Details

sample169.0ms

Algorithm

intervals

Results

61.0ms	269×	body	80	nan
50.0ms	112×	body	160	valid
33.0ms	144×	body	80	valid

simplify174.0ms

Calls

1 calls:

Slowest

174.0ms

(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.6b

localize29.0ms

Local error

Found 4 expressions with local error:

9.3b	(sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2)))))
0.7b	(/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))
0.5b	(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))
0.2b	(pow (/ t l) 2)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
20×	`*-un-lft-identity`
19×	`times-frac`
15×	`sqrt-prod`
7×	`add-exp-log`
6×	`add-cbrt-cube`
5×	`pow1`
4×	`add-log-exp`
4×	`associate-/r/`
4×	`unpow-prod-down`
3×	`associate-/l*`
3×	`div-inv`
3×	`associate-/r*`
2×	`associate-/l/`
2×	`flip-+`
2×	`flip3-+`
2×	`rem-sqrt-square`
1×	`unpow2`
1×	`flip--`
1×	`pow-exp`
1×	`div-exp`
1×	`div-sub`
1×	`sqrt-div`
1×	`pow1/2`
1×	`flip3--`
1×	`frac-2neg`
1×	`pow-pow`
1×	`clear-num`
1×	`asin-acos`
1×	`cbrt-undiv`
1×	`pow-to-exp`

Calls

4 calls:

Slowest

5.0ms	(/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))
3.0ms	(sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2)))))
1.0ms	(pow (/ t l) 2)
0.0ms	(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

series236.0ms

Calls

4 calls:

Slowest

134.0ms	(sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2)))))
71.0ms	(/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))
17.0ms	(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))
15.0ms	(pow (/ t l) 2)

simplify6.2s

Calls

66 calls:

Slowest

471.0ms	(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1))))
433.0ms	(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1))))
423.0ms	(- (* 1 1) (* (pow (/ Om Omc) 2) (pow (/ Om Omc) 2)))
320.0ms	(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1))))
307.0ms	(- (pow 1 3) (pow (pow (/ Om Omc) 2) 3))

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.5b

localize31.0ms

Local error

Found 4 expressions with local error:

15.5b	(cbrt (/ t l))
15.5b	(cbrt (/ t l))
9.3b	(sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (* (* (/ t l) (cbrt (/ t l))) (pow (cbrt (/ t l)) 2))))))
0.7b	(/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (* (* (/ t l) (cbrt (/ t l))) (pow (cbrt (/ t l)) 2)))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
21×	`*-un-lft-identity`
19×	`times-frac`
15×	`sqrt-prod`
8×	`cbrt-prod`
6×	`add-exp-log`
6×	`add-cbrt-cube`
4×	`add-log-exp`
4×	`div-inv`
4×	`associate-/r/`
4×	`pow1`
3×	`associate-/l*`
3×	`associate-/r*`
2×	`associate-/l/`
2×	`flip-+`
2×	`pow1/3`
2×	`flip3-+`
2×	`cbrt-div`
2×	`rem-sqrt-square`
1×	`flip--`
1×	`div-exp`
1×	`div-sub`
1×	`sqrt-div`
1×	`pow1/2`
1×	`flip3--`
1×	`frac-2neg`
1×	`clear-num`
1×	`cbrt-undiv`

Calls

4 calls:

Slowest

6.0ms	(/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (* (* (/ t l) (cbrt (/ t l))) (pow (cbrt (/ t l)) 2)))))
3.0ms	(sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (* (* (/ t l) (cbrt (/ t l))) (pow (cbrt (/ t l)) 2))))))
1.0ms	(cbrt (/ t l))
0.0ms	(cbrt (/ t l))

series328.0ms

Calls

4 calls:

Slowest

115.0ms	(sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (* (* (/ t l) (cbrt (/ t l))) (pow (cbrt (/ t l)) 2))))))
84.0ms	(cbrt (/ t l))
68.0ms	(cbrt (/ t l))
61.0ms	(/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (* (* (/ t l) (cbrt (/ t l))) (pow (cbrt (/ t l)) 2)))))

simplify11.7s

Calls

70 calls:

