Details

Time bar (total: 2.9m)

sample112.0ms

Algorithm
intervals
Results
45.0ms304×body80nan
31.0ms119×body160valid
17.0ms137×body80valid

simplify438.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
438.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.6b

localize27.0ms

Local error

Found 4 expressions with local error:

9.5b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
0.8b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
0.3b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
0.2b
(* (/ t l) (/ t l))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
73×add-sqr-sqrt
71×times-frac
58×*-un-lft-identity
51×add-cube-cbrt
19×sqrt-prod
18×add-cbrt-cube add-exp-log
14×difference-of-squares
13×swap-sqr associate-*r* associate-*l*
12×pow1
6×div-inv
5×cbrt-undiv div-exp associate-/l*
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×associate-/r*
2×rem-sqrt-square associate-/l/
1×pow2 frac-times asin-acos clear-num frac-2neg sqrt-pow1 pow-plus flip3-- pow1/2 sqrt-div div-sub pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip--
Counts
4 → 156
Calls
4 calls:
Slowest
26.0ms
(* (/ t l) (/ t l))
19.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
6.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

series337.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
208.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
84.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
28.0ms
(* (/ t l) (/ t l))
17.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify14.4s

Counts
152 → 168
Calls
152 calls:
Slowest
813.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
693.0ms
(/ (* (* (- 1 (* (/ Om Omc) (/ Om Omc))) (- 1 (* (/ Om Omc) (/ Om Omc)))) (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (* (fma (* (/ t l) (/ t l)) 2 1) (fma (* (/ t l) (/ t l)) 2 1)) (fma (* (/ t l) (/ t l)) 2 1)))
426.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
297.0ms
(sqrt (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))))
286.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (fma (/ (pow t 2) (pow l 2)) 2 1))))

prune2.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.5b

localize36.0ms

Local error

Found 4 expressions with local error:

9.5b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
0.8b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
0.3b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
0.2b
(* (/ t l) (/ t l))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
73×add-sqr-sqrt
71×times-frac
58×*-un-lft-identity
51×add-cube-cbrt
19×sqrt-prod
18×add-cbrt-cube add-exp-log
14×difference-of-squares
13×swap-sqr associate-*r* associate-*l*
12×pow1
6×div-inv
5×cbrt-undiv div-exp associate-/l*
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×associate-/r*
2×rem-sqrt-square associate-/l/
1×pow2 frac-times asin-acos clear-num frac-2neg sqrt-pow1 pow-plus flip3-- pow1/2 sqrt-div div-sub pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip--
Counts
4 → 156
Calls
4 calls:
Slowest
13.0ms
(* (/ t l) (/ t l))
13.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
6.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

series307.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
167.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
90.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
40.0ms
(* (/ t l) (/ t l))
10.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify14.4s

Counts
152 → 168
Calls
152 calls:
Slowest
649.0ms
(/ (* (* (- 1 (* (/ Om Omc) (/ Om Omc))) (- 1 (* (/ Om Omc) (/ Om Omc)))) (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (* (fma (* (/ t l) (/ t l)) 2 1) (fma (* (/ t l) (/ t l)) 2 1)) (fma (* (/ t l) (/ t l)) 2 1)))
461.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
411.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
287.0ms
(/ (- (sqrt 1) (/ Om Omc)) (fma (* (/ t l) (/ t l)) 2 1))
284.0ms
(/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))

prune2.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 10.5b

localize51.0ms

Local error

Found 4 expressions with local error:

