Details

Time bar (total: 7.6s)

analyze369.0ms (4.9%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
49.9%49.9%0.1%3
49.9%49.9%0.1%4
49.9%49.9%0.1%5
74.9%25%0.1%6
74.9%25%0.1%7
74.9%25%0.1%8
87.4%12.5%0.1%9
87.4%12.5%0.1%10
87.4%12.5%0.1%11
93.6%6.2%0.1%12
93.6%6.2%0.1%13
93.6%6.2%0.1%14
Compiler

Compiled 27 to 21 computations (22.2% saved)

sample94.0ms (1.2%)

Algorithm
intervals
Results
26.0ms29×body4096valid
22.0ms166×body128valid
17.0ms24×body2048valid
10.0ms19×body1024valid
7.0ms14×body512valid
1.0msbody256valid
Compiler

Compiled 56 to 44 computations (21.4% saved)

simplify65.0ms (0.9%)

Algorithm
egg-herbie
Rules
652×div-sub_binary64
554×fma-neg_binary64
550×hypot-def_binary64
431×fma-def_binary64
378×cancel-sign-sub-inv_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02036
14425
29625
326425
470625
5222325
6417525
7482525
8498325

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
16.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
16.1b
(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))
29.3b
(*.f64 180 (/.f64 (atan.f64 (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))) (PI.f64)))
Compiler

Compiled 132 to 91 computations (31.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))
0.0b
(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))
0.0b
(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
1.2b
(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))

series203.0ms (2.7%)

Counts
4 → 144
Calls

4 calls:

76.0ms
(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
62.0ms
(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))
37.0ms
(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))
27.0ms
(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))

rewrite40.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
81×*-un-lft-identity_binary64
71×add-sqr-sqrt_binary64
48×add-cube-cbrt_binary64
37×times-frac_binary64
24×prod-diff_binary64
Counts
4 → 161
Calls

4 calls:

9.0ms
(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
7.0ms
(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))
7.0ms
(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))
4.0ms
(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))

simplify153.0ms (2%)

Algorithm
egg-herbie
Rules
605×fma-def_binary64
355×associate-/l*_binary64
238×times-frac_binary64
205×sub-neg_binary64
198×associate-/r*_binary64
Counts
305 → 378
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
067410323
119509081
249719081

prune303.0ms (4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New3708378
Fresh101
Picked101
Done000
Total3728380
Error
0.5b
Counts
380 → 8
Alt Table
StatusErrorProgram
16.3b
(*.f64 180 (log.f64 (exp.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))))
55.2b
(*.f64 180 (/.f64 (atan.f64 (-.f64 (*.f64 1/2 (+.f64 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A)) (+.f64 (/.f64 (*.f64 B (*.f64 C C)) (pow.f64 A 3)) (/.f64 (*.f64 B (pow.f64 C 3)) (pow.f64 A 4))))) (fma.f64 1/8 (/.f64 (pow.f64 B 3) (pow.f64 A 3)) (*.f64 3/8 (/.f64 C (/.f64 (pow.f64 A 4) (pow.f64 B 3))))))) (PI.f64)))
42.2b
(*.f64 180 (/.f64 (atan.f64 (*.f64 -1/2 (+.f64 (/.f64 B C) (/.f64 A (/.f64 (*.f64 C C) B))))) (PI.f64)))
16.1b
(*.f64 180 (/.f64 (atan.f64 (*.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) (/.f64 1 B))) (PI.f64)))
41.7b
(*.f64 180 (/.f64 (atan.f64 (*.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A)))) (PI.f64)))
45.4b
(*.f64 180 (/.f64 (atan.f64 (*.f64 -1/2 (/.f64 B C))) (PI.f64)))
16.1b
(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
46.8b
(*.f64 180 (/.f64 (atan.f64 (/.f64 (*.f64 -1/2 (+.f64 (/.f64 (*.f64 B B) C) (/.f64 (*.f64 A (*.f64 B B)) (*.f64 C C)))) B)) (PI.f64)))
Compiler

Compiled 13486 to 5319 computations (60.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (atan.f64 (*.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) (/.f64 1 B))) (PI.f64))
0.0b
(*.f64 180 (/.f64 (atan.f64 (*.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) (/.f64 1 B))) (PI.f64)))
0.1b
(*.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) (/.f64 1 B))
1.2b
(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))

series144.0ms (1.9%)

Counts
3 → 108
Calls

3 calls:

77.0ms
(*.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) (/.f64 1 B))
39.0ms
(*.f64 180 (/.f64 (atan.f64 (*.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) (/.f64 1 B))) (PI.f64)))
27.0ms
(/.f64 (atan.f64 (*.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) (/.f64 1 B))) (PI.f64))

rewrite31.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt_binary64
33×*-un-lft-identity_binary64
30×times-frac_binary64
27×add-cube-cbrt_binary64
26×associate-*r*_binary64
Counts
3 → 108
Calls

3 calls:

