Details

Time bar (total: 3.7s)

sample61.0ms

Algorithm
intervals
Results
14.0ms33×body2560valid
10.0ms179×body80valid
7.0ms26×body1280valid
5.0ms101×body80nan
4.0ms20×body640valid
2.0ms14×body320valid
2.0ms4×body5120valid
0.0ms3×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
012817
112817

prune7.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 35.7b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.1b
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in 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 → 77
Calls
4 calls:
12.0ms
(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
8.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series59.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms
(- (* b b) (* 4.0 (* a c)))
17.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify40.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
050351467

prune162.0ms

Filtered
64 candidates to 89 candidates (-39.1%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New80989
Fresh000
Picked101
Done000
Total81990

Merged error: 5.1b

Counts
90 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* 4.0 (* a c)))
3.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
9.4b
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
22.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
77×add-sqr-sqrt
56×*-un-lft-identity
36×add-cube-cbrt
27×associate-/l*
20×difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-lft-out--
7×cbrt-undiv div-exp associate-/r*
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 138
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
17.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
11.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series125.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(- (* b b) (* 4.0 (* a c)))
44.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
59.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify56.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
049553663
149553663

prune266.0ms

Filtered
108 candidates to 150 candidates (-38.9%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1473150
Fresh178
Picked011
Done000
Total14811159

Merged error: 5.0b

Counts
159 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (* a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
0.8b
(- (* b b) (* 4.0 (* a c)))
15.4b
(* (/ 4.0 (/ 2.0 (* a c))) (/ 1 (* a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))))
22.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
133×add-exp-log
63×add-cbrt-cube
55×div-exp
50×prod-exp
37×times-frac
29×add-sqr-sqrt
26×associate-*l*
25×cbrt-undiv
23×add-cube-cbrt *-un-lft-identity
20×cbrt-unprod
10×pow1 rec-exp 1-exp
9×associate-*r*
6×div-inv add-log-exp
5×associate-*r/ associate-/r/
4×flip3-- flip--
3×sqrt-prod associate-/l*
2×pow-flip sqrt-div pow-prod-down unswap-sqr
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*l/ clear-num associate-/r* un-div-inv *-commutative inv-pow
Counts
4 → 147
Calls
4 calls:
10.0ms
(/ 1 (* a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
3.0ms
(- (* b b) (* 4.0 (* a c)))
23.0ms
(* (/ 4.0 (/ 2.0 (* a c))) (/ 1 (* a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series112.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(/ 1 (* a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
12.0ms
(- (* b b) (* 4.0 (* a c)))
44.0ms
(* (/ 4.0 (/ 2.0 (* a c))) (/ 1 (* a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify66.0ms

Algorithm
egg-herbie
Counts
159 → 159
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
049692969
149692969

prune212.0ms

Filtered
94 candidates to 159 candidates (-69.1%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1581159
Fresh189
Picked011
Done011
Total15911170

Merged error: 5.0b

Counts
170 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* a 2.0)))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.1b
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
19×add-sqr-sqrt
16×*-un-lft-identity
13×add-cbrt-cube
10×prod-exp add-log-exp
8×add-cube-cbrt
7×pow1 associate-*r* associate-*l*
5×flip3-- sqrt-prod flip--
4×div-exp cbrt-unprod distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv frac-times sub-neg rec-exp distribute-rgt-neg-in sqrt-div 1-exp associate-*l/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 85
Calls
4 calls:
14.0ms
(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* a 2.0)))
6.0ms
(- (* b b) (* 4.0 (* a c)))
8.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series57.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* a 2.0)))
8.0ms
(- (* b b) (* 4.0 (* a c)))
15.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify53.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
050011554

prune113.0ms

Filtered
65 candidates to 97 candidates (-49.2%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New97097
Fresh088
Picked011
Done022
Total9711108

Merged error: 5.0b

Counts
108 → 11

regimes332.0ms

Accuracy

86.2% (3.7b remaining)

Error of 9.4b against oracle of 5.7b and baseline of 32.5b

bsearch94.0ms

Steps
ItersRangePoint
11
5.225951737061154e+20
1.968377579606969e+42
3.918823717913356e+39
5
-1.321426828733923e-156
-3.601125866891099e-157
-4.7242588155711044e-157
8
-2.9867793841426044e+62
-4.166907913142383e+59
-5.216017683133391e+60

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04467
14467

end0.0ms

sample1.6s

Algorithm
intervals
Results
341.0ms1053×body2560valid
325.0ms5845×body80valid
236.0ms875×body1280valid
150.0ms2874×body80nan
96.0ms458×body640valid
42.0ms109×body5120valid
35.0ms225×body320valid
12.0ms114×body160valid

Profiling

Loading profile data...