9.5b
(sqrt (/ (+ 1 (/ Om Omc)) (/ (fma (* (/ t l) (/ t l)) 2 1) (- 1 (/ Om Omc)))))
0.8b
(asin (sqrt (/ (+ 1 (/ Om Omc)) (/ (fma (* (/ t l) (/ t l)) 2 1) (- 1 (/ Om Omc))))))
0.3b
(/ (+ 1 (/ Om Omc)) (/ (fma (* (/ t l) (/ t l)) 2 1) (- 1 (/ Om Omc))))
0.2b
(* (/ t l) (/ t l))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
553×times-frac
436×add-sqr-sqrt
432×*-un-lft-identity
202×add-cube-cbrt
125×sqrt-prod
108×difference-of-squares
61×distribute-lft-out
30×associate-/r*
27×distribute-lft-out--
21×add-cbrt-cube add-exp-log
20×associate-/r/
15×div-inv
13×swap-sqr associate-*r* associate-*l*
12×pow1
9×flip3-- flip--
7×cbrt-undiv div-exp
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u associate-/l* add-log-exp unswap-sqr
3×rem-sqrt-square
2×associate-/l/
1×pow2 frac-times asin-acos clear-num frac-2neg sqrt-pow1 flip3-+ pow-plus pow1/2 sqrt-div pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip-+
Counts
4 → 396
Calls
4 calls:
Slowest
40.0ms
(/ (+ 1 (/ Om Omc)) (/ (fma (* (/ t l) (/ t l)) 2 1) (- 1 (/ Om Omc))))
30.0ms
(* (/ t l) (/ t l))
27.0ms
(sqrt (/ (+ 1 (/ Om Omc)) (/ (fma (* (/ t l) (/ t l)) 2 1) (- 1 (/ Om Omc)))))
1.0ms
(asin (sqrt (/ (+ 1 (/ Om Omc)) (/ (fma (* (/ t l) (/ t l)) 2 1) (- 1 (/ Om Omc))))))

series310.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
163.0ms
(sqrt (/ (+ 1 (/ Om Omc)) (/ (fma (* (/ t l) (/ t l)) 2 1) (- 1 (/ Om Omc)))))
103.0ms
(/ (+ 1 (/ Om Omc)) (/ (fma (* (/ t l) (/ t l)) 2 1) (- 1 (/ Om Omc))))
27.0ms
(* (/ t l) (/ t l))
17.0ms
(asin (sqrt (/ (+ 1 (/ Om Omc)) (/ (fma (* (/ t l) (/ t l)) 2 1) (- 1 (/ Om Omc))))))

simplify1.5m

Counts
496 → 408
Calls
496 calls:
Slowest
765.0ms
(/ (+ 1 (/ Om Omc)) (/ (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (- 1 (sqrt (/ Om Omc)))))
573.0ms
(/ (cbrt (+ 1 (/ Om Omc))) (+ (* 1 1) (+ (* (/ Om Omc) (/ Om Omc)) (* 1 (/ Om Omc)))))
521.0ms
(sqrt (/ (sqrt (+ 1 (/ Om Omc))) (/ (sqrt (fma (* (/ t l) (/ t l)) 2 1)) 1)))
499.0ms
(sqrt (/ (sqrt (+ 1 (/ Om Omc))) (/ (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1))) (+ 1 (sqrt (/ Om Omc))))))
484.0ms
(/ (* (cbrt (+ 1 (/ Om Omc))) (cbrt (+ 1 (/ Om Omc)))) (/ (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1))) (+ (sqrt 1) (sqrt (/ Om Omc)))))

prune6.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 10.5b

localize77.0ms

Local error

Found 4 expressions with local error:

30.9b
(cbrt (* (/ t l) (/ t l)))
30.9b
(cbrt (* (/ t l) (/ t l)))
30.9b
(cbrt (* (/ t l) (/ t l)))
9.5b
(sqrt (/ (+ 1 (/ Om Omc)) (/ (fma (* (* (cbrt (* (/ t l) (/ t l))) (cbrt (* (/ t l) (/ t l)))) (cbrt (* (/ t l) (/ t l)))) 2 1) (- 1 (/ Om Omc)))))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
243×times-frac
191×*-un-lft-identity
185×add-sqr-sqrt
125×sqrt-prod
83×add-cube-cbrt
48×difference-of-squares
30×distribute-lft-out
12×distribute-lft-out--
9×cbrt-div associate-/r/
5×pow1 div-inv
4×expm1-log1p-u flip3-- add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u flip-- add-log-exp
3×cbrt-prod frac-times rem-sqrt-square pow1/3 associate-*l/ associate-*r/
1×sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 186
Calls
4 calls:
Slowest
38.0ms
(sqrt (/ (+ 1 (/ Om Omc)) (/ (fma (* (* (cbrt (* (/ t l) (/ t l))) (cbrt (* (/ t l) (/ t l)))) (cbrt (* (/ t l) (/ t l)))) 2 1) (- 1 (/ Om Omc)))))
6.0ms
(cbrt (* (/ t l) (/ t l)))
5.0ms
(cbrt (* (/ t l) (/ t l)))
5.0ms
(cbrt (* (/ t l) (/ t l)))

