Details

analyze305.0ms (3%)

Algorithm

1×

Search

True	Other	False	Iter
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)

sample4.0s (39.3%)

Results

1.2s	5602×	body	128	valid
1.2s	900×	body	4096	valid
916.0ms	891×	body	2048	valid
358.0ms	486×	body	1024	valid
181.0ms	122×	body	256	valid
143.0ms	255×	body	512	valid

Compiler

Compiled 80 to 62 computations (22.5% saved)

simplify64.0ms (0.6%)

Algorithm

1×	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)

Iter	Nodes	Cost
0	20	36
1	44	25
2	96	25
3	264	25
4	706	25
5	2223	25
6	4175	25
7	4825	25
8	4983	25

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

13.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	30.2b	(.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)))
▶	13.7b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))

Status

Error

Program

30.2b

(*.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)))

▶

13.7b

(*.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)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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))
✓	0.7b	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))

series165.0ms (1.6%)

Counts

4 → 144

Calls

4 calls:

57.0ms	(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
44.0ms	(-.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)))
26.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))

rewrite80.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

285×	`expm1-udef_binary64`
285×	`log1p-udef_binary64`
156×	`add-sqr-sqrt_binary64`
150×	`log1p-expm1-u_binary64`
150×	`expm1-log1p-u_binary64`

Counts

4 → 140

Calls

4 calls:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	76
1	299	76
2	4195	76
3	5022	76
0	0	0
1	0	0

simplify91.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

464×	`fma-def_binary64`
266×	`associate-+l+_binary64`
252×	`associate--r+_binary64`
231×	`associate-/l*_binary64`
224×	`associate--l+_binary64`

Counts

284 → 276

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	447	5489
1	1506	5060
2	5260	5060

prune257.0ms (2.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	270	6	276
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	272	6	278

Error

0.2b

Counts

278 → 6

Alt Table

Status	Error	Program
	55.7b	(.f64 180 (/.f64 (atan.f64 (/.f64 (fma.f64 1/2 (/.f64 (.f64 (.f64 B B) (.f64 C C)) (pow.f64 A 3)) (fma.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 B B) C) (.f64 A A)) (/.f64 (.f64 B B) A)) (*.f64 (/.f64 (pow.f64 B 4) (pow.f64 A 3)) -1/8))) B)) (PI.f64)))
	51.8b	(.f64 180 (/.f64 (atan.f64 (fma.f64 1/2 (/.f64 C (/.f64 (.f64 A A) B)) (fma.f64 1/2 (+.f64 (/.f64 B A) (/.f64 (.f64 B (.f64 C C)) (pow.f64 A 3))) (*.f64 (/.f64 (pow.f64 B 3) (pow.f64 A 3)) -1/8)))) (PI.f64)))
	22.0b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (fma.f64 (pow.f64 (cbrt.f64 (-.f64 C A)) 2) (cbrt.f64 (-.f64 C A)) (neg.f64 (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
	45.9b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (/.f64 B A))) (PI.f64)))
	47.5b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) (PI.f64)))
▶	13.7b	(*.f64 180 (/.f64 (atan.f64 (pow.f64 (/.f64 B (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))) -1)) (PI.f64)))

Compiler

Compiled 9397 to 4634 computations (50.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 B (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))))
✓	0.0b	(/.f64 (atan.f64 (pow.f64 (/.f64 B (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))) -1)) (PI.f64))
✓	0.1b	(pow.f64 (/.f64 B (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))) -1)
	0.7b	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))

series977.0ms (9.5%)

Counts

3 → 108

Calls

3 calls:

807.0ms

(pow.f64 (/.f64 B (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))) -1)

132.0ms

(/.f64 B (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))))

35.0ms

(/.f64 (atan.f64 (pow.f64 (/.f64 B (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))) -1)) (PI.f64))

rewrite75.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

273×	`expm1-udef_binary64`
273×	`log1p-udef_binary64`
253×	`fma-neg_binary64`
153×	`add-sqr-sqrt_binary64`
147×	`log1p-expm1-u_binary64`

