Details

Time bar (total: 7.8s)

analyze321.0ms (4.1%)

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)

sample3.9s (50.2%)

Results
1.2s908×body4096valid
1.2s5542×body128valid
896.0ms876×body2048valid
385.0ms505×body1024valid
158.0ms269×body512valid
65.0ms156×body256valid
Compiler

Compiled 80 to 62 computations (22.5% saved)

simplify64.0ms (0.8%)

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
12.7b
Counts
3 → 2
Alt Table
StatusErrorProgram
30.1b
(*.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)))
12.8b
(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (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 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
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))
1.1b
(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))

series194.0ms (2.5%)

Counts
4 → 144
Calls

4 calls:

72.0ms
(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
61.0ms
(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))
35.0ms
(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))
26.0ms
(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))

rewrite47.0ms (0.6%)

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:

12.0ms
(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
10.0ms
(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))
7.0ms
(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))
4.0ms
(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))

simplify151.0ms (1.9%)

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

prune262.0ms (3.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New3717378
Fresh101
Picked101
Done000
Total3737380
Error
0.3b
Counts
380 → 7
Alt Table
StatusErrorProgram
47.4b
(*.f64 180 (/.f64 (atan.f64 (*.f64 -1/2 (/.f64 B C))) (PI.f64)))
48.5b
(*.f64 180 (/.f64 (atan.f64 (/.f64 (*.f64 -1/2 (/.f64 (pow.f64 B 2) C)) B)) (PI.f64)))
46.2b
(*.f64 180 (/.f64 (atan.f64 (*.f64 1/2 (/.f64 B A))) (PI.f64)))
12.8b
(*.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)) 180)
12.8b
(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
13.1b
(*.f64 180 (log.f64 (exp.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))))
52.1b
(*.f64 180 (/.f64 (atan.f64 (/.f64 (+.f64 (fma.f64 (sqrt.f64 (-.f64 C A)) (sqrt.f64 (-.f64 C A)) (neg.f64 (*.f64 (cbrt.f64 (hypot.f64 B (-.f64 C A))) (*.f64 (cbrt.f64 (hypot.f64 B (-.f64 C A))) (cbrt.f64 (hypot.f64 B (-.f64 C A))))))) (fma.f64 (neg.f64 (cbrt.f64 (hypot.f64 B (-.f64 C A)))) (*.f64 (cbrt.f64 (hypot.f64 B (-.f64 C A))) (cbrt.f64 (hypot.f64 B (-.f64 C A)))) (*.f64 (cbrt.f64 (hypot.f64 B (-.f64 C A))) (*.f64 (cbrt.f64 (hypot.f64 B (-.f64 C A))) (cbrt.f64 (hypot.f64 B (-.f64 C A))))))) B)) (PI.f64)))
Compiler

Compiled 13444 to 5223 computations (61.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
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)
0.0b
(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
1.1b
(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))

series49.0ms (0.6%)

Counts
2 → 72
Calls

2 calls:

36.0ms
(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
13.0ms
(*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)))

rewrite12.0ms (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:

6.0ms
(/.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)))

