Details

Time bar (total: 6.2s)

analyze315.0ms (5.1%)

Algorithm
1×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)

sample3.8s (62.3%)

Results
1.2s895×body4096valid
1.1s5578×body128valid
875.0ms876×body2048valid
412.0ms508×body1024valid
154.0ms275×body512valid
46.0ms124×body256valid
Compiler

Compiled 80 to 62 computations (22.5% saved)

simplify25.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
554×fma-neg_binary64
423×fma-def_binary64
380×cancel-sign-sub-inv_binary64
305×div-sub_binary64
227×unsub-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02036
14425
210925
329625
496025
5345725
Stop Event
1×node limit
Counts
1 → 2

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
12.3b
Counts
3 → 2
Alt Table
StatusErrorProgram
▶12.3b
(*.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 A C))) B)) (/.f64 180 (PI.f64)))
28.9b
(*.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 93 computations (29.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 A C))) B))
✓0.0b
(hypot.f64 B (-.f64 A C))
✓0.0b
(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 A C))) B)
✓0.9b
(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 A C)))

series143.0ms (2.3%)

Counts
4 → 144
Calls

4 calls:

59.0ms
(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 A C))) B)
44.0ms
(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 A C)))
35.0ms
(hypot.f64 B (-.f64 A C))
5.0ms
(atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 A C))) B))

rewrite73.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
571×fma-def_binary64
319×fma-neg_binary64
234×expm1-udef_binary64
234×log1p-udef_binary64
186×egg-rr
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01054
124054
2379954
Stop Event
1×node limit
Counts
4 → 186
Calls

4 calls:

68.0ms
(atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 A C))) B))
68.0ms
(hypot.f64 B (-.f64 A C))
68.0ms
(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 A C))) B)
68.0ms
(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 A C)))

simplify78.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
614×fma-def_binary64
261×associate-/l*_binary64
229×sub-neg_binary64
221×times-frac_binary64
184×+-commutative_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
05436279
119705655
Stop Event
1×node limit
Counts
330 → 380

prune296.0ms (4.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New3764380
Fresh101
Picked011
Done000
Total3775382
Error
0.1b
Counts
382 → 5
Alt Table
StatusErrorProgram
50.1b
(*.f64 (atan.f64 (/.f64 (*.f64 1/2 (/.f64 (pow.f64 B 2) A)) B)) (/.f64 180 (PI.f64)))
✓12.3b
(*.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 A C))) B)) (/.f64 180 (PI.f64)))
49.0b
(*.f64 (atan.f64 (*.f64 1/2 (/.f64 B A))) (/.f64 180 (PI.f64)))
49.9b
(*.f64 (atan.f64 (/.f64 (*.f64 -1/2 (/.f64 (pow.f64 B 2) C)) B)) (/.f64 180 (PI.f64)))
▶48.9b
(*.f64 (atan.f64 (*.f64 -1/2 (/.f64 B C))) (/.f64 180 (PI.f64)))
Compiler

Compiled 13848 to 7025 computations (49.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(atan.f64 (*.f64 -1/2 (/.f64 B C)))
✓0.1b
(*.f64 (atan.f64 (*.f64 -1/2 (/.f64 B C))) (/.f64 180 (PI.f64)))

series21.0ms (0.3%)

Counts
2 → 24
Calls

2 calls:

18.0ms
(*.f64 (atan.f64 (*.f64 -1/2 (/.f64 B C))) (/.f64 180 (PI.f64)))
3.0ms
(atan.f64 (*.f64 -1/2 (/.f64 B C)))

rewrite45.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
570×log-prod_binary64
212×expm1-udef_binary64
212×log1p-udef_binary64
184×log-pow_binary64
120×log-div_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01125
123525
2295225
Stop Event
1×node limit
Counts
2 → 48
Calls

2 calls:

