Details

sample247.0ms

Algorithm

intervals

Results

114.0ms	483×	body	80	nan
83.0ms	286×	body	80	valid

simplify1.2s

Counts: 1 → 1

prune42.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.1b

localize64.0ms

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))))

rewrite245.0ms

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

106.0ms	(sqrt (* U (* 2 (* n (- t (fma (/ l Om) (* 2 l) (* (/ l Om) (* (/ l Om) (* (- U U*) n)))))))))
93.0ms	(* U (* 2 (* n (- t (fma (/ l Om) (* 2 l) (* (/ l Om) (* (/ l Om) (* (- U U*) n))))))))
37.0ms	(* (/ l Om) (* (- U U*) n))
0.0ms	(fma (/ l Om) (* 2 l) (* (/ l Om) (* (/ l Om) (* (- U U*) n))))

series3.1s

Counts

4 → 12

Calls

4 calls:

Slowest

2.3s	(sqrt (* U (* 2 (* n (- t (fma (/ l Om) (* 2 l) (* (/ l Om) (* (/ l Om) (* (- U U*) n)))))))))
489.0ms	(* U (* 2 (* n (- t (fma (/ l Om) (* 2 l) (* (/ l Om) (* (/ l Om) (* (- U U*) n))))))))
175.0ms	(fma (/ l Om) (* 2 l) (* (/ l Om) (* (/ l Om) (* (- U U*) n))))
128.0ms	(* (/ l Om) (* (- U U*) n))

simplify1.6s

Counts: 195 → 195

prune4.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 18.6b

localize54.0ms

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)

rewrite281.0ms

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

126.0ms	(sqrt (* U (* 2 (* n (- t (fma (/ l Om) (* 2 l) (* (/ l Om) (* (* (/ l Om) (- U U*)) n))))))))
83.0ms	(* U (* 2 (* n (- t (fma (/ l Om) (* 2 l) (* (/ l Om) (* (* (/ l Om) (- U U*)) n)))))))
38.0ms	(* (* (/ l Om) (- U U*)) n)
25.0ms	(* (/ l Om) (- U U*))

series3.0s

Counts

4 → 12

Calls

4 calls:

Slowest

2.2s	(sqrt (* U (* 2 (* n (- t (fma (/ l Om) (* 2 l) (* (/ l Om) (* (* (/ l Om) (- U U*)) n))))))))
583.0ms	(* U (* 2 (* n (- t (fma (/ l Om) (* 2 l) (* (/ l Om) (* (* (/ l Om) (- U U*)) n)))))))
120.0ms	(* (* (/ l Om) (- U U*)) n)
94.0ms	(* (/ l Om) (- U U*))

simplify793.0ms

Counts: 235 → 235

prune5.8s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 18.6b

localize102.0ms

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)))

rewrite392.0ms

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

190.0ms	(* (* (cbrt U) (cbrt U)) (* (* 2 (cbrt U)) (* (- t (* (/ l Om) (+ (* 2 l) (* (* (/ l Om) n) (- U U*))))) n)))
116.0ms	(sqrt (* (* (cbrt U) (cbrt U)) (* (* 2 (cbrt U)) (* (- t (* (/ l Om) (+ (* 2 l) (* (* (/ l Om) n) (- U U*))))) n))))
61.0ms	(* (* (/ l Om) n) (- U U*))
19.0ms	(* (/ l Om) n)

series4.7s

Counts

4 → 12

Calls

4 calls:

Slowest

3.9s	(sqrt (* (* (cbrt U) (cbrt U)) (* (* 2 (cbrt U)) (* (- t (* (/ l Om) (+ (* 2 l) (* (* (/ l Om) n) (- U U*))))) n))))
565.0ms	(* (* (cbrt U) (cbrt U)) (* (* 2 (cbrt U)) (* (- t (* (/ l Om) (+ (* 2 l) (* (* (/ l Om) n) (- U U*))))) n)))
143.0ms	(* (* (/ l Om) n) (- U U*))
46.0ms	(* (/ l Om) n)

simplify2.0s

Counts: 169 → 169

prune4.2s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 17.0b

localize88.0ms

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)

rewrite218.0ms

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

70.0ms	(* (* (* 2 (cbrt U)) (- t (* (fma l 2 (* (* (- U U*) (/ l Om)) n)) (/ l Om)))) n)
64.0ms	(sqrt (* (* (* 2 (cbrt U)) (- t (* (fma l 2 (* (* (- U U*) (/ l Om)) n)) (/ l Om)))) n))
45.0ms	(* (* (- U U*) (/ l Om)) n)
37.0ms	(* (- U U*) (/ l Om))

series9.1s

Counts

4 → 12

Calls

4 calls:

Slowest

7.4s	(sqrt (* (* (* 2 (cbrt U)) (- t (* (fma l 2 (* (* (- U U*) (/ l Om)) n)) (/ l Om)))) n))
1.4s	(* (* (* 2 (cbrt U)) (- t (* (fma l 2 (* (* (- U U*) (/ l Om)) n)) (/ l Om)))) n)
97.0ms	(* (* (- U U*) (/ l Om)) n)
81.0ms	(* (- U U*) (/ l Om))

simplify1.1s

Counts: 125 → 125

prune3.1s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 13.3b

regimes3.3s

Accuracy

39.2% (5.6b remaining)

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

bsearch213.0ms

end0.0ms

sample8.0s

Algorithm

intervals

Results

3.8s	15170×	body	80	nan
3.1s	9175×	body	80	valid