Slowest

431.0ms	(sqrt (/ (sqrt (- 1 (pow (/ Om Omc) 2))) (sqrt (+ 1 (* 2 (* (* (/ t l) (cbrt (/ t l))) (pow (cbrt (/ t l)) 2)))))))
421.0ms	(/ (sqrt (- 1 (pow (/ Om Omc) 2))) (sqrt (+ 1 (* 2 (* (* (/ t l) (cbrt (/ t l))) (pow (cbrt (/ t l)) 2))))))
412.0ms	(/ (sqrt (- 1 (pow (/ Om Omc) 2))) (sqrt (+ 1 (* 2 (* (* (/ t l) (cbrt (/ t l))) (pow (cbrt (/ t l)) 2))))))
407.0ms	(/ (cbrt (- 1 (pow (/ Om Omc) 2))) (cbrt (+ 1 (* 2 (* (* (/ t l) (cbrt (/ t l))) (pow (cbrt (/ t l)) 2))))))
405.0ms	(/ (sqrt (- 1 (pow (/ Om Omc) 2))) (* (cbrt (+ 1 (* 2 (* (* (/ t l) (cbrt (/ t l))) (pow (cbrt (/ t l)) 2))))) (cbrt (+ 1 (* 2 (* (* (/ t l) (cbrt (/ t l))) (pow (cbrt (/ t l)) 2)))))))

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 10.5b

localize36.0ms

Local error

Found 4 expressions with local error:

15.5b	(cbrt (/ t l))
9.3b	(sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (* (* (/ t l) (* (cbrt t) (cbrt (/ 1 l)))) (pow (cbrt (/ t l)) 2))))))
0.7b	(/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (* (* (/ t l) (* (cbrt t) (cbrt (/ 1 l)))) (pow (cbrt (/ t l)) 2)))))
0.6b	(cbrt t)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
20×	`*-un-lft-identity`
19×	`times-frac`
15×	`sqrt-prod`
6×	`add-exp-log`
6×	`add-cbrt-cube`
4×	`add-log-exp`
4×	`associate-/r/`
4×	`pow1`
4×	`cbrt-prod`
3×	`associate-/l*`
3×	`div-inv`
3×	`associate-/r*`
2×	`associate-/l/`
2×	`flip-+`
2×	`pow1/3`
2×	`flip3-+`
2×	`rem-sqrt-square`
1×	`flip--`
1×	`div-exp`
1×	`div-sub`
1×	`sqrt-div`
1×	`pow1/2`
1×	`flip3--`
1×	`frac-2neg`
1×	`clear-num`
1×	`cbrt-div`
1×	`cbrt-undiv`

Calls

4 calls:

Slowest

8.0ms	(/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (* (* (/ t l) (* (cbrt t) (cbrt (/ 1 l)))) (pow (cbrt (/ t l)) 2)))))
4.0ms	(sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (* (* (/ t l) (* (cbrt t) (cbrt (/ 1 l)))) (pow (cbrt (/ t l)) 2))))))
0.0ms	(cbrt (/ t l))
0.0ms	(cbrt t)

series703.0ms

Calls

4 calls:

Slowest

290.0ms	(cbrt t)
219.0ms	(sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (* (* (/ t l) (* (cbrt t) (cbrt (/ 1 l)))) (pow (cbrt (/ t l)) 2))))))
127.0ms	(/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (* (* (/ t l) (* (cbrt t) (cbrt (/ 1 l)))) (pow (cbrt (/ t l)) 2)))))
68.0ms	(cbrt (/ t l))

simplify10.4s

Calls

65 calls:

