Metrics for Migdal et al, Equation (64)

analyze15.0ms (0.4%)

Memory

4.5MiB live, 4.5MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 44 to 27 computations (38.6% saved)

sample3.1s (93.1%)

Memory

14.0MiB live, 949.9MiB allocated

Samples

777.0ms	8 256×	valid-baseline
727.0ms	8 256×	valid-rival
631.0ms	8 256×	valid-sollya

Precisions

Click to see Rival histograms. Total time spent on operations: 508.0ms

ival-cos: 179.0ms (35.2% of total)

ival-mult: 178.0ms (35% of total)

ival-sqrt: 54.0ms (10.6% of total)

ival-div: 49.0ms (9.6% of total)

ival-add: 33.0ms (6.5% of total)

ival-true: 7.0ms (1.4% of total)

...in/eval/compile.rkt:110:19: 4.0ms (0.8% of total)

ival-assert: 3.0ms (0.6% of total)

Precisions

Click to see Base histograms. Total time spent on operations: 502.0ms

ival-mult: 184.0ms (36.6% of total)

ival-cos: 165.0ms (32.9% of total)

ival-sqrt: 55.0ms (11% of total)

ival-div: 50.0ms (10% of total)

ival-add: 36.0ms (7.2% of total)

const: 11.0ms (2.2% of total)

Bogosity

preprocess180.0ms (5.3%)

Memory

8.9MiB live, 24.8MiB allocated

Algorithm

1×	egg-herbie

Rules

1 241×	`fma-define`
680×	`times-frac`
547×	`fmm-def`
457×	`div-sub`
352×	`associate-/r*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	606
1	145	562
2	421	562
3	1139	562
4	2837	562
5	5637	562
6	6570	562
7	7382	562
8	7458	562
9	7474	562

Stop Event

1×	node limit

Calls

Call 1

Inputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (neg.f64 a1) (neg.f64 a1))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (neg.f64 a2) (neg.f64 a2))))
(+.f64 (.f64 (/.f64 (cos.f64 (neg.f64 th)) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 (neg.f64 th)) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
(neg.f64 (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (neg.f64 a1) (neg.f64 a1))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))))
(neg.f64 (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (neg.f64 a2) (neg.f64 a2)))))
(neg.f64 (+.f64 (.f64 (/.f64 (cos.f64 (neg.f64 th)) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 (neg.f64 th)) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)))
(+.f64 (.f64 (/.f64 (cos.f64 a1) (sqrt.f64 #s(literal 2 binary64))) (.f64 th th)) (.f64 (/.f64 (cos.f64 a1) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
(+.f64 (.f64 (/.f64 (cos.f64 a2) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 a2) (sqrt.f64 #s(literal 2 binary64))) (.f64 th th)))

Outputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (neg.f64 a1) (neg.f64 a1))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (neg.f64 a2) (neg.f64 a2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (.f64 (/.f64 (cos.f64 (neg.f64 th)) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 (neg.f64 th)) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(neg.f64 (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (neg.f64 a1) (neg.f64 a1))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))))
(neg.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (fma.f64 a1 a1 (.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(neg.f64 (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 (neg.f64 a2) (neg.f64 a2)))))
(neg.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (fma.f64 a1 a1 (.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(neg.f64 (+.f64 (.f64 (/.f64 (cos.f64 (neg.f64 th)) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 (neg.f64 th)) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2))))
(neg.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (fma.f64 a1 a1 (.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (.f64 (/.f64 (cos.f64 a1) (sqrt.f64 #s(literal 2 binary64))) (.f64 th th)) (.f64 (/.f64 (cos.f64 a1) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 a1) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (.f64 th th) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 a1) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 th th (.f64 a2 a2)))
(.f64 (cos.f64 a1) (/.f64 (fma.f64 th th (.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (.f64 (/.f64 (cos.f64 a2) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 a2) (sqrt.f64 #s(literal 2 binary64))) (.f64 th th)))
(.f64 (/.f64 (cos.f64 a2) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (.f64 a1 a1) (*.f64 th th)))
(.f64 (/.f64 (cos.f64 a2) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (.f64 th th)))
(.f64 (cos.f64 a2) (/.f64 (fma.f64 th th (.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))

Symmetry

(abs a1)

(abs a2)

(abs th)

(sort a1 a2)

Compiler

Compiled 22 to 12 computations (45.5% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))

Compiler

Compiled 44 to 24 computations (45.5% saved)

simplify2.0ms (0.1%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative`
1×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	77
1	22	77

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))

Outputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (.f64 a2 a2)))

soundness0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Stop Event

1×

fuel

Compiler

Compiled 22 to 12 computations (45.5% saved)

preprocess36.0ms (1.1%)

Memory

-2.2MiB live, 32.0MiB allocated

Remove

(sort a1 a2)

(abs th)

(abs a2)

(abs a1)

Compiler

Compiled 440 to 240 computations (45.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze15.0ms (0.4%)

sample3.1s (93.1%)

preprocess180.0ms (5.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify2.0ms (0.1%)

soundness0.0ms (0%)

preprocess36.0ms (1.1%)

end0.0ms (0%)

Profiling