Details

Time bar (total: 6.8s)

sample42.0ms

Algorithm
intervals
Results
8.0ms36×body2560valid
8.0ms192×body80valid
5.0ms26×body1280valid
3.0ms83×body80nan
2.0ms12×body640valid
1.0ms9×body320valid
1.0ms3×body5120valid
0.0ms2×body160valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune5.0ms

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: 31.0b

Counts
2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
483×add-sqr-sqrt
330×associate-*l* prod-diff
309×*-un-lft-identity
229×add-cube-cbrt
177×associate-*r*
125×unswap-sqr
75×swap-sqr
65×*-commutative
60×times-frac
30×difference-of-squares
28×distribute-lft-out
24×sqrt-prod
17×distribute-rgt-neg-in
15×fma-neg
12×associate-/r* distribute-lft-out--
10×fma-def add-log-exp
9×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in
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 diff-log div-sub neg-log prod-exp clear-num cbrt-unprod div-inv
Counts
4 → 541
Calls
4 calls:
42.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
29.0ms
(- (* b b) (* (* 4.0 a) c))
35.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
41.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series343.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
48.0ms
(- (* b b) (* (* 4.0 a) c))
88.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
80.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify212.0ms

Algorithm
egg-herbie
Counts
553 → 553
Iterations

Useful iterations: 2 (130.0ms)

IterNodesCost
014429181
148926678
250016676

prune770.0ms

Filtered
553 candidates to 170 candidates (30.7%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New5449553
Fresh000
Picked101
Done000
Total5459554

Merged error: 4.5b

Counts
554 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a)
0.2b
(- (* b b) (* (* 4.0 a) c))
0.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
450×add-sqr-sqrt
330×prod-diff
312×associate-*l*
252×*-un-lft-identity
208×add-cube-cbrt
159×associate-*r*
119×unswap-sqr
75×swap-sqr
59×*-commutative
30×difference-of-squares
24×sqrt-prod
15×times-frac fma-neg
12×distribute-lft-out--
10×fma-def distribute-lft-out add-log-exp
8×distribute-rgt-neg-in
6×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in associate-/r*
2×neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div sum-log flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp neg-log clear-num div-inv
Counts
4 → 485
Calls
4 calls:
36.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a)
34.0ms
(- (* b b) (* (* 4.0 a) c))
35.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
41.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series357.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a)
49.0ms
(- (* b b) (* (* 4.0 a) c))
88.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
81.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify223.0ms

Algorithm
egg-herbie
Counts
497 → 497
Iterations

Useful iterations: 2 (135.0ms)

IterNodesCost
012568241
139515763
250015758

prune463.0ms

Filtered
497 candidates to 142 candidates (28.6%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New4907497
Fresh718
Picked011
Done000
Total4979506

Merged error: 4.5b

Counts
506 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
500×add-sqr-sqrt
339×*-un-lft-identity
330×prod-diff
312×associate-*l*
258×add-cube-cbrt
159×associate-*r*
123×times-frac
119×unswap-sqr
75×swap-sqr
59×*-commutative
30×difference-of-squares
28×distribute-lft-out
26×associate-/r*
24×sqrt-prod
19×associate-/r/
17×distribute-rgt-neg-in
15×add-exp-log fma-neg
12×distribute-lft-out--
10×fma-def add-log-exp
9×add-cbrt-cube
7×div-exp associate-/l*
6×pow1
5×flip3-+ flip-+ div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv distribute-lft-neg-in clear-num
2×rec-exp flip3-- frac-2neg sqrt-div 1-exp sum-log flip-- remove-double-div
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square pow-flip sqrt-pow1 pow1/2 diff-log neg-log inv-pow
Counts
4 → 567
Calls
4 calls:
46.0ms
(/ 1 (/ a (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
33.0ms
(- (* b b) (* (* 4.0 a) c))
33.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series394.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(/ 1 (/ a (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
53.0ms
(- (* b b) (* (* 4.0 a) c))
88.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
96.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify129.0ms

Algorithm
egg-herbie
Counts
579 → 579
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
014489524
150016889

prune565.0ms

Filtered
579 candidates to 170 candidates (29.4%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New5745579
Fresh437
Picked011
Done011
Total57810588

Merged error: 4.5b

Counts
588 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(* (/ 1 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite192.0ms

Algorithm
rewrite-expression-head
Rules
461×add-sqr-sqrt
330×prod-diff
325×associate-*l*
245×*-un-lft-identity
212×add-cube-cbrt
164×associate-*r*
122×unswap-sqr
75×swap-sqr
60×*-commutative
30×difference-of-squares
24×sqrt-prod
18×frac-times
15×fma-neg
13×add-exp-log
12×distribute-lft-out--
11×flip3-+ times-frac flip-+
10×fma-def add-log-exp
9×associate-*l/ associate-/r* add-cbrt-cube associate-/l*
7×pow1
5×distribute-rgt-neg-in
4×expm1-log1p-u prod-exp log1p-expm1-u distribute-lft-out
3×+-commutative distribute-lft-neg-in frac-2neg clear-num
2×distribute-rgt-in flip3-- distribute-lft-in sqrt-div associate-*r/ div-exp sum-log flip-- cbrt-unprod
1×cbrt-undiv neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square rec-exp sqrt-pow1 pow1/2 diff-log 1-exp pow-prod-down neg-log div-inv
Counts
4 → 516
Calls
4 calls:
33.0ms
(- (* b b) (* (* 4.0 a) c))
46.0ms
(* (/ 1 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
35.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series380.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(- (* b b) (* (* 4.0 a) c))
151.0ms
(* (/ 1 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
90.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
84.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify121.0ms

Algorithm
egg-herbie
Counts
528 → 528
Iterations

Useful iterations: 1 (41.0ms)

IterNodesCost
015748779
150026462

prune499.0ms

Filtered
528 candidates to 159 candidates (30.1%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New5262528
Fresh257
Picked101
Done022
Total5299538

Merged error: 4.5b

Counts
538 → 9

regimes184.0ms

Accuracy

83.3% (4.6b remaining)

Error of 10.5b against oracle of 5.9b and baseline of 33.3b

bsearch116.0ms

Steps
ItersRangePoint
6
5.170278655164064e-52
2.1804079894200568e-51
1.2688336265881624e-51
10
-2.7851241427016145e+159
-9.354797223898085e+144
-6.311729910477647e+146

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03618
13618

end0.0ms

sample1.2s

Algorithm
intervals
Results
246.0ms5955×body80valid
238.0ms1031×body2560valid
161.0ms853×body1280valid
119.0ms2987×body80nan
70.0ms462×body640valid
27.0ms222×body320valid
24.0ms86×body5120valid
7.0ms102×body160valid