Details

Time bar (total: 42.8s)

sample148.0ms

Algorithm
intervals
Results
77.0ms256×body80valid
9.0ms256×pre80true

simplify3.7s

Counts
1 → 1
Iterations
IterNodes
63778
51307
4450
3160
272
135
018

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)
0.1b
(pow (* -2 (log u1)) 0.5)
0.3b
(* u2 (* 2 PI))
0.4b
(* 1/6 (pow (* -2 (log u1)) 0.5))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log
12×pow1
11×add-sqr-sqrt add-cbrt-cube
9×prod-exp
8×*-un-lft-identity add-cube-cbrt
6×associate-*r* associate-*l*
4×expm1-log1p-u pow-prod-down pow-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×pow-unpow sqr-pow
2×pow-to-exp unpow-prod-down pow-pow *-commutative unswap-sqr
1×fma-udef
Counts
4 → 78
Calls
4 calls:
0.0ms
(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)
5.0ms
(pow (* -2 (log u1)) 0.5)
14.0ms
(* u2 (* 2 PI))
12.0ms
(* 1/6 (pow (* -2 (log u1)) 0.5))

series1.9s

Counts
4 → 12
Calls
4 calls:
445.0ms
(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)
418.0ms
(pow (* -2 (log u1)) 0.5)
36.0ms
(* u2 (* 2 PI))
982.0ms
(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify1.1s

Counts
90 → 90
Iterations
IterNodes
33303
2970
1350
0159

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* -2 (log u1)) 0.5)
0.2b
(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
0.3b
(* u2 (* 2 PI))
0.3b
(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log
19×prod-exp
17×add-sqr-sqrt
16×add-cbrt-cube
15×associate-*l*
14×pow1
11×*-un-lft-identity add-cube-cbrt
8×sqrt-prod
7×associate-*r* cbrt-unprod
6×pow-exp
5×pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp unswap-sqr sqr-pow
3×pow-to-exp pow-unpow *-commutative
2×unpow-prod-down pow-pow
Counts
4 → 98
Calls
4 calls:
5.0ms
(pow (* -2 (log u1)) 0.5)
28.0ms
(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
31.0ms
(* u2 (* 2 PI))
25.0ms
(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

series3.0s

Counts
4 → 12
Calls
4 calls:
881.0ms
(pow (* -2 (log u1)) 0.5)
1.1s
(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
52.0ms
(* u2 (* 2 PI))
995.0ms
(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

simplify1.5s

Counts
110 → 110
Iterations
IterNodes
33224
21079
1360
0159

prune1.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5)) (pow (* (log u1) -2) 0.5))
0.4b
(* 1/216 (* (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5)) (pow (* (log u1) -2) 0.5)))
0.5b
(cbrt (* 1/216 (* (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5)) (pow (* (log u1) -2) 0.5))))
0.5b
(* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5))

rewrite305.0ms

Algorithm
rewrite-expression-head
Rules
506×add-exp-log
455×prod-exp
212×pow-exp
106×pow-to-exp
20×add-cbrt-cube
15×add-sqr-sqrt
11×associate-*r*
10×*-un-lft-identity add-cube-cbrt cbrt-unprod sqr-pow
9×associate-*l*
6×pow1 unswap-sqr
5×unpow-prod-down swap-sqr
4×expm1-log1p-u pow-prod-down pow-prod-up insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×pow2 pow-sqr
1×cbrt-prod pow-plus pow1/3 pow3
Counts
4 → 245
Calls
4 calls:
62.0ms
(* (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5)) (pow (* (log u1) -2) 0.5))
136.0ms
(* 1/216 (* (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5)) (pow (* (log u1) -2) 0.5)))
69.0ms
(cbrt (* 1/216 (* (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5)) (pow (* (log u1) -2) 0.5))))
24.0ms
(* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5))

series4.1s

Counts
4 → 12
Calls
4 calls:
1.0s
(* (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5)) (pow (* (log u1) -2) 0.5))
1.1s
(* 1/216 (* (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5)) (pow (* (log u1) -2) 0.5)))
1.0s
(cbrt (* 1/216 (* (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5)) (pow (* (log u1) -2) 0.5))))
994.0ms
(* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5))

simplify3.0s

Counts
257 → 257
Iterations
IterNodes
35238
21501
1650
0256

prune3.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) (/ 0.5 2)))
0.4b
(* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) (/ 0.5 2)))
0.5b
(cbrt (* 1/216 (* (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) (/ 0.5 2))) (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) (/ 0.5 2))))))
0.5b
(* (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) (/ 0.5 2))) (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) (/ 0.5 2))))

rewrite267.0ms

Algorithm
rewrite-expression-head
Rules
1190×add-exp-log
1153×prod-exp
576×pow-exp
288×pow-to-exp
20×add-cbrt-cube sqr-pow
16×add-sqr-sqrt
11×pow1 associate-*r* associate-*l* pow-prod-up
10×cbrt-unprod
8×*-un-lft-identity pow3 add-cube-cbrt unswap-sqr
4×expm1-log1p-u unpow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×pow-prod-down pow-sqr *-commutative
1×cbrt-prod pow2 pow-plus pow1/3 swap-sqr
Counts
4 → 418
Calls
4 calls:
31.0ms
(* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) (/ 0.5 2)))
19.0ms
(* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) (/ 0.5 2)))
119.0ms
(cbrt (* 1/216 (* (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) (/ 0.5 2))) (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) (/ 0.5 2))))))
82.0ms
(* (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) (/ 0.5 2))) (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) (/ 0.5 2))))

series4.0s

Counts
4 → 12
Calls
4 calls:
1.0s
(* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) (/ 0.5 2)))
974.0ms
(* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) (/ 0.5 2)))
1.0s
(cbrt (* 1/216 (* (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) (/ 0.5 2))) (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) (/ 0.5 2))))))
896.0ms
(* (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) (/ 0.5 2))) (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) (/ 0.5 2))))

simplify2.6s

Counts
430 → 430
Iterations
IterNodes
33604
21209
1569
0263

prune6.9s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes416.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify9.0ms

Iterations
IterNodes
222
122
017

end0.0ms

sample2.8s

Algorithm
intervals
Results
2.1s8000×body80valid
455.0ms8000×pre80true