Details

Time bar (total: 6.8s)

sample1.9s

Algorithm
intervals
sampling

Space saved by range analysis: 99.998264%

Space saved by search: 99.999091%

Guaranteed chance to sample good point: 88.065532%

Results
15.0ms167×body160valid
10.0ms274×pre80true
5.0ms36×body320valid
3.0ms53×body80valid
1.0ms18×body80nan

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 44.5b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
39.3b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite26.0ms

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:
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
7.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series64.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(- (* b b) (* (* 4.0 a) c))
27.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
15.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify44.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0396773
11550683
25001673

prune117.0ms

Filtered
63 candidates to 82 candidates (-30.2%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New79382
Fresh000
Picked011
Done000
Total79483

Merged error: 0.2b

Counts
83 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
82×add-sqr-sqrt *-un-lft-identity
38×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
11×distribute-rgt-neg-in sqrt-prod
10×add-log-exp
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 div-inv
3×diff-log associate-/l/
2×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 151
Calls
4 calls:
8.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series124.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
41.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
58.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify113.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
06432666
132102408
250012396

prune285.0ms

Filtered
106 candidates to 163 candidates (-53.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1558163
Fresh202
Picked101
Done101
Total1598167

Merged error: 0b

Counts
167 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
27×add-exp-log add-cbrt-cube
16×add-sqr-sqrt
14×*-un-lft-identity
10×prod-exp cbrt-unprod add-log-exp
7×associate-*r*
6×pow1 cbrt-undiv add-cube-cbrt div-exp
4×sub-neg flip3-- associate-*r/ flip-- distribute-lft-out-- difference-of-squares
3×diff-log associate-*l*
2×distribute-rgt-in distribute-rgt-neg-in distribute-lft-in sqrt-prod associate-/r/
1×associate--l- neg-sub0 frac-2neg times-frac pow-prod-down neg-log clear-num associate-/r* *-commutative div-inv associate-/l* unswap-sqr
Counts
4 → 85
Calls
4 calls:
10.0ms
(* 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))
13.0ms
(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series93.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
15.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
45.0ms
(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify87.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
05181106
13294871
25002864

prune140.0ms

Filtered
62 candidates to 97 candidates (-56.5%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New96197
Fresh167
Picked011
Done000
Total978105

Merged error: 0b

Counts
105 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 4.0 (* a c)) a)
0.1b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(/ (/ (* 4.0 (* a c)) a) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b
(- (* b b) (* (* 4.0 a) c))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
66×add-sqr-sqrt *-un-lft-identity
30×add-cube-cbrt
27×add-exp-log add-cbrt-cube
18×distribute-lft-out-- difference-of-squares
10×cbrt-undiv div-exp associate-/r* div-inv add-log-exp
9×distribute-rgt-neg-in sqrt-prod
8×associate-/l*
6×prod-exp cbrt-unprod
4×pow1
3×flip3-- diff-log flip--
2×sub-neg frac-2neg clear-num associate-/r/
1×associate--l- neg-sub0 neg-log associate-/l/
Counts
4 → 137
Calls
4 calls:
6.0ms
(/ (* 4.0 (* a c)) a)
8.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms
(/ (/ (* 4.0 (* a c)) a) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
3.0ms
(- (* b b) (* (* 4.0 a) c))

series70.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(/ (* 4.0 (* a c)) a)
15.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(/ (/ (* 4.0 (* a c)) a) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
9.0ms
(- (* b b) (* (* 4.0 a) c))

simplify88.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
06412033
133651826
250011800

prune189.0ms

Filtered
92 candidates to 149 candidates (-62.0%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1472149
Fresh246
Picked101
Done011
Total1507157

Merged error: 0b

Counts
157 → 7

regimes178.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02311
12311

end0.0ms

sample3.2s

Algorithm
intervals
sampling

Space saved by range analysis: 99.998264%

Space saved by search: 99.999091%

Guaranteed chance to sample good point: 88.065532%

Results
464.0ms4839×body160valid
250.0ms8508×pre80true
186.0ms1342×body320valid
91.0ms1819×body80valid
23.0ms508×body80nan

Profiling

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