Details

Time bar (total: 3.6m)

sample197.0ms

Algorithm
intervals
Results
66.0ms256×body80valid
20.0ms256×pre80true

simplify643.0ms

Calls
1 calls:
Slowest
642.0ms
(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize58.0ms

Local error

Found 4 expressions with local error:

0.3b
(* u2 (* 2 PI))
0.2b
(/ (pow (* -2 (log u1)) 0.5) 6)
0.1b
(pow (* -2 (log u1)) 0.5)
0.0b
(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
65×unpow-prod-down
63×add-sqr-sqrt
51×times-frac
46×*-un-lft-identity add-cube-cbrt
35×associate-*r*
21×associate-*l*
20×add-exp-log
17×pow1 associate-/l*
11×add-cbrt-cube
9×unswap-sqr
7×*-commutative
5×prod-exp log-pow sqr-pow
4×expm1-log1p-u div-exp pow-prod-down pow-exp insert-posit16 log1p-expm1-u add-log-exp
3×pow-unpow associate-/r* cbrt-unprod
2×pow-to-exp pow-pow
1×cbrt-undiv clear-num frac-2neg fma-udef div-inv
Calls
4 calls:
Slowest
48.0ms
(* u2 (* 2 PI))
23.0ms
(/ (pow (* -2 (log u1)) 0.5) 6)
8.0ms
(pow (* -2 (log u1)) 0.5)
0.0ms
(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)

series1.9s

Calls
4 calls:
Slowest
979.0ms
(/ (pow (* -2 (log u1)) 0.5) 6)
519.0ms
(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)
381.0ms
(pow (* -2 (log u1)) 0.5)
59.0ms
(* u2 (* 2 PI))

simplify30.7s

Calls
177 calls:
Slowest
863.0ms
(+ (* 1/6 (* (cos (* 2 (* u2 PI))) (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5))) 0.5)
762.0ms
(/ (pow (* (sqrt -2) (log u1)) 0.5) 6)
729.0ms
(* 1/6 (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5))
662.0ms
(/ (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (* (* 6 6) 6))
473.0ms
(/ (pow (* (sqrt -2) (sqrt (log u1))) 0.5) 1)

prune2.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (pow (* -2 (log u1)) 0.5) (/ 1 6))
0.3b
(* u2 (* 2 PI))
0.1b
(pow (* -2 (log u1)) 0.5)
0.0b
(fma (cos (* u2 (* 2 PI))) (* (pow (* -2 (log u1)) 0.5) (/ 1 6)) 0.5)

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
48×add-exp-log
36×associate-*r*
32×unpow-prod-down
30×*-un-lft-identity
29×associate-*l*
25×add-cube-cbrt
24×prod-exp
21×unswap-sqr
17×times-frac
16×pow1
14×add-cbrt-cube
10×pow-exp
9×associate-*r/
8×div-exp
5×pow-to-exp pow-prod-down *-commutative cbrt-unprod sqr-pow
4×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×pow-unpow associate-/r* un-div-inv
2×clear-num pow-pow log-pow
1×cbrt-undiv frac-2neg fma-udef div-inv
Calls
4 calls:
Slowest
57.0ms
(* (pow (* -2 (log u1)) 0.5) (/ 1 6))
21.0ms
(* u2 (* 2 PI))
12.0ms
(pow (* -2 (log u1)) 0.5)
0.0ms
(fma (cos (* u2 (* 2 PI))) (* (pow (* -2 (log u1)) 0.5) (/ 1 6)) 0.5)

series1.9s

Calls
4 calls:
Slowest
1.0s
(* (pow (* -2 (log u1)) 0.5) (/ 1 6))
522.0ms
(fma (cos (* u2 (* 2 PI))) (* (pow (* -2 (log u1)) 0.5) (/ 1 6)) 0.5)
353.0ms
(pow (* -2 (log u1)) 0.5)
39.0ms
(* u2 (* 2 PI))

simplify19.8s

Calls
133 calls:
Slowest
749.0ms
(+ (* 1/6 (* (cos (* 2 (* u2 PI))) (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5))) 0.5)
695.0ms
(* (pow (* (sqrt -2) (sqrt (log u1))) 0.5) (sqrt (/ 1 6)))
683.0ms
(* (pow (sqrt (* -2 (log u1))) 0.5) (sqrt (/ 1 6)))
671.0ms
(* 1/6 (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5))
654.0ms
(* (pow (* -2 (log u1)) (/ 0.5 2)) (sqrt (/ 1 6)))

