Details

sample464.0ms

Algorithm

intervals

Results

141.0ms	483×	body	80	nan
70.0ms	286×	body	80	valid

simplify1.8s

Counts: 1 → 1

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.1b

localize75.0ms

Local error

Found 4 expressions with local error:

18.3b	(sqrt (* U (* 2 (* n (- t (fma (/ l Om) (* 2 l) (* (/ l Om) (* (/ l Om) (* (- U U*) n)))))))))
11.5b	(* (/ l Om) (* (- U U*) n))
5.7b	(* U (* 2 (* n (- t (fma (/ l Om) (* 2 l) (* (/ l Om) (* (/ l Om) (* (- U U*) n))))))))
2.2b	(fma (/ l Om) (* 2 l) (* (/ l Om) (* (/ l Om) (* (- U U*) n))))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

132×	`distribute-rgt-in` `distribute-lft-in`
72×	`prod-diff`
60×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
28×	`pow1`
25×	`add-cbrt-cube` `add-exp-log`
16×	`associate-l`
15×	`pow-prod-down`
14×	`associate-*r/`
12×	`prod-exp` `cbrt-unprod`
9×	`times-frac`
8×	`sub-neg`
5×	`associate-*l/`
4×	`expm1-log1p-u` `sqrt-pow1` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--` `add-log-exp`
2×	`frac-times` `cbrt-undiv` `sqrt-div` `div-exp` `associate-r` `*-commutative`
1×	`pow1/2` `sqrt-prod` `fma-udef` `div-inv`

Counts

4 → 183

Calls

4 calls:

Slowest

80.0ms	(sqrt (* U (* 2 (* n (- t (fma (/ l Om) (* 2 l) (* (/ l Om) (* (/ l Om) (* (- U U*) n)))))))))
75.0ms	(* U (* 2 (* n (- t (fma (/ l Om) (* 2 l) (* (/ l Om) (* (/ l Om) (* (- U U*) n))))))))
29.0ms	(* (/ l Om) (* (- U U*) n))
0.0ms	(fma (/ l Om) (* 2 l) (* (/ l Om) (* (/ l Om) (* (- U U*) n))))

series2.9s

Counts

4 → 12

Calls

4 calls:

Slowest

2.1s	(sqrt (* U (* 2 (* n (- t (fma (/ l Om) (* 2 l) (* (/ l Om) (* (/ l Om) (* (- U U*) n)))))))))
478.0ms	(* U (* 2 (* n (- t (fma (/ l Om) (* 2 l) (* (/ l Om) (* (/ l Om) (* (- U U*) n))))))))
161.0ms	(fma (/ l Om) (* 2 l) (* (/ l Om) (* (/ l Om) (* (- U U*) n))))
144.0ms	(* (/ l Om) (* (- U U*) n))

simplify1.7s

Counts: 195 → 195

prune4.8s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 18.6b

localize61.0ms

Local error

Found 4 expressions with local error:

18.3b	(sqrt (* U (* 2 (* n (- t (fma (/ l Om) (* 2 l) (* (/ l Om) (* (* (/ l Om) (- U U*)) n))))))))
5.7b	(* U (* 2 (* n (- t (fma (/ l Om) (* 2 l) (* (/ l Om) (* (* (/ l Om) (- U U*)) n)))))))
5.2b	(* (/ l Om) (- U U*))
4.8b	(* (* (/ l Om) (- U U*)) n)

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

143×	`distribute-rgt-in` `distribute-lft-in`
90×	`prod-diff`
81×	`add-sqr-sqrt`
76×	`*-un-lft-identity`
74×	`add-cube-cbrt`
30×	`pow1`
27×	`add-cbrt-cube` `add-exp-log`
17×	`associate-l`
16×	`pow-prod-down` `associate-*r/`
13×	`prod-exp` `cbrt-unprod`
10×	`sub-neg` `times-frac`
9×	`associate-r`
7×	`associate-*l/`
6×	`flip3--` `flip--`
4×	`expm1-log1p-u` `frac-times` `sqrt-pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `unswap-sqr`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 223

Calls

4 calls:

Slowest

70.0ms	(sqrt (* U (* 2 (* n (- t (fma (/ l Om) (* 2 l) (* (/ l Om) (* (* (/ l Om) (- U U*)) n))))))))
60.0ms	(* U (* 2 (* n (- t (fma (/ l Om) (* 2 l) (* (/ l Om) (* (* (/ l Om) (- U U*)) n)))))))
31.0ms	(* (* (/ l Om) (- U U*)) n)
22.0ms	(* (/ l Om) (- U U*))

series2.4s

Counts

4 → 12

Calls

4 calls:

Slowest

1.8s	(sqrt (* U (* 2 (* n (- t (fma (/ l Om) (* 2 l) (* (/ l Om) (* (* (/ l Om) (- U U*)) n))))))))
427.0ms	(* U (* 2 (* n (- t (fma (/ l Om) (* 2 l) (* (/ l Om) (* (* (/ l Om) (- U U*)) n)))))))
115.0ms	(* (* (/ l Om) (- U U*)) n)
66.0ms	(* (/ l Om) (- U U*))

simplify635.0ms

Counts: 235 → 235

prune4.4s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 18.6b

localize70.0ms

Local error

Found 4 expressions with local error:

