Details

sample112.0ms

Algorithm

intervals

Results

29.0ms	273×	body	80	nan
26.0ms	124×	body	160	valid
14.0ms	132×	body	80	valid

simplify2.4s

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ Om Omc) 2.0)
0.3b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.5b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.0b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
65×	`times-frac`
51×	`*-un-lft-identity`
37×	`add-cube-cbrt`
30×	`sqrt-prod`
28×	`difference-of-squares`
27×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-/l*` `sqr-pow`
7×	`distribute-lft-out--`
6×	`pow1` `add-cbrt-cube`
4×	`associate-/r/` `add-log-exp`
3×	`pow-unpow` `associate-/r*` `div-inv`
2×	`rem-sqrt-square` `flip3-+` `div-exp` `pow-exp` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `asin-acos` `flip3--` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `clear-num` `flip--`

Counts

4 → 130

Calls

4 calls:

6.0ms	(pow (/ Om Omc) 2.0)
90.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
1.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
65.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series986.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(pow (/ Om Omc) 2.0)
369.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
22.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
493.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify960.0ms

Counts: 142 → 142

prune881.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.8b

localize60.0ms

Local error

Found 4 expressions with local error:

0.5b	(asin (sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
9.0b	(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1`
8×	`add-sqr-sqrt`
7×	`sqrt-div` `sqrt-prod`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `sqrt-pow1` `add-cbrt-cube` `add-log-exp`
3×	`pow1/2`
2×	`rem-sqrt-square` `flip3-+` `flip-+`
1×	`frac-times` `asin-acos` `associate-r/` `pow-prod-down` `associate-l/`

Counts

4 → 52

Calls

4 calls:

1.0ms	(asin (sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
71.0ms	(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.2s

Counts

4 → 12

Calls

4 calls:

63.0ms	(asin (sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
555.0ms	(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
287.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
258.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.5s

Counts: 64 → 64

prune531.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.8b

localize49.0ms

Local error

Found 4 expressions with local error:

9.0b	(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (* (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-sqr-sqrt` `sqrt-prod`
9×	`sqrt-div`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`sqrt-pow1`
4×	`add-exp-log` `pow1/2` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `flip3-+` `flip-+`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/`

Counts

4 → 59

Calls

4 calls:

146.0ms	(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (* (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.5s

Counts

4 → 12

Calls

4 calls:

608.0ms	(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (* (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
307.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
291.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
266.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.3s

Counts: 71 → 71

prune740.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.8b

localize59.0ms

Local error

Found 4 expressions with local error:

9.0b	(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (* (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.9b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.9b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`sqrt-div`
4×	`add-exp-log` `cbrt-div` `sqrt-prod` `add-cbrt-cube` `add-log-exp`
3×	`sqrt-pow1` `flip3-+` `flip-+`
2×	`pow1/2` `pow1/3`
1×	`frac-times` `rem-sqrt-square` `associate-r/` `pow-prod-down` `associate-l/`

Counts

4 → 55

Calls

4 calls:

134.0ms	(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (* (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.8s

Counts

4 → 12

Calls

4 calls:

809.0ms	(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (* (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
208.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
395.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
402.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify641.0ms

Counts: 67 → 67

prune844.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.8b

regimes952.0ms

Accuracy

0% (0.2b remaining)

Error of 10.5b against oracle of 10.3b and baseline of 10.5b

bsearch0.0ms

simplify1.5s

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.5s	8083×	body	80	nan
974.0ms	3695×	body	160	valid
546.0ms	4305×	body	80	valid