Details

Time bar (total: 15.8s)

analyze336.0ms (2.1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%50%50%2
0%50%50%3
0%50%50%4
12.5%37.5%50%5
15.6%31.2%53.2%6
17.2%25%57.9%7
18%20.3%61.8%8
18.3%16.4%65.3%9
18.5%13.7%67.8%10
18.6%11.5%69.9%11
18.7%10%71.3%12
18.7%8.9%72.4%13
18.7%8.2%73.1%14
Compiler

Compiled 19 to 16 computations (15.8% saved)

sample3.1s (19.7%)

Results
1.3s8256×body128valid
1.1s1413×body1024invalid
362.0ms666×body512invalid
182.0ms1143×body128invalid
110.0ms343×body256invalid
Compiler

Compiled 56 to 47 computations (16.1% saved)

simplify52.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
672×associate-/l*_binary64
625×associate-/r*_binary64
461×div-sub_binary64
445×distribute-frac-neg_binary64
288×distribute-rgt-neg-out_binary64
Counts
1 → 2
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01425
13222
26522
312922
428022
563420
6133220
7312120
8491420
9455020

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.4b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.5b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶0.5b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
Compiler

Compiled 97 to 77 computations (20.6% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.3b
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
✓0.3b
(*.f64 (*.f64 2 (PI.f64)) n)
✓0.3b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

series517.0ms (3.3%)

Counts
3 → 48
Calls

3 calls:

275.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
238.0ms
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
3.0ms
(*.f64 (*.f64 2 (PI.f64)) n)

rewrite22.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
36×times-frac_binary64
26×*-un-lft-identity_binary64
26×add-sqr-sqrt_binary64
26×add-cube-cbrt_binary64
26×add-exp-log_binary64
Counts
3 → 108
Calls

3 calls:

8.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
4.0ms
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
4.0ms
(*.f64 (*.f64 2 (PI.f64)) n)

simplify132.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
405×distribute-rgt-in_binary64
399×distribute-lft-in_binary64
243×fma-neg_binary64
211×associate-/l*_binary64
162×associate-*l*_binary64
Counts
156 → 168
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02134057
14283712
213903636
345063636
449603636

prune208.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1608168
Fresh101
Picked101
Done000
Total1628170
Error
0b
Counts
170 → 8
Alt Table
StatusErrorProgram
▶0.4b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
1.2b
(*.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))) (/.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
0.6b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))
0.7b
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
3.8b
(exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
0.5b
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
16.9b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (-.f64 (fma.f64 1/8 (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2))) (sqrt.f64 2)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3))))))) (sqrt.f64 k))
0.6b
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
Compiler

Compiled 4379 to 2870 computations (34.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
✓0.3b
(*.f64 n (*.f64 2 (PI.f64)))
0.3b
(*.f64 (*.f64 2 (PI.f64)) n)
✓0.3b
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))

series117.0ms (0.7%)

Counts
3 → 12
Calls

3 calls:

79.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
34.0ms
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))
3.0ms
(*.f64 n (*.f64 2 (PI.f64)))

rewrite60.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
308×times-frac_binary64
140×*-un-lft-identity_binary64
140×add-sqr-sqrt_binary64
140×add-cube-cbrt_binary64
130×sqrt-prod_binary64
Counts
3 → 267
Calls

3 calls:

14.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
6.0ms
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))
4.0ms
(*.f64 n (*.f64 2 (PI.f64)))

simplify366.0ms (2.3%)

Algorithm
1×egg-herbie
Rules
725×associate-/r*_binary64
365×fma-neg_binary64
297×associate-/r/_binary64
237×associate-/l/_binary64
218×*-commutative_binary64
Counts
279 → 383
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
036512747
173512412
2260312184
3340512184
4487812184
5515612184

prune560.0ms (3.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New4083411
Fresh347
Picked011
Done000
Total4118419
Error
0b
Counts
419 → 8
Alt Table
StatusErrorProgram
0.6b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))
✓0.4b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
0.5b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (*.f64 (/.f64 1 (sqrt.f64 n)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (PI.f64))))))
▶0.3b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k -1/2)) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 n (*.f64 k -1/2))))
0.4b
(/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (sqrt.f64 k)) (/.f64 1 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
0.5b
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
16.9b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (-.f64 (fma.f64 1/8 (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2))) (sqrt.f64 2)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3))))))) (sqrt.f64 k))
0.6b
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
Compiler

Compiled 14477 to 8897 computations (38.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))
✓0.2b
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k -1/2)) (sqrt.f64 k))
✓0.3b
(*.f64 n (PI.f64))
✓0.3b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k -1/2)) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 n (*.f64 k -1/2))))

series156.0ms (1%)