44.0ms
(atan.f64 (*.f64 -1/2 (/.f64 B C)))
44.0ms
(*.f64 (atan.f64 (*.f64 -1/2 (/.f64 B C))) (/.f64 180 (PI.f64)))

simplify15.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
6×*-commutative_binary64
4×associate-/l*_binary64
2×associate-*r/_binary64
2×associate-*l/_binary64
2×associate-/r/_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
011384
117384
225384
333384
435384
Stop Event
1×saturated
Counts
72 → 50

prune33.0ms (0.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New46450
Fresh123
Picked011
Done011
Total47855
Error
0.1b
Counts
55 → 8
Alt Table
StatusErrorProgram
50.1b
(*.f64 (atan.f64 (/.f64 (*.f64 1/2 (/.f64 (pow.f64 B 2) A)) B)) (/.f64 180 (PI.f64)))
✓12.3b
(*.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 A C))) B)) (/.f64 180 (PI.f64)))
✓48.9b
(*.f64 (atan.f64 (*.f64 -1/2 (/.f64 B C))) (/.f64 180 (PI.f64)))
49.0b
(/.f64 (/.f64 (*.f64 (atan.f64 (/.f64 -1/2 (/.f64 C B))) 180) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
49.0b
(*.f64 (atan.f64 (*.f64 1/2 (/.f64 B A))) (/.f64 180 (PI.f64)))
▶48.9b
(/.f64 1 (/.f64 (PI.f64) (*.f64 (atan.f64 (/.f64 -1/2 (/.f64 C B))) 180)))
55.3b
(-.f64 (exp.f64 (log1p.f64 (*.f64 (atan.f64 (/.f64 -1/2 (/.f64 C B))) (/.f64 180 (PI.f64))))) 1)
51.5b
(cbrt.f64 (*.f64 (pow.f64 (atan.f64 (/.f64 -1/2 (/.f64 C B))) 3) (pow.f64 (/.f64 180 (PI.f64)) 3)))
Compiler

Compiled 954 to 683 computations (28.4% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(/.f64 (PI.f64) (*.f64 (atan.f64 (/.f64 -1/2 (/.f64 C B))) 180))
✓0.1b
(*.f64 (atan.f64 (/.f64 -1/2 (/.f64 C B))) 180)
✓0.2b
(/.f64 1 (/.f64 (PI.f64) (*.f64 (atan.f64 (/.f64 -1/2 (/.f64 C B))) 180)))
✓0.3b
(/.f64 -1/2 (/.f64 C B))

series57.0ms (0.9%)

Counts
4 → 96
Calls

4 calls:

27.0ms
(/.f64 (PI.f64) (*.f64 (atan.f64 (/.f64 -1/2 (/.f64 C B))) 180))
17.0ms
(/.f64 1 (/.f64 (PI.f64) (*.f64 (atan.f64 (/.f64 -1/2 (/.f64 C B))) 180)))
7.0ms
(/.f64 -1/2 (/.f64 C B))
5.0ms
(*.f64 (atan.f64 (/.f64 -1/2 (/.f64 C B))) 180)

rewrite61.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
244×expm1-udef_binary64
244×log1p-udef_binary64
214×log-pow_binary64
140×add-sqr-sqrt_binary64
130×add-cbrt-cube_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01354
128251
2371851
Stop Event
1×node limit
Counts
4 → 129
Calls

4 calls:

58.0ms
(/.f64 (PI.f64) (*.f64 (atan.f64 (/.f64 -1/2 (/.f64 C B))) 180))
58.0ms
(*.f64 (atan.f64 (/.f64 -1/2 (/.f64 C B))) 180)
58.0ms
(/.f64 1 (/.f64 (PI.f64) (*.f64 (atan.f64 (/.f64 -1/2 (/.f64 C B))) 180)))
57.0ms
(/.f64 -1/2 (/.f64 C B))

simplify33.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
9×*-commutative_binary64
6×associate-/l*_binary64
3×associate-*r/_binary64
3×associate-/r/_binary64
2×associate-*l/_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0151224
1241224
2341224
3441224
4471224
Stop Event
1×saturated
Counts
225 → 136

prune82.0ms (1.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1351136
Fresh145
Picked101
Done022
Total1377144
Error
0.1b
Counts
144 → 7
Alt Table
StatusErrorProgram
50.1b
(*.f64 (atan.f64 (/.f64 (*.f64 1/2 (/.f64 (pow.f64 B 2) A)) B)) (/.f64 180 (PI.f64)))
✓12.3b
(*.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 A C))) B)) (/.f64 180 (PI.f64)))
✓48.9b
(*.f64 (atan.f64 (*.f64 -1/2 (/.f64 B C))) (/.f64 180 (PI.f64)))
49.0b
(/.f64 (/.f64 (*.f64 (atan.f64 (/.f64 -1/2 (/.f64 C B))) 180) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
49.0b
(*.f64 (atan.f64 (*.f64 1/2 (/.f64 B A))) (/.f64 180 (PI.f64)))
▶48.9b
(/.f64 1 (/.f64 (PI.f64) (*.f64 (atan.f64 (*.f64 B (/.f64 -1/2 C))) 180)))
55.3b
(-.f64 (exp.f64 (log1p.f64 (*.f64 (atan.f64 (/.f64 -1/2 (/.f64 C B))) (/.f64 180 (PI.f64))))) 1)
Compiler