18.3b	(sqrt (* (* (cbrt U) (cbrt U)) (* (* 2 (cbrt U)) (* (- t (* (/ l Om) (+ (* 2 l) (* (* (/ l Om) n) (- U U*))))) n))))
7.6b	(* (* (/ l Om) n) (- U U*))
4.5b	(* (/ l Om) n)
3.8b	(* (* (cbrt U) (cbrt U)) (* (* 2 (cbrt U)) (* (- t (* (/ l Om) (+ (* 2 l) (* (* (/ l Om) n) (- U U*))))) n)))

rewrite271.0ms

Algorithm

rewrite-expression-head

Rules

94×	`pow1`
66×	`pow-prod-down`
59×	`add-exp-log`
45×	`add-cbrt-cube`
38×	`prod-exp` `cbrt-unprod`
32×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
25×	`add-cube-cbrt`
18×	`prod-diff`
15×	`associate-l`
11×	`distribute-rgt-in` `distribute-lft-in` `sqrt-pow1`
10×	`times-frac` `associate-*r/`
9×	`associate-r` `associate-*l/`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--` `add-log-exp`
3×	`*-commutative`
2×	`frac-times` `cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `unswap-sqr`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 157

Calls

4 calls:

Slowest

122.0ms	(sqrt (* (* (cbrt U) (cbrt U)) (* (* 2 (cbrt U)) (* (- t (* (/ l Om) (+ (* 2 l) (* (* (/ l Om) n) (- U U*))))) n))))
101.0ms	(* (* (cbrt U) (cbrt U)) (* (* 2 (cbrt U)) (* (- t (* (/ l Om) (+ (* 2 l) (* (* (/ l Om) n) (- U U*))))) n)))
35.0ms	(* (* (/ l Om) n) (- U U*))
9.0ms	(* (/ l Om) n)

series4.0s

Counts

4 → 12

Calls

4 calls:

Slowest

3.3s	(sqrt (* (* (cbrt U) (cbrt U)) (* (* 2 (cbrt U)) (* (- t (* (/ l Om) (+ (* 2 l) (* (* (/ l Om) n) (- U U*))))) n))))
512.0ms	(* (* (cbrt U) (cbrt U)) (* (* 2 (cbrt U)) (* (- t (* (/ l Om) (+ (* 2 l) (* (* (/ l Om) n) (- U U*))))) n)))
108.0ms	(* (* (/ l Om) n) (- U U*))
36.0ms	(* (/ l Om) n)

simplify1.4s

Counts: 169 → 169

prune3.1s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 17.0b

localize48.0ms

Local error

Found 4 expressions with local error:

15.0b	(sqrt (* (* (* 2 (cbrt U)) (- t (* (fma l 2 (* (* (- U U*) (/ l Om)) n)) (/ l Om)))) n))
5.2b	(* (- U U*) (/ l Om))
4.8b	(* (* (- U U*) (/ l Om)) n)
3.4b	(* (* (* 2 (cbrt U)) (- t (* (fma l 2 (* (* (- U U*) (/ l Om)) n)) (/ l Om)))) n)

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1`
27×	`add-exp-log`
26×	`add-cbrt-cube`
21×	`add-sqr-sqrt`
19×	`associate-r`
16×	`*-un-lft-identity` `pow-prod-down`
14×	`add-cube-cbrt`
13×	`associate-*l/` `prod-exp` `cbrt-unprod`
10×	`times-frac`
7×	`associate-l`
6×	`flip3--` `associate-*r/` `flip--`
4×	`expm1-log1p-u` `frac-times` `sqrt-pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `unswap-sqr`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 113

Calls

4 calls:

Slowest

51.0ms	(* (* (* 2 (cbrt U)) (- t (* (fma l 2 (* (* (- U U*) (/ l Om)) n)) (/ l Om)))) n)
49.0ms	(sqrt (* (* (* 2 (cbrt U)) (- t (* (fma l 2 (* (* (- U U*) (/ l Om)) n)) (/ l Om)))) n))
31.0ms	(* (* (- U U*) (/ l Om)) n)
18.0ms	(* (- U U*) (/ l Om))

series6.5s

Counts

4 → 12

Calls

4 calls:

Slowest

5.3s	(sqrt (* (* (* 2 (cbrt U)) (- t (* (fma l 2 (* (* (- U U*) (/ l Om)) n)) (/ l Om)))) n))
991.0ms	(* (* (* 2 (cbrt U)) (- t (* (fma l 2 (* (* (- U U*) (/ l Om)) n)) (/ l Om)))) n)
76.0ms	(* (* (- U U*) (/ l Om)) n)
46.0ms	(* (- U U*) (/ l Om))

simplify879.0ms

Counts: 125 → 125

prune1.8s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 13.3b

regimes1.9s

Accuracy

39.2% (5.6b remaining)

Error of 20.9b against oracle of 15.3b and baseline of 24.5b

bsearch136.0ms

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.6s	15170×	body	80	nan
1.6s	9175×	body	80	valid