10.0ms
(*.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) (/.f64 1 B))
7.0ms
(*.f64 180 (/.f64 (atan.f64 (*.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) (/.f64 1 B))) (PI.f64)))
4.0ms
(/.f64 (atan.f64 (*.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) (/.f64 1 B))) (PI.f64))

simplify155.0ms (2%)

Algorithm
egg-herbie
Rules
384×sub-neg_binary64
271×fma-neg_binary64
243×fma-def_binary64
211×*-commutative_binary64
197×+-commutative_binary64
Counts
216 → 249
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04346928
112326342
243616308
351986308

prune320.0ms (4.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New3842386
Fresh257
Picked011
Done000
Total3868394
Error
0.5b
Counts
394 → 8
Alt Table
StatusErrorProgram
16.3b
(*.f64 180 (log.f64 (exp.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))))
55.2b
(*.f64 180 (/.f64 (atan.f64 (-.f64 (*.f64 1/2 (+.f64 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A)) (+.f64 (/.f64 (*.f64 B (*.f64 C C)) (pow.f64 A 3)) (/.f64 (*.f64 B (pow.f64 C 3)) (pow.f64 A 4))))) (fma.f64 1/8 (/.f64 (pow.f64 B 3) (pow.f64 A 3)) (*.f64 3/8 (/.f64 C (/.f64 (pow.f64 A 4) (pow.f64 B 3))))))) (PI.f64)))
16.1b
(*.f64 180 (/.f64 (atan.f64 (*.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) (/.f64 1 B))) (PI.f64)))
41.7b
(*.f64 180 (/.f64 (atan.f64 (*.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A)))) (PI.f64)))
33.4b
(*.f64 180 (/.f64 (atan.f64 (-.f64 (/.f64 (-.f64 C (+.f64 A (sqrt.f64 (fma.f64 A A (*.f64 C (-.f64 C (*.f64 A 2))))))) B) (*.f64 1/2 (*.f64 B (sqrt.f64 (/.f64 1 (fma.f64 A A (*.f64 C (-.f64 C (*.f64 A 2)))))))))) (PI.f64)))
45.4b
(*.f64 180 (/.f64 (atan.f64 (*.f64 -1/2 (/.f64 B C))) (PI.f64)))
16.1b
(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
46.8b
(*.f64 180 (/.f64 (atan.f64 (*.f64 (*.f64 -1/2 (+.f64 (/.f64 (*.f64 B B) C) (/.f64 (*.f64 A (*.f64 B B)) (*.f64 C C)))) (/.f64 1 B))) (PI.f64)))
Compiler

Compiled 14220 to 6483 computations (54.4% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
0.0b
(*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)))
0.0b
(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
1.2b
(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))

series51.0ms (0.7%)

Counts
2 → 72
Calls

2 calls:

37.0ms
(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
14.0ms
(*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)))

rewrite13.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
Counts
2 → 43
Calls

2 calls:

5.0ms
(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
4.0ms
(*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)))

simplify183.0ms (2.4%)

Algorithm
egg-herbie
Rules
759×div-sub_binary64
446×sub-neg_binary64
354×unswap-sqr_binary64
332×*-commutative_binary64
298×fma-def_binary64
Counts
115 → 75
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0923008
11892775
25202775
317762775
421662775
526652775
635232775
739582775
843182775
949602775

prune304.0ms (4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New3343337
Fresh156
Picked011
Done011
Total33510345
Error
0.4b
Counts
345 → 10
Alt Table
StatusErrorProgram
33.4b
(*.f64 180 (/.f64 (atan.f64 (-.f64 (/.f64 (-.f64 C (+.f64 A (sqrt.f64 (fma.f64 A A (*.f64 C (-.f64 C (*.f64 A 2))))))) B) (*.f64 1/2 (*.f64 B (sqrt.f64 (/.f64 1 (fma.f64 A A (*.f64 C (-.f64 C (*.f64 A 2)))))))))) (PI.f64)))
45.3b
(/.f64 (*.f64 180 (atan.f64 (*.f64 -1/2 (/.f64 B C)))) (PI.f64))
16.1b
(*.f64 180 (/.f64 (atan.f64 (*.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) (/.f64 1 B))) (PI.f64)))
41.7b
(*.f64 180 (/.f64 (atan.f64 (*.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A)))) (PI.f64)))
16.3b
(*.f64 180 (log.f64 (exp.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))))
45.4b
(*.f64 180 (/.f64 (atan.f64 (*.f64 -1/2 (/.f64 B C))) (PI.f64)))
16.1b
(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
41.7b
(/.f64 (*.f64 180 (atan.f64 (*.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A))))) (PI.f64))
55.3b
(/.f64 (*.f64 180 (atan.f64 (-.f64 (*.f64 1/2 (+.f64 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A)) (+.f64 (/.f64 (*.f64 B (*.f64 C C)) (pow.f64 A 3)) (/.f64 (*.f64 B (pow.f64 C 3)) (pow.f64 A 4))))) (fma.f64 1/8 (/.f64 (pow.f64 B 3) (pow.f64 A 3)) (*.f64 3/8 (/.f64 C (/.f64 (pow.f64 A 4) (pow.f64 B 3)))))))) (PI.f64))
46.8b
(*.f64 180 (/.f64 (atan.f64 (*.f64 (*.f64 -1/2 (+.f64 (/.f64 (*.f64 B B) C) (/.f64 (*.f64 A (*.f64 B B)) (*.f64 C C)))) (/.f64 1 B))) (PI.f64)))
Compiler

