
2.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
370×add-sqr-sqrt
200×prod-diff
188×sqrt-prod
182×*-un-lft-identity
112×difference-of-squares
90×add-cube-cbrt
77×unswap-sqr
64×distribute-rgt-neg-in
63×distribute-lft-neg-in
46×distribute-lft-out--
44×associate-*l*
22×swap-sqr *-commutative
21×neg-mul-1
10×fma-neg
8×add-log-exp
6×cbrt-prod
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
2×flip3-- pow1/3 sqrt-div diff-log flip--
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 287
Calls
4 calls:
1.0ms
(cbrt a)
1.0ms
(cbrt a)
31.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series505.0ms

Counts
4 → 12
Calls
4 calls:
184.0ms
(cbrt a)
180.0ms
(cbrt a)
74.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
67.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify93.0ms

Algorithm
egg-herbie
Counts
299 → 299
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
06097366
116785625
250015412

prune334.0ms

Filtered
299 candidates to 93 candidates (68.9%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New2981299
Fresh066
Picked011
Done022
Total29810308

Merged error: 5.0b

Counts
308 → 10

regimes257.0ms

Accuracy

85.3% (4.2b remaining)

Error of 9.7b against oracle of 5.5b and baseline of 34.3b

bsearch48.0ms

Steps
ItersRangePoint
0
1.3836563058951246e+50
1.390978468581987e+50
1.3873173872385558e+50
9
-2.816841330355383e-75
-7.368877589091801e-81
-1.0996442222619662e-75

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02914
12914

end0.0ms

sample1.0s

Algorithm
intervals
Results
214.0ms1103×body2560valid
192.0ms5871×body80valid
143.0ms888×body1280valid
87.0ms2794×body80nan
57.0ms454×body640valid
25.0ms232×body320valid
25.0ms104×body5120valid
7.0ms115×body160valid