Details

Time bar (total: 6.1s)

sample58.0ms

Algorithm
intervals
Results
10.0ms35×body2560valid
9.0ms185×body80valid
7.0ms32×body1280valid
4.0ms91×body80nan
2.0ms13×body640valid
2.0ms7×body320valid
1.0ms3×body5120valid
0.0ms2×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

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: 34.5b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b
(- (* b b) (* 4.0 (* a c)))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
14.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series336.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
80.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
48.0ms
(- (* b b) (* 4.0 (* a c)))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0394773
11501683
25002673

prune355.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New721082
Fresh000
Picked011
Done000
Total721183

Merged error: 5.5b

Counts
83 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.4b
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b
(- (* b b) (* 4.0 (* a c)))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
53×times-frac
45×*-un-lft-identity
26×add-sqr-sqrt
25×add-exp-log add-cube-cbrt
13×add-cbrt-cube
12×div-exp
11×associate-/r*
10×distribute-lft-out add-log-exp
9×associate-/r/
6×pow1
5×cbrt-undiv distribute-rgt-neg-in flip3-+ flip-+ div-inv
3×rec-exp 1-exp prod-exp sqrt-prod associate-/l*
2×flip3-- sqrt-div sum-log flip--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 diff-log neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 114
Calls
4 calls:
13.0ms
(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
8.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series381.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
81.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms
(- (* b b) (* 4.0 (* a c)))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify69.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05251585
125501372
250011305

prune376.0ms

Filtered
126 candidates to 72 candidates (57.1%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1215126
Fresh549
Picked101
Done101
Total1289137

Merged error: 5.5b

Counts
137 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 (* 2.0 a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
0.4b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
0.8b
(- (* b b) (* 4.0 (* a c)))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
19×add-sqr-sqrt
13×add-cbrt-cube
12×*-un-lft-identity
10×prod-exp
8×add-cube-cbrt add-log-exp
7×pow1 associate-*l*
6×associate-*r*
5×flip3-- sqrt-prod flip--
4×sub-neg div-exp cbrt-unprod difference-of-squares
3×times-frac
2×cbrt-undiv distribute-rgt-in frac-times rec-exp distribute-lft-in sqrt-div diff-log 1-exp associate-*r/ distribute-lft-out--
1×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-*l/ *-commutative div-inv unswap-sqr
Counts
4 → 84
Calls
4 calls:
13.0ms
(* (/ 1 (* 2.0 a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
7.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.0ms
(- (* b b) (* 4.0 (* a c)))
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series380.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(* (/ 1 (* 2.0 a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
77.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
48.0ms
(- (* b b) (* 4.0 (* a c)))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify54.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0453918
12083801
25002799

prune336.0ms

Filtered
96 candidates to 66 candidates (68.8%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New96096
Fresh088
Picked011
Done000
Total969105

Merged error: 5.5b

Counts
105 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* 4.0 (* a c)))
3.5b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
10.2b
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
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 → 148
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
17.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
16.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series633.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* 4.0 (* a c)))
236.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
280.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify97.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
06262580
129912341
250032328

prune537.0ms

Filtered
160 candidates to 105 candidates (65.6%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1600160
Fresh077
Picked011
Done011
Total1609169

Merged error: 5.5b

Counts
169 → 9

regimes555.0ms

Accuracy

88.2% (3.4b remaining)

Error of 9.0b against oracle of 5.6b and baseline of 33.9b

bsearch200.0ms

Steps
ItersRangePoint
9
20077549570157524.0
7.523642411179348e+25
2.8427003056265324e+18
7
1.471046234538781e-117
6.312365209461493e-116
1.656387539268232e-117
9
-9.716082514065232e+101
-6.034489676023526e+92
-1.6207747271392166e+100

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04831
14831

end0.0ms

sample1.5s

Algorithm
intervals
Results
296.0ms1039×body2560valid
293.0ms5908×body80valid
222.0ms915×body1280valid
137.0ms2922×body80nan
89.0ms456×body640valid
34.0ms99×body5120valid
30.0ms217×body320valid
10.0ms114×body160valid

Profiling

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