Details

Time bar (total: 5.1s)

sample47.0ms

Algorithm
intervals
Results
9.0ms193×body80valid
9.0ms34×body2560valid
7.0ms30×body1280valid
4.0ms85×body80nan
2.0ms13×body640valid
1.0ms4×body5120valid
0.0ms3×body320valid
0.0ms3×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

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: 34.3b

Counts
2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (* a c))
0.1b
(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
14×add-exp-log add-cbrt-cube
10×pow1
9×add-sqr-sqrt
8×add-cube-cbrt add-log-exp
6×distribute-lft-out
5×times-frac associate-/l*
4×prod-exp cbrt-unprod
3×distribute-rgt-neg-in associate-*l* pow-prod-down sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-+ sqrt-div div-exp sum-log flip-+ associate-/l/
1×+-commutative rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 div-sub associate-*r* neg-log clear-num associate-/r* *-commutative flip-- div-inv
Counts
4 → 76
Calls
4 calls:
5.0ms
(* 4.0 (* a c))
12.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series275.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* 4.0 (* a c))
106.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
78.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify49.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0450742
11681648
25001637

prune213.0ms

Filtered
88 candidates to 64 candidates (72.7%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New81788
Fresh000
Picked011
Done000
Total81889

Merged error: 7.0b

Counts
89 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
9.8b
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
23.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-rgt-neg-in
8×associate-/r* add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 154
Calls
4 calls:
8.0ms
(- (neg b) (sqrt (- (* 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))
13.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series467.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
145.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
177.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify100.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
06402694
129112439
250012426

prune365.0ms

Filtered
166 candidates to 111 candidates (66.9%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1633166
Fresh246
Picked011
Done011
Total1659174

Merged error: 6.9b

Counts
174 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (* a c))
0.2b
(* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.6b
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
18×add-cbrt-cube
17×*-un-lft-identity
13×prod-exp
12×pow1 add-sqr-sqrt
9×add-cube-cbrt
8×associate-*r* associate-*l* add-log-exp
7×cbrt-unprod
4×div-exp pow-prod-down distribute-lft-out
3×flip3-+ times-frac sqrt-prod flip-+
2×cbrt-undiv frac-times rec-exp distribute-rgt-neg-in sqrt-div 1-exp associate-*l/ sum-log *-commutative
1×+-commutative neg-sub0 associate-+l- rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ neg-log un-div-inv flip-- div-inv unswap-sqr
Counts
4 → 86
Calls
4 calls:
5.0ms
(* 4.0 (* a c))
15.0ms
(* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
8.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series269.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* 4.0 (* a c))
104.0ms
(* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
77.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify66.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0526883
12306753
25003744

prune201.0ms

Filtered
98 candidates to 66 candidates (67.3%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New97198
Fresh156
Picked011
Done022
Total989107

Merged error: 6.9b

Counts
107 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(/ 4.0 (/ 2.0 (* a c)))
16.4b
(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a))
23.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
221×times-frac
165×add-sqr-sqrt
138×*-un-lft-identity
103×add-exp-log
96×add-cube-cbrt
85×associate-*r*
67×add-cbrt-cube
54×div-exp
32×cbrt-undiv
26×associate-*l* prod-exp
20×distribute-lft-out-- difference-of-squares
16×cbrt-unprod
13×sqrt-prod div-inv
10×distribute-rgt-neg-in
8×associate-/r/ add-log-exp unswap-sqr
7×pow1 associate-/r*
5×flip3-- flip--
4×rec-exp 1-exp
3×associate-/l*
2×sqrt-div diff-log
1×associate--l- neg-sub0 frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative
Counts
4 → 244
Calls
4 calls:
8.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
6.0ms
(/ 4.0 (/ 2.0 (* a c)))
60.0ms
(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series315.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.0ms
(/ 4.0 (/ 2.0 (* a c)))
149.0ms
(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify58.0ms

Algorithm
egg-herbie
Counts
256 → 256
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013943426
150012942

prune564.0ms

Filtered
256 candidates to 165 candidates (64.5%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New2551256
Fresh145
Picked011
Done123
Total2578265

Merged error: 6.9b

Counts
265 → 8

regimes246.0ms

Accuracy

85.7% (3.8b remaining)

Error of 9.4b against oracle of 5.6b and baseline of 32.4b

bsearch212.0ms

Steps
ItersRangePoint
10
2.564731655063431e+70
8.71581363662453e+81
2.1868634635914353e+71
11
3.073059094578084e-151
9.813570662590159e-116
3.288204035546746e-123
6
-1.555584016455579e+44
-1.807486675368764e+43
-1.5338208594244521e+44

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample1.4s

Algorithm
intervals
Results
313.0ms1112×body2560valid
299.0ms5838×body80valid
211.0ms917×body1280valid
139.0ms2863×body80nan
81.0ms447×body640valid
38.0ms113×body5120valid
30.0ms222×body320valid
11.0ms118×body160valid

Profiling

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