Compiled 12080 to 5276 computations (56.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))
0.0b
(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
0.9b
(log.f64 (exp.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))))
1.2b
(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))

series33.0ms (0.4%)

Counts
1 → 36
Calls

1 calls:

32.0ms
(log.f64 (exp.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))))

rewrite8.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
14×log-pow_binary64
13×exp-prod_binary64
*-un-lft-identity_binary64
times-frac_binary64
add-sqr-sqrt_binary64
Counts
1 → 27
Calls

1 calls:

5.0ms
(log.f64 (exp.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))))

simplify122.0ms (1.6%)

Algorithm
egg-herbie
Rules
1081×fma-def_binary64
561×fma-neg_binary64
462×log-prod_binary64
380×associate-/l*_binary64
311×times-frac_binary64
Counts
63 → 51
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0841601
11191531
22231531
33831531
46441531
511301531
619851531
737501531
847291531
950501531

prune322.0ms (4.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New3660366
Fresh077
Picked011
Done022
Total36610376
Error
0.4b
Counts
376 → 10
Alt Table
StatusErrorProgram
33.4b
(*.f64 180 (/.f64 (atan.f64 (-.f64 (/.f64 (-.f64 C (+.f64 A (sqrt.f64 (fma.f64 A A (*.f64 C (-.f64 C (*.f64 A 2))))))) B) (*.f64 1/2 (*.f64 B (sqrt.f64 (/.f64 1 (fma.f64 A A (*.f64 C (-.f64 C (*.f64 A 2)))))))))) (PI.f64)))
45.3b
(/.f64 (*.f64 180 (atan.f64 (*.f64 -1/2 (/.f64 B C)))) (PI.f64))
16.1b
(*.f64 180 (/.f64 (atan.f64 (*.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) (/.f64 1 B))) (PI.f64)))
41.7b
(*.f64 180 (/.f64 (atan.f64 (*.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A)))) (PI.f64)))
16.3b
(*.f64 180 (log.f64 (exp.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))))
45.4b
(*.f64 180 (/.f64 (atan.f64 (*.f64 -1/2 (/.f64 B C))) (PI.f64)))
16.1b
(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
41.7b
(/.f64 (*.f64 180 (atan.f64 (*.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A))))) (PI.f64))
55.3b
(/.f64 (*.f64 180 (atan.f64 (-.f64 (*.f64 1/2 (+.f64 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A)) (+.f64 (/.f64 (*.f64 B (*.f64 C C)) (pow.f64 A 3)) (/.f64 (*.f64 B (pow.f64 C 3)) (pow.f64 A 4))))) (fma.f64 1/8 (/.f64 (pow.f64 B 3) (pow.f64 A 3)) (*.f64 3/8 (/.f64 C (/.f64 (pow.f64 A 4) (pow.f64 B 3)))))))) (PI.f64))
46.8b
(*.f64 180 (/.f64 (atan.f64 (*.f64 (*.f64 -1/2 (+.f64 (/.f64 (*.f64 B B) C) (/.f64 (*.f64 A (*.f64 B B)) (*.f64 C C)))) (/.f64 1 B))) (PI.f64)))
Compiler

Compiled 13738 to 5769 computations (58% saved)

regimes1.5s (19.6%)

Accuracy

Total 12.6b remaining (96.8%)

Threshold costs 0b (0%)

Counts
161 → 4
Compiler

Compiled 26658 to 18636 computations (30.1% saved)

bsearch230.0ms (3%)

Steps
ItersRangePoint
7
1.266325924470509e+219
1.7618398794577736e+221
1.2860608303654123e+219
8
1.6176075860910384e+152
9.502691513295511e+154
1.3262682172405047e+154
10
18.30133968785524
472933991005.21106
1116359.8079724736
Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (0.1%)

Algorithm
egg-herbie
Rules
20×*-commutative_binary64
17×+-commutative_binary64
16×sub-neg_binary64
10×neg-sub0_binary64
10×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
055142
185142
2114142
3138142
4152142
5158142
6160142
7157142

end1.0ms (0%)

Compiler

Compiled 95 to 62 computations (34.7% saved)

sample2.9s (38.3%)

Algorithm
intervals
Results
809.0ms865×body4096valid
676.0ms5506×body128valid
569.0ms816×body2048valid
241.0ms446×body1024valid
91.0ms237×body512valid
33.0ms130×body256valid
Compiler

Compiled 388 to 270 computations (30.4% saved)

Profiling

Loading profile data...