Details

Time bar (total: 3.4s)

sample31.0ms

Algorithm
intervals
Results
15.0ms97×body1280valid
4.0ms125×body80valid
3.0ms22×body640valid
1.0ms7×body320valid
0.0ms5×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0196
1246
2286
3306
4356
5376
6376

prune2.0ms

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: 14.3b

Counts
2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot 1.0 x)
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b
(/ 1.0 (hypot 1.0 x))
2.1b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt *-un-lft-identity
12×add-cube-cbrt
9×times-frac
7×pow1
6×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×sqrt-pow1 sqrt-div associate-*r/
1×cbrt-undiv sub-neg flip3-- frac-2neg flip3-+ pow1/2 diff-log div-exp pow-prod-down clear-num sqrt-prod flip-- flip-+ div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 61
Calls
4 calls:
1.0ms
(hypot 1.0 x)
149.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series163.0ms

Counts
4 → 12
Calls
4 calls:
1.0ms
(hypot 1.0 x)
71.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.0ms
(/ 1.0 (hypot 1.0 x))
85.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify66.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0201433
1602413
22000411
35001411

prune133.0ms

Filtered
73 candidates to 52 candidates (71.2%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New70373
Fresh000
Picked101
Done000
Total71374

Merged error: 13.8b

Counts
74 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
1.6b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
20×add-sqr-sqrt add-cube-cbrt
18×times-frac
8×add-exp-log add-cbrt-cube add-log-exp
6×associate-/r* associate-/l*
4×pow1 associate-*r/ associate--l+
3×sub-neg
2×cbrt-undiv distribute-rgt-in flip3-- frac-2neg distribute-lft-in div-exp clear-num frac-sub flip-- div-inv
1×+-commutative flip3-+ diff-log sum-log flip-+ distribute-lft-out
Counts
4 → 84
Calls
4 calls:
3.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
3.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series121.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
5.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
33.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify142.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0306616
11080568
24851560
35001560

prune216.0ms

Filtered
96 candidates to 69 candidates (71.9%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New93396
Fresh112
Picked101
Done000
Total95499

Merged error: 13.8b

Counts
99 → 4

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x))
0.0b
(/ (* 1.0 (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
0.0b
(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
1.6b
(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
28×associate-*l*
20×add-exp-log add-cbrt-cube
18×*-un-lft-identity associate-*r/
16×difference-of-squares
12×unpow-prod-down cube-prod
10×associate-*l/
8×pow1 add-cube-cbrt frac-sub sqr-pow
7×flip3-- flip--
6×flip3-+ associate-*r* prod-exp cbrt-unprod flip-+ associate-/l/ add-log-exp
5×distribute-lft-out--
4×cbrt-undiv div-exp
2×distribute-rgt-in distribute-lft-in pow-prod-down associate-/r/ *-commutative associate--r+ unswap-sqr
1×difference-cubes sub-neg frac-2neg times-frac diff-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 111
Calls
4 calls:
16.0ms
(* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x))
31.0ms
(/ (* 1.0 (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
9.0ms
(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
17.0ms
(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

series151.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x))
66.0ms
(/ (* 1.0 (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
26.0ms
(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
36.0ms
(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

simplify115.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
06801725
140971461
250021461

prune436.0ms

Filtered
123 candidates to 83 candidates (67.5%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1194123
Fresh123
Picked101
Done000
Total1216127

Merged error: 13.5b

Counts
127 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.5b
(* (sqrt 0.5) (sqrt (+ (* 1.0 (/ 1 (hypot 1.0 x))) 1.0)))
1.6b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
24×add-cube-cbrt *-un-lft-identity
18×times-frac
12×add-exp-log
10×sqrt-prod add-cbrt-cube
9×pow1
6×associate-*r/ associate-*r* associate-*l* associate-/r* associate-/l* add-log-exp
4×associate--l+ unswap-sqr
3×sub-neg div-exp pow-prod-down
2×cbrt-undiv distribute-rgt-in flip3-- frac-2neg distribute-lft-in sqrt-pow1 pow1/2 sqrt-div clear-num frac-sub flip-- div-inv
1×rec-exp pow-flip flip3-+ sqrt-unprod diff-log 1-exp prod-exp *-commutative cbrt-unprod flip-+ inv-pow
Counts
4 → 108
Calls
4 calls:
3.0ms
(/ 1 (hypot 1.0 x))
3.0ms
(/ 1.0 (hypot 1.0 x))
11.0ms
(* (sqrt 0.5) (sqrt (+ (* 1.0 (/ 1 (hypot 1.0 x))) 1.0)))
6.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series119.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
76.0ms
(* (sqrt 0.5) (sqrt (+ (* 1.0 (/ 1 (hypot 1.0 x))) 1.0)))
33.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify56.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0399795
11648738
25001717

prune240.0ms

Filtered
120 candidates to 73 candidates (60.8%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1200120
Fresh055
Picked011
Done000
Total1206126

Merged error: 13.5b

Counts
126 → 6

regimes282.0ms

Accuracy

0% (0.3b remaining)

Error of 14.7b against oracle of 14.4b and baseline of 14.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02615
12615

end0.0ms

sample809.0ms

Algorithm
intervals
Results
471.0ms2883×body1280valid
113.0ms4029×body80valid
86.0ms637×body640valid
25.0ms284×body320valid
9.0ms167×body160valid

Profiling

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