Details

Time bar (total: 3.5s)

sample54.0ms

Algorithm
intervals
Results
10.0ms200×body80valid
9.0ms30×body2560valid
7.0ms31×body1280valid
4.0ms85×body80nan
3.0ms15×body640valid
1.0ms4×body5120valid
0.0ms3×body320valid
0.0ms2×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune4.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 32.4b

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))
0.6b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b
(- (* b b) (* (* 4.0 a) c))
20.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite27.0ms

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:
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))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series65.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
15.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0396773
11550683
25001673

prune147.0ms

Filtered
82 candidates to 63 candidates (23.2%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New78482
Fresh000
Picked011
Done000
Total78583

Merged error: 5.1b

Counts
83 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

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))))
0.8b
(- (* b b) (* (* 4.0 a) c))
20.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
16×*-un-lft-identity
13×add-cbrt-cube
11×add-sqr-sqrt
10×prod-exp add-log-exp
8×add-cube-cbrt
7×pow1 associate-*r*
5×associate-*l*
4×div-exp cbrt-unprod distribute-lft-out
3×flip3-+ times-frac sqrt-prod flip-+
2×cbrt-undiv frac-times rec-exp flip3-- distribute-rgt-neg-in sqrt-div 1-exp associate-*l/ sum-log flip--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 80
Calls
4 calls:
17.0ms
(* (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
8.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series64.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
15.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify63.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0472914
12176788
25001776

prune130.0ms

Filtered
92 candidates to 65 candidates (29.3%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New91192
Fresh033
Picked011
Done011
Total91697

Merged error: 5.1b

Counts
97 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.5b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.1b
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
20.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite49.0ms

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))))
18.0ms
(/ (/ (+ 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)))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series134.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
61.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify119.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
06462693
131632447
250032434

prune273.0ms

Filtered
166 candidates to 111 candidates (33.1%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New1642166
Fresh123
Picked011
Done022
Total1657172

Merged error: 5.0b

Counts
172 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0b
(/ (* 2.0 a) (* 4.0 (* a c)))
20.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
10×add-sqr-sqrt add-log-exp
9×*-un-lft-identity prod-exp cbrt-unprod
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×sqrt-prod
3×flip3-- diff-log flip--
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 70
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
9.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series41.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify69.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
0426636
12470542
25003534

prune100.0ms

Filtered
82 candidates to 55 candidates (32.9%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New81182
Fresh123
Picked101
Done033
Total83689

Merged error: 5.0b

Counts
89 → 6

regimes324.0ms

Accuracy

95.6% (1.1b remaining)

Error of 6.5b against oracle of 5.5b and baseline of 29.4b

bsearch87.0ms

Steps
ItersRangePoint
6
3.740966656805541e+90
3.763859088204499e+91
2.1173930570711685e+91
8
-2.450180232760445e-303
-6.101116520471646e-307
-7.878728067861033e-306
9
-3.6502939682616286e+159
-2.0984588557191883e+153
-2.336606735933724e+153

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04525
14525

end0.0ms

sample1.5s

Algorithm
intervals
Results
313.0ms1043×body2560valid
299.0ms5859×body80valid
224.0ms919×body1280valid
137.0ms2796×body80nan
92.0ms485×body640valid
40.0ms113×body5120valid
33.0ms237×body320valid
9.0ms98×body160valid

Profiling

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