Details

Time bar (total: 3.6s)

sample54.0ms

Algorithm
intervals
Results
10.0ms193×body80valid
8.0ms27×body2560valid
7.0ms29×body1280valid
4.0ms95×body80nan
4.0ms6×body320valid
3.0ms18×body640valid
1.0ms6×body160valid
0.0ms1×body5120valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
08816
18816

prune11.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.6b

Counts
2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.3b
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.6b
(- (* b b) (* (* 3.0 a) c))
22.1b
(sqrt (- (* b b) (* (* 3.0 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) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms
(- (* b b) (* (* 3.0 a) c))
3.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series65.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
15.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
10.0ms
(- (* b b) (* (* 3.0 a) c))
14.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify61.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
049531232
149531232

prune170.0ms

Filtered
64 candidates to 82 candidates (-28.1%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New711182
Fresh101
Picked011
Done000
Total721284

Merged error: 5.2b

Counts
84 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

2.4b
(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
3.1b
(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
9.2b
(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
22.1b
(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log add-cbrt-cube
34×times-frac
32×add-sqr-sqrt
31×*-un-lft-identity
17×cbrt-undiv div-exp
14×associate-/l*
13×prod-exp cbrt-unprod
11×add-cube-cbrt
10×distribute-lft-out-- difference-of-squares
8×associate-/r* sqrt-prod add-log-exp
6×associate-/r/
5×pow1 flip3-- distribute-rgt-neg-in flip--
4×div-inv
2×frac-2neg sqrt-div diff-log clear-num
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log associate-/l/
Counts
4 → 120
Calls
4 calls:
8.0ms
(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
15.0ms
(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
12.0ms
(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
6.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

series126.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
41.0ms
(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
55.0ms
(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
14.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

simplify38.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
054552572

prune185.0ms

Filtered
84 candidates to 132 candidates (-57.1%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1302132
Fresh2810
Picked011
Done011
Total13212144

Merged error: 5.1b

Counts
144 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 3.0 (* a c))
1.6b
(- (* b b) (* 3.0 (* a c)))
2.4b
(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
22.1b
(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1 *-un-lft-identity add-log-exp
9×add-exp-log add-cbrt-cube
6×add-cube-cbrt
4×sqrt-prod
3×flip3-- diff-log associate-*l* pow-prod-down prod-exp flip-- cbrt-unprod
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 associate-*r* neg-log *-commutative
Counts
4 → 63
Calls
4 calls:
5.0ms
(* 3.0 (* a c))
4.0ms
(- (* b b) (* 3.0 (* a c)))
8.0ms
(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
5.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

series40.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* 3.0 (* a c))
8.0ms
(- (* b b) (* 3.0 (* a c)))
15.0ms
(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
14.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

simplify44.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
04969890
14969890

prune115.0ms

Filtered
51 candidates to 75 candidates (-47.1%)
Pruning

13 alts after pruning (10 fresh and 3 done)

PrunedKeptTotal
New73275
Fresh189
Picked011
Done022
Total741387

Merged error: 5.0b

Counts
87 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) a)
1.3b
(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
1.6b
(- (* b b) (* 3.0 (* a c)))
22.1b
(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-exp-log add-cbrt-cube associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp clear-num div-inv
Counts
4 → 84
Calls
4 calls:
9.0ms
(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) a)
6.0ms
(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
3.0ms
(- (* b b) (* 3.0 (* a c)))
3.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

series60.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) a)
14.0ms
(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
8.0ms
(- (* b b) (* 3.0 (* a c)))
13.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

simplify60.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
049541643
149541643

prune123.0ms

Filtered
70 candidates to 96 candidates (-37.1%)
Pruning

13 alts after pruning (9 fresh and 4 done)

PrunedKeptTotal
New93396
Fresh369
Picked011
Done033
Total9613109

Merged error: 5.0b

Counts
109 → 13

regimes605.0ms

Accuracy

94.3% (1.4b remaining)

Error of 6.9b against oracle of 5.6b and baseline of 29.4b

bsearch99.0ms

Steps
ItersRangePoint
8
1.838480289737433e+68
1.744360026235418e+71
1.0729035470079235e+71
9
-6.695429941707738e-297
-7.676761036242019e-305
-9.418142104424273e-298
9
-6.247250655316605e+139
-3.660489123272618e+133
-3.8900654094429814e+133

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05569
15569

end0.0ms

sample1.6s

Algorithm
intervals
Results
319.0ms1069×body2560valid
304.0ms5817×body80valid
219.0ms911×body1280valid
144.0ms2946×body80nan
91.0ms472×body640valid
39.0ms111×body5120valid
30.0ms217×body320valid
11.0ms118×body160valid

Profiling

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