simplify184.0ms (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

prune267.0ms (3.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New3343337
Fresh156
Picked011
Done000
Total3359344
Error
0.3b
Counts
344 → 9
Alt Table
StatusErrorProgram
13.1b
(*.f64 180 (log.f64 (exp.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))))
44.4b
(/.f64 (*.f64 180 (atan.f64 (*.f64 -1/2 (+.f64 (/.f64 B C) (/.f64 A (/.f64 (*.f64 C C) B)))))) (PI.f64))
46.2b
(*.f64 180 (/.f64 (atan.f64 (*.f64 1/2 (/.f64 B A))) (PI.f64)))
43.3b
(/.f64 (*.f64 180 (atan.f64 (*.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A))))) (PI.f64))
47.4b
(*.f64 180 (/.f64 (atan.f64 (*.f64 -1/2 (/.f64 B C))) (PI.f64)))
12.8b
(*.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)) 180)
12.8b
(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
52.1b
(*.f64 180 (/.f64 (atan.f64 (/.f64 (+.f64 (fma.f64 (sqrt.f64 (-.f64 C A)) (sqrt.f64 (-.f64 C A)) (neg.f64 (*.f64 (cbrt.f64 (hypot.f64 B (-.f64 C A))) (*.f64 (cbrt.f64 (hypot.f64 B (-.f64 C A))) (cbrt.f64 (hypot.f64 B (-.f64 C A))))))) (fma.f64 (neg.f64 (cbrt.f64 (hypot.f64 B (-.f64 C A)))) (*.f64 (cbrt.f64 (hypot.f64 B (-.f64 C A))) (cbrt.f64 (hypot.f64 B (-.f64 C A)))) (*.f64 (cbrt.f64 (hypot.f64 B (-.f64 C A))) (*.f64 (cbrt.f64 (hypot.f64 B (-.f64 C A))) (cbrt.f64 (hypot.f64 B (-.f64 C A))))))) B)) (PI.f64)))
48.7b
(/.f64 (*.f64 180 (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 12047 to 5176 computations (57% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
0.0b
(*.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)) 180)
0.0b
(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))
1.1b
(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))

series36.0ms (0.5%)

Counts
1 → 36
Calls

1 calls:

36.0ms
(*.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)) 180)

rewrite9.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt_binary64
13×associate-*l*_binary64
10×times-frac_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
Counts
1 → 34
Calls

1 calls:

6.0ms
(*.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)) 180)

simplify183.0ms (2.3%)

Algorithm
egg-herbie
Rules
684×fma-def_binary64
681×fma-neg_binary64
450×fabs-mul_binary64
445×associate-*l/_binary64
445×associate-/l*_binary64
Counts
70 → 61
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0912007
11931863
24481863
310321863
423501863
527551863
632611863
738421863
844511863
948601863
1049541863
1151041863

prune291.0ms (3.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New3760376
Fresh077
Picked011
Done011
Total3769385
Error
0.3b
Counts
385 → 9
Alt Table
StatusErrorProgram
13.1b
(*.f64 180 (log.f64 (exp.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))))
44.4b
(/.f64 (*.f64 180 (atan.f64 (*.f64 -1/2 (+.f64 (/.f64 B C) (/.f64 A (/.f64 (*.f64 C C) B)))))) (PI.f64))
46.2b
(*.f64 180 (/.f64 (atan.f64 (*.f64 1/2 (/.f64 B A))) (PI.f64)))
43.3b
(/.f64 (*.f64 180 (atan.f64 (*.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A))))) (PI.f64))
47.4b
(*.f64 180 (/.f64 (atan.f64 (*.f64 -1/2 (/.f64 B C))) (PI.f64)))
12.8b
(*.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)) 180)
12.8b
(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
52.1b
(*.f64 180 (/.f64 (atan.f64 (/.f64 (+.f64 (fma.f64 (sqrt.f64 (-.f64 C A)) (sqrt.f64 (-.f64 C A)) (neg.f64 (*.f64 (cbrt.f64 (hypot.f64 B (-.f64 C A))) (*.f64 (cbrt.f64 (hypot.f64 B (-.f64 C A))) (cbrt.f64 (hypot.f64 B (-.f64 C A))))))) (fma.f64 (neg.f64 (cbrt.f64 (hypot.f64 B (-.f64 C A)))) (*.f64 (cbrt.f64 (hypot.f64 B (-.f64 C A))) (cbrt.f64 (hypot.f64 B (-.f64 C A)))) (*.f64 (cbrt.f64 (hypot.f64 B (-.f64 C A))) (*.f64 (cbrt.f64 (hypot.f64 B (-.f64 C A))) (cbrt.f64 (hypot.f64 B (-.f64 C A))))))) B)) (PI.f64)))
48.7b
(/.f64 (*.f64 180 (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 13484 to 5269 computations (60.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 180 (log.f64 (exp.f64 (/.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))
1.1b
(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))
1.3b
(log.f64 (exp.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))))

series70.0ms (0.9%)