Counts

3 → 117

Calls

3 calls:

71.0ms

(/.f64 B (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))))

71.0ms

(/.f64 (atan.f64 (pow.f64 (/.f64 B (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))) -1)) (PI.f64))

71.0ms

(pow.f64 (/.f64 B (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))) -1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	60
1	295	54
2	3969	54
3	5026	54
0	0	0
1	0	0

simplify309.0ms (3%)

Algorithm

1×	egg-herbie

Rules

537×	`*-commutative_binary64`
359×	`associate-+r+_binary64`
338×	`fma-def_binary64`
223×	`associate-/l*_binary64`
198×	`associate-r_binary64`

Counts

225 → 245

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1393	25353
1	4998	25353
2	5019	25353

prune646.0ms (6.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	356	2	358
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	358	6	364

Error

0.2b

Counts

364 → 6

Alt Table

Status	Error	Program
	47.3b	(.f64 180 (/.f64 (atan.f64 (pow.f64 (/.f64 B (.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 B B) C) (.f64 A A)) (/.f64 (.f64 B B) A)))) -1)) (PI.f64)))
	47.5b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) (PI.f64)))
▶	22.0b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (fma.f64 (pow.f64 (cbrt.f64 (-.f64 C A)) 2) (cbrt.f64 (-.f64 C A)) (neg.f64 (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
	40.8b	(.f64 180 (/.f64 (atan.f64 (pow.f64 (.f64 2 (-.f64 (/.f64 A B) (/.f64 C B))) -1)) (PI.f64)))
	45.9b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (/.f64 B A))) (PI.f64)))
✓	13.7b	(*.f64 180 (/.f64 (atan.f64 (pow.f64 (/.f64 B (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))) -1)) (PI.f64)))

Compiler

Compiled 40787 to 21087 computations (48.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (atan.f64 (/.f64 (fma.f64 (pow.f64 (cbrt.f64 (-.f64 C A)) 2) (cbrt.f64 (-.f64 C A)) (neg.f64 (hypot.f64 B (-.f64 C A)))) B)) (PI.f64))
✓	0.5b	(pow.f64 (cbrt.f64 (-.f64 C A)) 2)
✓	0.6b	(cbrt.f64 (-.f64 C A))
✓	21.8b	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 C A)) 2) (cbrt.f64 (-.f64 C A)) (neg.f64 (hypot.f64 B (-.f64 C A))))

series185.0ms (1.8%)

Counts

4 → 120

Calls

4 calls:

70.0ms	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 C A)) 2) (cbrt.f64 (-.f64 C A)) (neg.f64 (hypot.f64 B (-.f64 C A))))
51.0ms	(/.f64 (atan.f64 (/.f64 (fma.f64 (pow.f64 (cbrt.f64 (-.f64 C A)) 2) (cbrt.f64 (-.f64 C A)) (neg.f64 (hypot.f64 B (-.f64 C A)))) B)) (PI.f64))
40.0ms	(pow.f64 (cbrt.f64 (-.f64 C A)) 2)
24.0ms	(cbrt.f64 (-.f64 C A))

rewrite101.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

745×	`prod-diff_binary64`
230×	`egg-rr`
163×	`add-sqr-sqrt_binary64`
155×	`log1p-expm1-u_binary64`
155×	`expm1-log1p-u_binary64`

Counts

4 → 230

Calls

4 calls:

92.0ms	(/.f64 (atan.f64 (/.f64 (fma.f64 (pow.f64 (cbrt.f64 (-.f64 C A)) 2) (cbrt.f64 (-.f64 C A)) (neg.f64 (hypot.f64 B (-.f64 C A)))) B)) (PI.f64))
92.0ms	(pow.f64 (cbrt.f64 (-.f64 C A)) 2)
92.0ms	(cbrt.f64 (-.f64 C A))
92.0ms	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 C A)) 2) (cbrt.f64 (-.f64 C A)) (neg.f64 (hypot.f64 B (-.f64 C A))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	54
1	323	50
2	3776	50
3	5144	50
0	0	0
1	0	0

simplify114.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

475×	`fma-neg_binary64`
347×	`fma-def_binary64`
302×	`associate-r_binary64`
228×	`+-commutative_binary64`
224×	`associate-l_binary64`

