Details

Time bar (total: 1.9m)

sample127.0ms

Algorithm
intervals
Results
48.0ms265×body80nan
33.0ms113×body160valid
23.0ms143×body80valid

simplify379.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
379.0ms
(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: 8.1b

localize30.0ms

Local error

Found 4 expressions with local error:

7.2b
(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
(* (/ t l) (/ t l))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
99×add-sqr-sqrt
96×times-frac
72×*-un-lft-identity
69×add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
19×pow1 sqrt-prod
9×div-inv
8×cbrt-undiv div-exp prod-exp cbrt-unprod unswap-sqr
6×difference-of-squares
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×pow2 frac-times rem-sqrt-square pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
1×asin-acos sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 185
Calls
4 calls:
Slowest
25.0ms
(* (/ t l) (/ t l))
20.0ms
(* (/ Om Omc) (/ Om Omc))
5.0ms
(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))))

series246.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
151.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
42.0ms
(* (/ Om Omc) (/ Om Omc))
35.0ms
(* (/ t l) (/ t l))
18.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify23.7s

Counts
247 → 197
Calls
247 calls:
Slowest
520.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
444.0ms
(* (* (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))) (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))) (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
437.0ms
(/ (pow t 2) (pow l 2))
388.0ms
(* (/ t l) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
378.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))

prune2.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.0b

localize69.0ms

Local error

Found 4 expressions with local error:

7.2b
(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1)))
3.7b
(log (exp (* (/ Om Omc) (/ Om Omc))))
0.8b
(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1))))
0.3b
(* (/ t l) (/ t l))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
68×add-sqr-sqrt
62×times-frac
56×*-un-lft-identity
44×add-cube-cbrt
25×sqrt-prod
16×pow1 add-cbrt-cube add-exp-log
13×swap-sqr associate-*r* associate-*l*
6×log-pow distribute-lft-out-- difference-of-squares
5×div-inv add-log-exp
4×expm1-log1p-u cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u unswap-sqr
3×log-prod
2×rem-sqrt-square
1×pow2 frac-times asin-acos exp-prod sqrt-pow1 pow-plus exp-to-pow pow1/2 sqrt-div rem-log-exp pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
4 → 138
Calls
4 calls:
Slowest
26.0ms
(* (/ t l) (/ t l))
19.0ms
(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1)))
8.0ms
(log (exp (* (/ Om Omc) (/ Om Omc))))
1.0ms
(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1))))

series265.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
172.0ms
(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1)))
50.0ms
(log (exp (* (/ Om Omc) (/ Om Omc))))
32.0ms
(* (/ t l) (/ t l))
11.0ms
(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify28.9s

Counts
192 → 150
Calls
192 calls:
Slowest
772.0ms
(real->posit16 (asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1)))))
439.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
435.0ms
(sqrt (/ (+ 1 (sqrt (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
405.0ms
(sqrt (/ (- 1 (sqrt (log (exp (* (/ Om Omc) (/ Om Omc)))))) (fma (* (/ t l) (/ t l)) 2 1)))
388.0ms
(sqrt (/ (+ (sqrt 1) (sqrt (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

prune2.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.0b

localize44.0ms

Local error

Found 4 expressions with local error:

7.2b
(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
(* (/ t l) (/ t l))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
99×add-sqr-sqrt
96×times-frac
72×*-un-lft-identity
69×add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
19×pow1 sqrt-prod
9×div-inv
8×cbrt-undiv div-exp prod-exp cbrt-unprod unswap-sqr
6×difference-of-squares
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×pow2 frac-times rem-sqrt-square pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
1×asin-acos sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 185
Calls
4 calls:
Slowest
23.0ms
(* (/ t l) (/ t l))
19.0ms
(* (/ Om Omc) (/ Om Omc))
5.0ms
(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))))

series260.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
166.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
48.0ms
(* (/ Om Omc) (/ Om Omc))
36.0ms
(* (/ t l) (/ t l))
10.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify23.4s

Counts
247 → 197
Calls
247 calls:
Slowest
470.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
469.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
429.0ms
(* (/ t l) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
421.0ms
(* (* (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))) (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))) (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
350.0ms
(* (/ Om Omc) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))

prune3.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.0b

localize65.0ms

Local error

Found 4 expressions with local error:

7.3b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
0.8b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
0.3b
(* (/ t l) (/ t l))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
86×add-sqr-sqrt
80×times-frac
61×*-un-lft-identity add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
19×pow1
8×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-prod
2×pow2 frac-times pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
1×rem-sqrt-square asin-acos sqrt-pow1 pow1/2
Counts
4 → 167
Calls
4 calls:
Slowest
21.0ms
(* (/ Om Omc) (/ Om Omc))
13.0ms
(* (/ t l) (/ t l))
1.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

series181.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
89.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
43.0ms
(* (/ Om Omc) (/ Om Omc))
32.0ms
(* (/ t l) (/ t l))
17.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

simplify16.4s

Counts
213 → 179
Calls
213 calls:
Slowest
550.0ms
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
500.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
419.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
403.0ms
(* (/ Om Omc) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
352.0ms
(* (/ t l) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))

prune2.9s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.0b

regimes623.0ms

Accuracy

98.6% (0.1b remaining)

Error of 5.8b against oracle of 5.7b and baseline of 10.5b

bsearch17.0ms

end0.0ms

sample5.5s

Algorithm
intervals
Results
2.1s7947×body80nan
1.7s3769×body160valid
1.0s4231×body80valid