Slowest

414.0ms	(- (* 1 1) (* (pow (/ Om Omc) 2) (pow (/ Om Omc) 2)))
384.0ms	(- 1 (* 2 (* (* (/ t l) (* (cbrt t) (cbrt (/ 1 l)))) (pow (cbrt (/ t l)) 2))))
340.0ms	(/ (* (cbrt (- 1 (pow (/ Om Omc) 2))) (cbrt (- 1 (pow (/ Om Omc) 2)))) (* (cbrt (+ 1 (* 2 (* (* (/ t l) (* (cbrt t) (cbrt (/ 1 l)))) (pow (cbrt (/ t l)) 2))))) (cbrt (+ 1 (* 2 (* (* (/ t l) (* (cbrt t) (cbrt (/ 1 l)))) (pow (cbrt (/ t l)) 2)))))))
330.0ms	(- (pow 1 3) (pow (pow (/ Om Omc) 2) 3))
315.0ms	(/ (cbrt (- 1 (pow (/ Om Omc) 2))) (+ 1 (* 2 (* (* (/ t l) (* (cbrt t) (cbrt (/ 1 l)))) (pow (cbrt (/ t l)) 2)))))

prune1.7s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 10.5b

localize20.0ms

Local error

Found 4 expressions with local error:

30.4b	(cbrt (pow (/ t l) 2))
30.4b	(cbrt (pow (/ t l) 2))
30.4b	(cbrt (pow (/ t l) 2))
9.3b	(sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (* (* (cbrt (pow (/ t l) 2)) (cbrt (pow (/ t l) 2))) (cbrt (pow (/ t l) 2)))))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
20×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
17×	`*-un-lft-identity`
15×	`sqrt-prod`
12×	`unpow-prod-down`
10×	`times-frac`
4×	`add-log-exp`
4×	`div-inv`
4×	`add-exp-log`
4×	`add-cbrt-cube`
4×	`pow1`
3×	`unpow2`
3×	`pow1/3`
2×	`associate-/r/`
2×	`rem-sqrt-square`
1×	`flip-+`
1×	`sqrt-div`
1×	`pow1/2`
1×	`flip3-+`

Calls

4 calls:

Slowest

6.0ms	(sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (* (* (cbrt (pow (/ t l) 2)) (cbrt (pow (/ t l) 2))) (cbrt (pow (/ t l) 2)))))))
1.0ms	(cbrt (pow (/ t l) 2))
1.0ms	(cbrt (pow (/ t l) 2))
1.0ms	(cbrt (pow (/ t l) 2))

series386.0ms

Calls

4 calls:

Slowest

119.0ms	(sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (* (* (cbrt (pow (/ t l) 2)) (cbrt (pow (/ t l) 2))) (cbrt (pow (/ t l) 2)))))))
92.0ms	(cbrt (pow (/ t l) 2))
90.0ms	(cbrt (pow (/ t l) 2))
86.0ms	(cbrt (pow (/ t l) 2))

simplify4.3s

Calls

54 calls:

Slowest

381.0ms	(exp (* 1/3 (- (* 2 (log (/ -1 l))) (* 2 (log (/ -1 t))))))
361.0ms	(exp (* 1/3 (- (* 2 (log (/ -1 l))) (* 2 (log (/ -1 t))))))
321.0ms	(exp (* 1/3 (- (* 2 (log (/ -1 l))) (* 2 (log (/ -1 t))))))
262.0ms	(sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ (pow 1 3) (pow (* 2 (* (* (cbrt (pow (/ t l) 2)) (cbrt (pow (/ t l) 2))) (cbrt (pow (/ t l) 2)))) 3))))
241.0ms	(sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (* (* (cbrt (pow (/ t l) 2)) (cbrt (pow (/ t l) 2))) (cbrt (pow (/ t l) 2)))))))

prune1.5s

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 10.5b

regimes1.2s

Accuracy

0% (0.1b remaining)

Error of 10.7b against oracle of 10.6b and baseline of 10.7b

bsearch2.0ms

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.5s	7839×	body	80	nan
1.8s	3749×	body	160	valid
944.0ms	4251×	body	80	valid