Counts
4 → 0
Calls

4 calls:

117.0ms
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k -1/2)) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 n (*.f64 k -1/2))))
23.0ms
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k -1/2)) (sqrt.f64 k))
11.0ms
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))
4.0ms
(*.f64 n (PI.f64))

rewrite41.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
80×add-exp-log_binary64
60×times-frac_binary64
44×add-sqr-sqrt_binary64
42×*-un-lft-identity_binary64
42×add-cube-cbrt_binary64
Counts
4 → 163
Calls

4 calls:

14.0ms
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k -1/2)) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 n (*.f64 k -1/2))))
5.0ms
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k -1/2)) (sqrt.f64 k))
3.0ms
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))
3.0ms
(*.f64 n (PI.f64))

simplify170.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
521×associate-/l*_binary64
518×*-commutative_binary64
500×associate-*l/_binary64
326×associate-*r/_binary64
260×fma-neg_binary64
Counts
163 → 211
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02044980
14384607
213834531
340774531
448694531
549674531

prune307.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2101211
Fresh156
Picked011
Done101
Total2127219
Error
0b
Counts
219 → 7
Alt Table
StatusErrorProgram
0.6b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))
0.5b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (*.f64 (/.f64 1 (sqrt.f64 n)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (PI.f64))))))
✓0.3b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k -1/2)) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 n (*.f64 k -1/2))))
▶0.4b
(/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (sqrt.f64 k)) (/.f64 1 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
0.5b
(*.f64 (sqrt.f64 (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k -1/2)) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 n (*.f64 k -1/2))))) (sqrt.f64 (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k -1/2)) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 n (*.f64 k -1/2))))))
16.9b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (-.f64 (fma.f64 1/8 (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2))) (sqrt.f64 2)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3))))))) (sqrt.f64 k))
0.6b
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
Compiler

Compiled 7543 to 4738 computations (37.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (sqrt.f64 k)) (/.f64 1 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
✓0.2b
(/.f64 1 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))
0.3b
(*.f64 n (*.f64 2 (PI.f64)))
0.3b
(*.f64 (*.f64 2 (PI.f64)) n)

series98.0ms (0.6%)

Counts
2 → 0
Calls

2 calls:

82.0ms
(/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (sqrt.f64 k)) (/.f64 1 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
16.0ms
(/.f64 1 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))

rewrite190.0ms (1.2%)

Algorithm
1×rewrite-expression-head
Rules
1486×times-frac_binary64
580×*-un-lft-identity_binary64
580×add-sqr-sqrt_binary64
580×add-cube-cbrt_binary64
364×sqrt-prod_binary64
Counts
2 → 677
Calls

2 calls:

26.0ms
(/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (sqrt.f64 k)) (/.f64 1 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
5.0ms
(/.f64 1 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))

simplify1.1s (6.8%)

Algorithm
1×egg-herbie
Rules
594×associate-/l/_binary64
478×fma-neg_binary64
339×associate-/r/_binary64
298×associate-/r*_binary64
292×associate-*l/_binary64
Counts
677 → 727
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
046140876
1114539211
2358238371
3332638367
4487438367
5522938367

prune1.3s (8.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New7832785
Fresh235
Picked011
Done011
Total7857792
Error
0b
Counts
792 → 7
Alt Table
StatusErrorProgram
✓0.3b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k -1/2)) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 n (*.f64 k -1/2))))
✓0.4b
(/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (sqrt.f64 k)) (/.f64 1 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
0.4b
(/.f64 1 (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 -1/2 k))))
0.4b
(/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (sqrt.f64 k)) (*.f64 (/.f64 1 (sqrt.f64 n)) (/.f64 1 (sqrt.f64 (*.f64 2 (PI.f64))))))
0.5b
(*.f64 (sqrt.f64 (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k -1/2)) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 n (*.f64 k -1/2))))) (sqrt.f64 (*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k -1/2)) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 n (*.f64 k -1/2))))))
16.9b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (-.f64 (fma.f64 1/8 (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2))) (sqrt.f64 2)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3))))))) (sqrt.f64 k))
0.6b
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
Compiler

Compiled 33357 to 22767 computations (31.7% saved)

regimes6.8s (42.8%)

Accuracy

Total 0.5b remaining (93.6%)

Threshold costs 0.5b (93.6%)

Counts
828 → 1
Compiler

Compiled 124368 to 92738 computations (25.4% saved)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Rules
3×*-commutative_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01932
12332
22032

end164.0ms (1%)

Compiler

Compiled 270 to 208 computations (23% saved)

Profiling

Loading profile data...