series572.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
165.0ms
(sqrt (/ (+ 1 (/ Om Omc)) (/ (fma (* (* (cbrt (* (/ t l) (/ t l))) (cbrt (* (/ t l) (/ t l)))) (cbrt (* (/ t l) (/ t l)))) 2 1) (- 1 (/ Om Omc)))))
144.0ms
(cbrt (* (/ t l) (/ t l)))
133.0ms
(cbrt (* (/ t l) (/ t l)))
130.0ms
(cbrt (* (/ t l) (/ t l)))

simplify31.0s

Counts
154 → 198
Calls
154 calls:
Slowest
899.0ms
(sqrt (/ (sqrt (+ 1 (/ Om Omc))) (/ (* (cbrt (fma (* (* (cbrt (* (/ t l) (/ t l))) (cbrt (* (/ t l) (/ t l)))) (cbrt (* (/ t l) (/ t l)))) 2 1)) (cbrt (fma (* (* (cbrt (* (/ t l) (/ t l))) (cbrt (* (/ t l) (/ t l)))) (cbrt (* (/ t l) (/ t l)))) 2 1))) (+ 1 (sqrt (/ Om Omc))))))
501.0ms
(sqrt (/ (sqrt (+ 1 (/ Om Omc))) (/ (fma (* (* (cbrt (* (/ t l) (/ t l))) (cbrt (* (/ t l) (/ t l)))) (cbrt (* (/ t l) (/ t l)))) 2 1) (- (* 1 1) (* (/ Om Omc) (/ Om Omc))))))
486.0ms
(sqrt (/ (* (cbrt (+ 1 (/ Om Omc))) (cbrt (+ 1 (/ Om Omc)))) (/ 1 (+ 1 (/ (sqrt Om) (sqrt Omc))))))
462.0ms
(sqrt (/ (sqrt (+ 1 (/ Om Omc))) (/ (* (cbrt (fma (* (* (cbrt (* (/ t l) (/ t l))) (cbrt (* (/ t l) (/ t l)))) (cbrt (* (/ t l) (/ t l)))) 2 1)) (cbrt (fma (* (* (cbrt (* (/ t l) (/ t l))) (cbrt (* (/ t l) (/ t l)))) (cbrt (* (/ t l) (/ t l)))) 2 1))) (+ (sqrt 1) (sqrt (/ Om Omc))))))
440.0ms
(sqrt (/ 1 (/ (* (cbrt (fma (* (* (cbrt (* (/ t l) (/ t l))) (cbrt (* (/ t l) (/ t l)))) (cbrt (* (/ t l) (/ t l)))) 2 1)) (cbrt (fma (* (* (cbrt (* (/ t l) (/ t l))) (cbrt (* (/ t l) (/ t l)))) (cbrt (* (/ t l) (/ t l)))) 2 1))) (+ (sqrt 1) (/ (sqrt Om) (sqrt Omc))))))

prune3.9s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 10.5b

regimes384.0ms

Accuracy

0% (0.2b remaining)

Error of 10.0b against oracle of 9.7b and baseline of 10.0b

bsearch4.0ms

end0.0ms

sample6.0s

Algorithm
intervals
Results
2.2s8129×body80nan
1.8s3836×body160valid
1.4s4164×body80valid