Toniolo and Linder, Equation (2)

Time bar (total: 7.3s)

analyze410.0ms (5.6%)

Memory
5.3MiB live, 154.4MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.8%0.2%0%0%0%0
0%0%99.8%0.2%0%0%0%1
0%0%99.8%0.2%0%0%0%2
0%0%99.8%0.2%0%0%0%3
0%0%99.8%0.2%0%0%0%4
0%0%99.8%0.2%0%0%0%5
0%0%99.8%0.2%0%0%0%6
0%0%99.8%0.2%0%0%0%7
0%0%99.8%0.2%0%0%0%8
19.2%18.7%78.8%0.2%0%2.3%0%9
19.4%18.7%77.6%0.2%0%3.5%0%10
22.8%21.8%73.9%0.2%0%4.1%0%11
23.3%21.8%71.8%0.2%0%6.1%0%12
Compiler

Compiled 45 to 35 computations (22.2% saved)

sample6.7s (92.3%)

Memory
62.5MiB live, 2 039.6MiB allocated
Samples
933.0ms3 910×146valid-baseline
846.0ms3 910×146valid-rival
564.0ms3 910×146valid-sollya
500.0ms4 344×73valid-baseline
439.0ms4 344×73valid-sollya
426.0ms4 344×73valid-rival
0.0ms146valid-rival+baseline-real
0.0ms73valid-rival+sollya-real
Precisions
Click to see Rival histograms. Total time spent on operations: 1.5s
ival-pow: 461.0ms (29.8% of total)
ival-div: 401.0ms (25.9% of total)
ival-asin: 155.0ms (10% of total)
ival-sqrt: 129.0ms (8.3% of total)
ival-mult: 113.0ms (7.3% of total)
ival-sub: 88.0ms (5.7% of total)
ival-add: 87.0ms (5.6% of total)
adjust: 78.0ms (5% of total)
ival-true: 14.0ms (0.9% of total)
...in/eval/compile.rkt:110:19: 13.0ms (0.8% of total)
ival-assert: 6.0ms (0.4% of total)
Precisions
Click to see Base histograms. Total time spent on operations: 1.5s
ival-pow: 465.0ms (30.9% of total)
ival-div: 410.0ms (27.2% of total)
ival-asin: 164.0ms (10.9% of total)
ival-sqrt: 127.0ms (8.4% of total)
ival-mult: 115.0ms (7.6% of total)
ival-sub: 101.0ms (6.7% of total)
ival-add: 92.0ms (6.1% of total)
const: 32.0ms (2.1% of total)
Bogosity

preprocess116.0ms (1.6%)

Memory
10.2MiB live, 25.6MiB allocated
Algorithm
egg-herbie
Rules
633×div-sub
576×fma-define
474×unsub-neg
379×fmm-def
351×distribute-lft-neg-in
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01071136
12081056
24271056
311111056
431471056
568101056
Stop Event
node limit
Calls
Call 1
Inputs
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 (neg.f64 t) l) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t (neg.f64 l)) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (neg.f64 Om) Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om (neg.f64 Omc)) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 (neg.f64 t) l) #s(literal 2 binary64))))))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t (neg.f64 l)) #s(literal 2 binary64))))))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (neg.f64 Om) Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64))))))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om (neg.f64 Omc)) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64))))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 l t) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 t Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 Om l) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om t) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 Omc l) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 l Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t Om) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om l) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t Omc) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Omc Om) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))
Outputs
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (fma.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (fma.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 (neg.f64 t) l) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (fma.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t (neg.f64 l)) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (fma.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (neg.f64 Om) Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (fma.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om (neg.f64 Omc)) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (fma.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 (neg.f64 t) l) #s(literal 2 binary64))))))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t (neg.f64 l)) #s(literal 2 binary64))))))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (fma.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)) #s(literal 1 binary64))))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t (neg.f64 l)) #s(literal 2 binary64))))))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (fma.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)) #s(literal 1 binary64))))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (neg.f64 Om) Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64))))))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t (neg.f64 l)) #s(literal 2 binary64))))))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (fma.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)) #s(literal 1 binary64))))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om (neg.f64 Omc)) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64))))))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t (neg.f64 l)) #s(literal 2 binary64))))))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (fma.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)) #s(literal 1 binary64))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 l t) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (fma.f64 #s(literal 2 binary64) (pow.f64 (/.f64 l t) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 t Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 Om l) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 t Omc) #s(literal 2 binary64))) (fma.f64 #s(literal 2 binary64) (pow.f64 (/.f64 Om l) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om t) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 Omc l) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om t) #s(literal 2 binary64))) (fma.f64 #s(literal 2 binary64) (pow.f64 (/.f64 Omc l) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 l Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t Om) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 l Omc) #s(literal 2 binary64))) (fma.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t Om) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om l) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t Omc) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om l) #s(literal 2 binary64))) (fma.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t Omc) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Omc Om) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Omc Om) #s(literal 2 binary64))) (fma.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)) #s(literal 1 binary64)))))
Symmetry

(abs t)

(abs l)

(abs Om)

(abs Omc)

Compiler

Compiled 23 to 16 computations (30.4% saved)

eval0.0ms (0%)

Memory
0.2MiB live, 0.2MiB allocated
Compiler

Compiled 4 to 4 computations (0% saved)

prune1.0ms (0%)

Memory
-14.8MiB live, 1.0MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
83.4%
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))
Compiler

Compiled 46 to 32 computations (30.4% saved)

simplify2.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Algorithm
egg-herbie
Rules
1-exp
+-commutative
sub-neg
*-commutative
neg-sub0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02469
13369
23769
33969
44069
Stop Event
saturated
Calls
Call 1
Inputs
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))
Outputs
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))

soundness0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Stop Event
fuel
Compiler

Compiled 23 to 16 computations (30.4% saved)

preprocess28.0ms (0.4%)

Memory
15.2MiB live, 30.9MiB allocated
Remove

(abs Omc)

(abs Om)

(abs l)

(abs t)

Compiler

Compiled 460 to 320 computations (30.4% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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