Counts
2 → 72
Calls

2 calls:

38.0ms
(*.f64 180 (log.f64 (exp.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))))
31.0ms
(log.f64 (exp.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))))

rewrite22.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
28×log-pow_binary64
26×exp-prod_binary64
23×add-sqr-sqrt_binary64
21×*-un-lft-identity_binary64
21×add-cube-cbrt_binary64
Counts
2 → 67
Calls

2 calls:

9.0ms
(*.f64 180 (log.f64 (exp.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))))
5.0ms
(log.f64 (exp.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))))

simplify270.0ms (3.5%)

Algorithm
egg-herbie
Rules
801×fma-def_binary64
532×associate-/r*_binary64
506×fma-neg_binary64
402×associate-/r/_binary64
234×associate-*l/_binary64
Counts
139 → 122
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01413858
12193642
24173636
37663636
417143636
528353636
636473636
744933636
849623636
950253636

prune230.0ms (3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New3111312
Fresh156
Picked011
Done022
Total3129321
Error
0.3b
Counts
321 → 9
Alt Table
StatusErrorProgram
13.1b
(*.f64 180 (log.f64 (exp.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))))
44.4b
(/.f64 (*.f64 180 (atan.f64 (*.f64 -1/2 (+.f64 (/.f64 B C) (/.f64 A (/.f64 (*.f64 C C) B)))))) (PI.f64))
52.1b
(*.f64 180 (log.f64 (exp.f64 (/.f64 (atan.f64 (/.f64 (+.f64 (fma.f64 (sqrt.f64 (-.f64 C A)) (sqrt.f64 (-.f64 C A)) (neg.f64 (*.f64 (cbrt.f64 (hypot.f64 B (-.f64 C A))) (*.f64 (cbrt.f64 (hypot.f64 B (-.f64 C A))) (cbrt.f64 (hypot.f64 B (-.f64 C A))))))) (fma.f64 (neg.f64 (cbrt.f64 (hypot.f64 B (-.f64 C A)))) (*.f64 (cbrt.f64 (hypot.f64 B (-.f64 C A))) (cbrt.f64 (hypot.f64 B (-.f64 C A)))) (*.f64 (cbrt.f64 (hypot.f64 B (-.f64 C A))) (*.f64 (cbrt.f64 (hypot.f64 B (-.f64 C A))) (cbrt.f64 (hypot.f64 B (-.f64 C A))))))) B)) (PI.f64)))))
46.2b
(*.f64 180 (/.f64 (atan.f64 (*.f64 1/2 (/.f64 B A))) (PI.f64)))
43.3b
(/.f64 (*.f64 180 (atan.f64 (*.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A))))) (PI.f64))
47.4b
(*.f64 180 (/.f64 (atan.f64 (*.f64 -1/2 (/.f64 B C))) (PI.f64)))
12.8b
(*.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)) 180)
12.8b
(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
48.7b
(/.f64 (*.f64 180 (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 11124 to 3756 computations (66.2% saved)

regimes941.0ms (12.1%)

Accuracy

Total 11.9b remaining (97.2%)

Threshold costs 0b (0%)

Counts
111 → 2
Compiler

Compiled 16431 to 11839 computations (27.9% saved)

bsearch90.0ms (1.2%)

Steps
ItersRangePoint
8
-7.021718204400751e+65
-8.376081796597673e+61
-6.914447845681458e+65
Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02759
13559
24359
34759
44959
54959

end141.0ms (1.8%)

Compiler

Compiled 320 to 181 computations (43.4% saved)

Profiling

Loading profile data...