Details

Time bar (total: 5.8s)

sample38.0ms

Algorithm
intervals
Results
20.0ms94×body1280valid
5.0ms118×body80valid
4.0ms21×body640valid
2.0ms14×body320valid
1.0ms9×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0196
1246
2286
3306
4356
5376
6376

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 15.1b

Counts
2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b
(hypot 1.0 x)
0.0b
(/ 1.0 (hypot 1.0 x))
2.6b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite14.0ms

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:
6.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.0ms
(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))))))

series34.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.0ms
(hypot 1.0 x)
4.0ms
(/ 1.0 (hypot 1.0 x))
13.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify58.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0201433
1602413
21986411
35001411

prune128.0ms

Filtered
52 candidates to 73 candidates (-40.4%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New69473
Fresh000
Picked101
Done000
Total70474

Merged error: 14.6b

Counts
74 → 4

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))
2.2b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite16.0ms

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))
6.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series30.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
4.0ms
(/ 1.0 (hypot 1.0 x))
4.0ms
(/ 1.0 (hypot 1.0 x))
8.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify140.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0306616
11080568
24837560
35001560

prune218.0ms

Filtered
69 candidates to 96 candidates (-39.1%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New93396
Fresh123
Picked101
Done000
Total955100

Merged error: 14.6b

Counts
100 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 1.0 0.5) (hypot 1.0 x))
0.0b
(* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x))
0.0b
(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x)))
2.2b
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log add-cbrt-cube
14×associate-*r/ associate-*l/
12×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-cube-cbrt associate-*l* frac-sub
7×flip3-- flip--
6×flip3-+ associate-*r* prod-exp cbrt-unprod flip-+ associate-/l/ add-log-exp
4×cbrt-undiv div-exp
2×pow-prod-down associate-/r/ *-commutative associate--r+ unswap-sqr
1×distribute-rgt-in sub-neg frac-2neg distribute-lft-in times-frac diff-log clear-num associate-/r* div-inv distribute-lft-out associate-/l* difference-of-squares
Counts
4 → 89
Calls
4 calls:
5.0ms
(* (+ 1.0 0.5) (hypot 1.0 x))
6.0ms
(* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x))
13.0ms
(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x)))
6.0ms
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

series17.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(* (+ 1.0 0.5) (hypot 1.0 x))
2.0ms
(* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x))
10.0ms
(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x)))
3.0ms
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

simplify82.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
05501145
13114962
25003962

prune318.0ms

Filtered
72 candidates to 101 candidates (-40.3%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New983101
Fresh224
Picked101
Done000
Total1015106

Merged error: 14.6b

Counts
106 → 5

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))))
0.1b
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
2.1b
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
271×associate-*r/
104×frac-add
74×flip3-- associate-/r/ flip--
68×frac-times
47×add-sqr-sqrt
37×*-un-lft-identity
36×times-frac
27×add-cube-cbrt
26×associate-*l/
21×sqr-pow
20×difference-of-squares
17×flip3-+ flip-+
14×add-exp-log add-cbrt-cube
12×associate-/l*
9×cube-div
7×pow1
6×associate-/r* add-log-exp
5×difference-cubes distribute-lft-out--
4×frac-sub associate-/l/
3×cbrt-undiv pow-unpow div-exp pow-exp rem-cube-cbrt
2×pow-pow frac-2neg prod-exp clear-num cbrt-unprod div-inv
1×cube-mult pow-to-exp sub-neg unpow-prod-down diff-log unpow3 div-sub cube-prod pow-prod-down
Counts
4 → 202
Calls
4 calls:
3.0ms
(/ 1.0 (hypot 1.0 x))
29.0ms
(/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))))
5.0ms
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
10.0ms
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

series85.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(/ 1.0 (hypot 1.0 x))
52.0ms
(/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))))
13.0ms
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
15.0ms
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

simplify274.0ms

Algorithm
egg-herbie
Counts
214 → 214
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
019146422
150036294

prune2.7s

Filtered
161 candidates to 214 candidates (-32.9%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2113214
Fresh134
Picked101
Done000
Total2136219

Merged error: 14.2b

Counts
219 → 6

regimes399.0ms

Accuracy

0% (0.3b remaining)

Error of 15.1b against oracle of 14.8b and baseline of 15.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03337
13337

end0.0ms

sample1.1s

Algorithm
intervals
Results
613.0ms2907×body1280valid
157.0ms4011×body80valid
105.0ms637×body640valid
34.0ms288×body320valid
12.0ms157×body160valid

Profiling

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