Compiled 2392 to 1825 computations (23.7% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(/.f64 (PI.f64) (*.f64 (atan.f64 (*.f64 B (/.f64 -1/2 C))) 180))
✓0.1b
(*.f64 (atan.f64 (*.f64 B (/.f64 -1/2 C))) 180)
✓0.2b
(/.f64 1 (/.f64 (PI.f64) (*.f64 (atan.f64 (*.f64 B (/.f64 -1/2 C))) 180)))
✓0.2b
(*.f64 B (/.f64 -1/2 C))

series58.0ms (0.9%)

Counts
4 → 96
Calls

4 calls:

27.0ms
(/.f64 (PI.f64) (*.f64 (atan.f64 (*.f64 B (/.f64 -1/2 C))) 180))
17.0ms
(/.f64 1 (/.f64 (PI.f64) (*.f64 (atan.f64 (*.f64 B (/.f64 -1/2 C))) 180)))
8.0ms
(*.f64 B (/.f64 -1/2 C))
5.0ms
(*.f64 (atan.f64 (*.f64 B (/.f64 -1/2 C))) 180)

rewrite62.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
238×expm1-udef_binary64
238×log1p-udef_binary64
209×log-pow_binary64
165×log-div_binary64
136×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01354
127651
2350851
Stop Event
1×node limit
Counts
4 → 125
Calls

4 calls:

60.0ms
(/.f64 (PI.f64) (*.f64 (atan.f64 (*.f64 B (/.f64 -1/2 C))) 180))
60.0ms
(*.f64 (atan.f64 (*.f64 B (/.f64 -1/2 C))) 180)
60.0ms
(/.f64 1 (/.f64 (PI.f64) (*.f64 (atan.f64 (*.f64 B (/.f64 -1/2 C))) 180)))
60.0ms
(*.f64 B (/.f64 -1/2 C))

simplify33.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
9×*-commutative_binary64
6×associate-/l*_binary64
3×associate-*r/_binary64
3×associate-/r/_binary64
2×associate-*l/_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0151224
1241224
2341224
3441224
4471224
Stop Event
1×saturated
Counts
221 → 133

prune86.0ms (1.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New1330133
Fresh044
Picked011
Done022
Total1337140
Error
0.1b
Counts
140 → 7
Alt Table
StatusErrorProgram
50.1b
(*.f64 (atan.f64 (/.f64 (*.f64 1/2 (/.f64 (pow.f64 B 2) A)) B)) (/.f64 180 (PI.f64)))
✓12.3b
(*.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 A C))) B)) (/.f64 180 (PI.f64)))
✓48.9b
(*.f64 (atan.f64 (*.f64 -1/2 (/.f64 B C))) (/.f64 180 (PI.f64)))
49.0b
(/.f64 (/.f64 (*.f64 (atan.f64 (/.f64 -1/2 (/.f64 C B))) 180) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
49.0b
(*.f64 (atan.f64 (*.f64 1/2 (/.f64 B A))) (/.f64 180 (PI.f64)))
✓48.9b
(/.f64 1 (/.f64 (PI.f64) (*.f64 (atan.f64 (*.f64 B (/.f64 -1/2 C))) 180)))
55.3b
(-.f64 (exp.f64 (log1p.f64 (*.f64 (atan.f64 (/.f64 -1/2 (/.f64 C B))) (/.f64 180 (PI.f64))))) 1)
Compiler

Compiled 2254 to 1715 computations (23.9% saved)

regimes642.0ms (10.4%)

Accuracy

Total 11.1b remaining (96.8%)

Threshold costs 0b (0%)

Counts
86 → 3
Compiler

Compiled 10764 to 8643 computations (19.7% saved)

bsearch3.0ms (0%)

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify5.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
039135
158135
274135
385135
490135
Stop Event
1×saturated

end121.0ms (2%)

Compiler

Compiled 291 to 194 computations (33.3% saved)

Profiling

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