prune2.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite244.0ms

Algorithm
rewrite-expression-head
Rules
174×add-sqr-sqrt
148×unpow-prod-down
127×times-frac
110×associate-*r*
92×*-un-lft-identity
91×add-cube-cbrt
76×add-exp-log
53×associate-*l*
43×unswap-sqr
35×associate-/l*
34×prod-exp
24×pow1
23×associate-*r/
22×pow-exp
20×div-exp
19×sqr-pow
16×add-cbrt-cube
13×pow-unpow *-commutative
11×pow-to-exp
10×log-pow
6×associate-/r*
5×pow-prod-down cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num div-inv
2×cbrt-undiv pow-pow frac-2neg un-div-inv
Calls
4 calls:
Slowest
156.0ms
(* (pow (* -2 (log u1)) (/ 0.5 2)) (/ (pow (* -2 (log u1)) (/ 0.5 2)) 6))
42.0ms
(/ (pow (* -2 (log u1)) (/ 0.5 2)) 6)
18.0ms
(pow (* -2 (log u1)) (/ 0.5 2))
17.0ms
(* u2 (* 2 PI))

series2.4s

Calls
4 calls:
Slowest
996.0ms
(* (pow (* -2 (log u1)) (/ 0.5 2)) (/ (pow (* -2 (log u1)) (/ 0.5 2)) 6))
981.0ms
(/ (pow (* -2 (log u1)) (/ 0.5 2)) 6)
382.0ms
(pow (* -2 (log u1)) (/ 0.5 2))
49.0ms
(* u2 (* 2 PI))

simplify1.3m

Calls
345 calls:
Slowest
649.0ms
(* (sqrt (pow (* -2 (log u1)) (/ 0.5 2))) (/ (pow (* (sqrt -2) (sqrt (log u1))) (/ 0.5 2)) (sqrt 6)))
644.0ms
(* 1/6 (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5))
639.0ms
(* 1/6 (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.25))
563.0ms
(/ (pow (* -2 (log u1)) (/ (/ 0.5 2) 2)) (sqrt 6))
560.0ms
(/ (pow (* -2 (log u1)) (/ (/ 0.5 2) 2)) (sqrt 6))

prune3.8s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (* (log (* -2 (log u1))) (/ 0.5 2)) (log 6))
0.3b
(* (pow (* -2 (log u1)) (/ 0.5 2)) (exp (- (* (log (* -2 (log u1))) (/ 0.5 2)) (log 6))))
0.3b
(* u2 (* 2 PI))
0.1b
(log (* -2 (log u1)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
245×associate-*r*
222×add-sqr-sqrt
200×prod-diff
157×*-un-lft-identity
149×add-cube-cbrt
103×pow1
102×exp-sum
91×times-frac
80×associate-*l* log-pow
31×unswap-sqr
25×fma-neg
24×add-exp-log
19×log-prod
16×pow-prod-down
15×unpow-prod-down
14×prod-exp *-commutative
11×add-cbrt-cube
9×div-inv
8×distribute-lft-out--
7×add-log-exp
6×associate--r+
4×expm1-log1p-u exp-diff pow-exp associate-*r/ cbrt-unprod insert-posit16 log1p-expm1-u
3×difference-of-squares
2×pow-to-exp sub-neg diff-log rem-log-exp sqr-pow
1×flip3-- flip--
Calls
4 calls:
Slowest
976.0ms
(* (pow (* -2 (log u1)) (/ 0.5 2)) (exp (- (* (log (* -2 (log u1))) (/ 0.5 2)) (log 6))))
202.0ms
(- (* (log (* -2 (log u1))) (/ 0.5 2)) (log 6))
18.0ms
(* u2 (* 2 PI))
7.0ms
(log (* -2 (log u1)))

series2.4s

Calls
4 calls:
Slowest
1.6s
(* (pow (* -2 (log u1)) (/ 0.5 2)) (exp (- (* (log (* -2 (log u1))) (/ 0.5 2)) (log 6))))
496.0ms
(- (* (log (* -2 (log u1))) (/ 0.5 2)) (log 6))
291.0ms
(log (* -2 (log u1)))
47.0ms
(* u2 (* 2 PI))

simplify56.6s

Calls
431 calls:
Slowest
813.0ms
(fma (* (log (* -2 (log u1))) (/ 1 (sqrt 2))) (/ 0.5 (sqrt 2)) (- (* (cbrt (log 6)) (* (cbrt (log 6)) (cbrt (log 6))))))
740.0ms
(* (pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.25) (exp (- (* 0.25 (log (* -2 (log u1)))) (log 6))))
495.0ms
(cbrt (exp (- (* (log (* -2 (log u1))) (/ 0.5 2)) (log 6))))
473.0ms
(exp (- (* (log (* -2 (log u1))) (/ 0.5 2)) (log 6)))
462.0ms
(* (pow (sqrt (* -2 (log u1))) (/ 0.5 2)) (sqrt (exp (- (* (log (* -2 (log u1))) (/ 0.5 2)) (log 6)))))

prune7.0s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes339.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
2.1s8000×body80valid
485.0ms8000×pre80true