Counts

350 → 361

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	401	4741
1	1273	4033
2	4562	4008
3	4975	4008

prune313.0ms (3.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	418	1	419
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	419	6	425

Error

0.2b

Counts

425 → 6

Alt Table

Status	Error	Program
	47.3b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 1/2 (+.f64 (/.f64 (.f64 B B) A) (/.f64 (.f64 (.f64 B B) C) (.f64 A A)))) B)) (PI.f64)))
✓	22.0b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (fma.f64 (pow.f64 (cbrt.f64 (-.f64 C A)) 2) (cbrt.f64 (-.f64 C A)) (neg.f64 (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
▶	40.8b	(.f64 180 (/.f64 (atan.f64 (pow.f64 (.f64 2 (-.f64 (/.f64 A B) (/.f64 C B))) -1)) (PI.f64)))
	45.9b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (/.f64 B A))) (PI.f64)))
	47.5b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) (PI.f64)))
✓	13.7b	(*.f64 180 (/.f64 (atan.f64 (pow.f64 (/.f64 B (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))) -1)) (PI.f64)))

Compiler

Compiled 17288 to 7620 computations (55.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (atan.f64 (pow.f64 (*.f64 2 (-.f64 (/.f64 A B) (/.f64 C B))) -1)) (PI.f64))
✓	0.2b	(.f64 180 (/.f64 (atan.f64 (pow.f64 (.f64 2 (-.f64 (/.f64 A B) (/.f64 C B))) -1)) (PI.f64)))
✓	0.8b	(pow.f64 (*.f64 2 (-.f64 (/.f64 A B) (/.f64 C B))) -1)
✓	2.1b	(-.f64 (/.f64 A B) (/.f64 C B))

series205.0ms (2%)

Counts

4 → 62

Calls

4 calls:

94.0ms	(.f64 180 (/.f64 (atan.f64 (pow.f64 (.f64 2 (-.f64 (/.f64 A B) (/.f64 C B))) -1)) (PI.f64)))
74.0ms	(/.f64 (atan.f64 (pow.f64 (*.f64 2 (-.f64 (/.f64 A B) (/.f64 C B))) -1)) (PI.f64))
26.0ms	(pow.f64 (*.f64 2 (-.f64 (/.f64 A B) (/.f64 C B))) -1)
11.0ms	(-.f64 (/.f64 A B) (/.f64 C B))

rewrite84.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

323×	`log1p-udef_binary64`
181×	`add-sqr-sqrt_binary64`
171×	`log1p-expm1-u_binary64`
171×	`expm1-log1p-u_binary64`
168×	`add-cbrt-cube_binary64`

Counts

4 → 143

Calls

4 calls:

80.0ms	(/.f64 (atan.f64 (pow.f64 (*.f64 2 (-.f64 (/.f64 A B) (/.f64 C B))) -1)) (PI.f64))
80.0ms	(.f64 180 (/.f64 (atan.f64 (pow.f64 (.f64 2 (-.f64 (/.f64 A B) (/.f64 C B))) -1)) (PI.f64)))
80.0ms	(pow.f64 (*.f64 2 (-.f64 (/.f64 A B) (/.f64 C B))) -1)
80.0ms	(-.f64 (/.f64 A B) (/.f64 C B))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	61
1	358	52
2	4780	52
3	5203	52
0	0	0
1	0	0

simplify71.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

851×	`fma-neg_binary64`
645×	`cancel-sign-sub-inv_binary64`
360×	`times-frac_binary64`
311×	`fma-def_binary64`
278×	`distribute-rgt-neg-in_binary64`

