Details

Time bar (total: 53.5s)

sample171.0ms

Algorithm
intervals
Results
73.0ms127×body160valid
45.0ms239×body80nan
26.0ms129×body80valid

simplify468.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
468.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.3b

localize53.0ms

Local error

Found 4 expressions with local error:

9.5b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
0.4b
(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))

rewrite45.0ms

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
18.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
12.0ms
(* (/ t l) (/ t l))
11.0ms
(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))))

series345.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
163.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
136.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
29.0ms
(* (/ t l) (/ t l))
18.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify14.0s

Counts
152 → 168
Calls
152 calls:
Slowest
627.0ms
(/ (* (* (- 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)))
451.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
441.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
290.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1))))
289.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (fma (/ (pow t 2) (pow l 2)) 2 1))))

prune2.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.2b

localize39.0ms

Local error

Found 4 expressions with local error:

9.8b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
0.4b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
0.2b
(* (/ t l) (/ t l))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite61.0ms

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
26.0ms
(* (/ Om Omc) (/ Om Omc))
26.0ms
(* (/ t l) (/ t l))
3.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
2.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

series193.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
109.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
45.0ms
(* (/ Om Omc) (/ Om Omc))
30.0ms
(* (/ t l) (/ t l))
9.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

simplify7.4s

Counts
167 → 179
Calls
167 calls:
Slowest
459.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
451.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
401.0ms
(/ (sqrt Om) (cbrt Omc))
245.0ms
(* (* (* (/ t l) (/ t l)) (/ t l)) (* (* (/ t l) (/ t l)) (/ t l)))
241.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (fma (/ (pow t 2) (pow l 2)) 2 1))))

prune2.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.3b

localize77.0ms

Local error

Found 4 expressions with local error:

9.8b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
9.8b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
6.4b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
6.4b
(sqrt (/ 1 (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
89×sqrt-prod
56×add-sqr-sqrt
54×times-frac
44×*-un-lft-identity
36×add-cube-cbrt
12×difference-of-squares
10×pow1 rem-sqrt-square
9×sqrt-pow1
5×pow1/2
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow-flip
2×sqrt-div div-inv
1×inv-pow
Counts
4 → 126
Calls
4 calls:
Slowest
13.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
7.0ms
(sqrt (/ 1 (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
2.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
2.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

series623.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
287.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
178.0ms
(sqrt (/ 1 (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
80.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
78.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

simplify11.2s

Counts
94 → 138
Calls
94 calls:
Slowest
361.0ms
(/ (* (exp (* 1/4 (- (+ (* 2 (log (/ -1 t))) (log 1/2)) (* 2 (log (/ -1 l)))))) (* (sqrt -1) Om)) Omc)
273.0ms
(sqrt (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))
273.0ms
(/ (* (sqrt -1) (* (exp (* 1/4 (- (+ (log 1/2) (* 2 (log (/ 1 t)))) (* 2 (log (/ 1 l)))))) Om)) Omc)
259.0ms
(sqrt (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))))))
238.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

prune2.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.3b

localize56.0ms

Local error

Found 4 expressions with local error:

9.8b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
9.8b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
9.8b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
6.4b
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
19×sqrt-prod
14×add-sqr-sqrt
9×pow1 *-un-lft-identity add-cube-cbrt
7×sqrt-pow1
5×rem-sqrt-square pow1/2
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 70
Calls
4 calls:
Slowest
2.0ms
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
1.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

series445.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
200.0ms
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
84.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
82.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
78.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

simplify3.4s

Counts
38 → 82
Calls
38 calls:
Slowest
219.0ms
(exp (* 1/4 (- (+ (log 2) (* 2 (log (/ -1 l)))) (* 2 (log (/ -1 t))))))
189.0ms
(sqrt (* (cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))
188.0ms
(exp (* 1/4 (- (+ (log 2) (* 2 (log (/ 1 l)))) (* 2 (log (/ 1 t))))))
186.0ms
(sqrt (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
185.0ms
(sqrt (sqrt (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))))

prune1.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.3b

regimes642.0ms

Accuracy

96.9% (0.1b remaining)

Error of 5.7b against oracle of 5.6b and baseline of 10.2b

bsearch8.0ms

end0.0ms

sample5.3s

Algorithm
intervals
Results
2.2s7938×body80nan
1.7s3865×body160valid
870.0ms4135×body80valid