Details

Time bar (total: 1.6m)

sample211.0ms

Algorithm
intervals
Results
86.0ms131×body160valid
59.0ms252×body80nan
31.0ms125×body80valid

simplify372.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
372.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.3b

localize57.0ms

Local error

Found 4 expressions with local error:

7.2b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
0.8b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.3b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
73×add-sqr-sqrt
71×times-frac
58×*-un-lft-identity
51×add-cube-cbrt
21×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×prod-exp associate-/r/ cbrt-unprod insert-posit16 add-log-exp unswap-sqr
3×associate-/r*
2×rem-sqrt-square flip3-+ flip-+ 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 → 152
Calls
4 calls:
Slowest
34.0ms
(* (/ Om Omc) (/ Om Omc))
30.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
16.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

series343.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
173.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
105.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
45.0ms
(* (/ Om Omc) (/ Om Omc))
20.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify15.9s

Counts
156 → 164
Calls
156 calls:
Slowest
521.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
437.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
327.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1))))
312.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
308.0ms
(sqrt (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))

prune2.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.3b

localize51.0ms

Local error

Found 4 expressions with local error:

7.2b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
0.8b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))))
0.3b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))
0.2b
(* (/ l t) (/ l t))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
84×*-un-lft-identity
81×times-frac
77×add-sqr-sqrt
53×add-cube-cbrt
26×sqrt-prod
18×add-cbrt-cube add-exp-log difference-of-squares
13×swap-sqr associate-*r* associate-*l*
12×pow1
11×distribute-lft-out
6×div-inv
5×cbrt-undiv div-exp associate-/l*
4×associate-/r* prod-exp associate-/r/ cbrt-unprod insert-posit16 add-log-exp unswap-sqr
2×rem-sqrt-square flip3-+ flip-+ 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 → 163
Calls
4 calls:
Slowest
52.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
41.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))
13.0ms
(* (/ l t) (/ l t))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))))

series325.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
168.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
110.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))
34.0ms
(* (/ l t) (/ l t))
13.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))))

simplify16.8s

Counts
172 → 175
Calls
172 calls:
Slowest
522.0ms
(+ (* (/ 2 (* (/ l t) (/ l t))) (/ 2 (* (/ l t) (/ l t)))) (- (* 1 1) (* (/ 2 (* (/ l t) (/ l t))) 1)))
430.0ms
(* (/ (* (cbrt l) (cbrt l)) (* (cbrt t) (cbrt t))) (/ (* (cbrt l) (cbrt l)) (* (cbrt t) (cbrt t))))
430.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
429.0ms
(sqrt (+ (/ 2 (* (/ l t) (/ l t))) 1))
414.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (+ (/ 2 (* (/ l t) (/ l t))) 1)))

prune2.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.3b

localize42.0ms

Local error

Found 4 expressions with local error:

7.2b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
0.8b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.3b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
73×add-sqr-sqrt
71×times-frac
58×*-un-lft-identity
51×add-cube-cbrt
21×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×prod-exp associate-/r/ cbrt-unprod insert-posit16 add-log-exp unswap-sqr
3×associate-/r*
2×rem-sqrt-square flip3-+ flip-+ 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 → 152
Calls
4 calls:
Slowest
15.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
14.0ms
(* (/ Om Omc) (/ Om Omc))
8.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

series311.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
151.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
103.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
45.0ms
(* (/ Om Omc) (/ Om Omc))
11.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify15.8s

Counts
156 → 164
Calls
156 calls:
Slowest
431.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
400.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
345.0ms
(/ (- 1 (/ Om Omc)) (+ 1 (* 2 (* (/ t l) (/ t l)))))
324.0ms
(/ (* (* (- 1 (* (/ Om Omc) (/ Om Omc))) (- 1 (* (/ Om Omc) (/ Om Omc)))) (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (* (+ 1 (* 2 (* (/ t l) (/ t l)))) (+ 1 (* 2 (* (/ t l) (/ t l))))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
307.0ms
(sqrt (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))

prune2.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 8.3b

localize64.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
88×times-frac
85×add-sqr-sqrt
72×*-un-lft-identity
65×add-cube-cbrt sqrt-prod
18×add-cbrt-cube add-exp-log
14×difference-of-squares
13×swap-sqr associate-*r* associate-*l*
12×pow1
8×associate-/l*
6×associate-/r* sqrt-div
5×cbrt-undiv div-exp div-inv
4×prod-exp cbrt-unprod insert-posit16 add-log-exp unswap-sqr
2×flip3-+ associate-/r/ flip-+ associate-/l/
1×pow2 frac-times rem-sqrt-square asin-acos sqrt-undiv clear-num frac-2neg sqrt-pow1 pow-plus flip3-- pow1/2 pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip--
Counts
4 → 173
Calls
4 calls:
Slowest
23.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
13.0ms
(* (/ Om Omc) (/ Om Omc))
7.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
2.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

series283.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
156.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
80.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
36.0ms
(* (/ Om Omc) (/ Om Omc))
11.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify26.8s

Counts
210 → 185
Calls
210 calls:
Slowest
616.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
464.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
450.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
448.0ms
(/ (* (* (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (* (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
396.0ms
(sqrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)))

prune2.9s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 4.7b

regimes489.0ms

Accuracy

98.6% (0.1b remaining)

Error of 5.7b against oracle of 5.6b and baseline of 10.5b

bsearch10.0ms

end0.0ms

sample5.7s

Algorithm
intervals
Results
1.8s7919×body80nan
1.8s3793×body160valid
1.4s4207×body80valid