Counts

205 → 170

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	80	1096
1	245	1040
2	747	953
3	2969	953
4	4854	953
5	5176	953

prune118.0ms (1.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	162	8	170
Fresh	3	0	3
Picked	1	0	1
Done	0	2	2
Total	166	10	176

Error

0.1b

Counts

176 → 10

Alt Table

Status	Error	Program
	39.5b	(/.f64 (*.f64 180 (atan.f64 (/.f64 1/2 (/.f64 (-.f64 A C) B)))) (PI.f64))
	39.1b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (/.f64 B (-.f64 A C)))) (PI.f64)))
	39.7b	(.f64 180 (.f64 (pow.f64 (cbrt.f64 (atan.f64 (/.f64 1/2 (/.f64 (-.f64 A C) B)))) 2) (*.f64 (cbrt.f64 (atan.f64 (/.f64 1/2 (/.f64 (-.f64 A C) B)))) (/.f64 1 (PI.f64)))))
	39.7b	(pow.f64 (cbrt.f64 (*.f64 180 (/.f64 (atan.f64 (/.f64 1/2 (/.f64 (-.f64 A C) B))) (PI.f64)))) 3)
	39.5b	(/.f64 1 (/.f64 (PI.f64) (*.f64 180 (atan.f64 (/.f64 1/2 (/.f64 (-.f64 A C) B))))))
	39.5b	(/.f64 180 (/.f64 (PI.f64) (atan.f64 (/.f64 1/2 (/.f64 (-.f64 A C) B)))))
✓	22.0b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (fma.f64 (pow.f64 (cbrt.f64 (-.f64 C A)) 2) (cbrt.f64 (-.f64 C A)) (neg.f64 (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
	41.0b	(.f64 180 (/.f64 (atan.f64 (pow.f64 (.f64 2 (/.f64 (/.f64 (-.f64 (.f64 A B) (.f64 B C)) B) B)) -1)) (PI.f64)))
✓	13.7b	(*.f64 180 (/.f64 (atan.f64 (pow.f64 (/.f64 B (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))) -1)) (PI.f64)))
	39.8b	(*.f64 180 (pow.f64 (cbrt.f64 (/.f64 (atan.f64 (/.f64 1/2 (/.f64 (-.f64 A C) B))) (PI.f64))) 3))

Compiler

Compiled 3522 to 2035 computations (42.2% saved)

regimes1.8s (17.8%)

Accuracy

Total 7.5b remaining (97.8%)

Threshold costs 0b (0%)

Counts

199 → 3

Compiler

Compiled 29048 to 21264 computations (26.8% saved)

bsearch7.0ms (0.1%)

Compiler: Compiled 21 to 15 computations (28.6% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
9×	`*-commutative_binary64`
9×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	138
1	59	138
2	72	138
3	80	138
4	84	138
5	83	138

end174.0ms (1.7%)

Compiler: Compiled 383 to 255 computations (33.4% saved)

Details

analyze305.0ms (3%)

sample4.0s (39.3%)

simplify64.0ms (0.6%)

prune5.0ms (0%)

localize10.0ms (0.1%)

series165.0ms (1.6%)

rewrite80.0ms (0.8%)

simplify91.0ms (0.9%)

prune257.0ms (2.5%)

localize12.0ms (0.1%)

series977.0ms (9.5%)

rewrite75.0ms (0.7%)

simplify309.0ms (3%)

prune646.0ms (6.3%)

localize14.0ms (0.1%)

series185.0ms (1.8%)

rewrite101.0ms (1%)

simplify114.0ms (1.1%)

prune313.0ms (3.1%)

localize11.0ms (0.1%)

series205.0ms (2%)

rewrite84.0ms (0.8%)

simplify71.0ms (0.7%)

prune118.0ms (1.2%)

regimes1.8s (17.8%)

bsearch7.0ms (0.1%)

simplify5.0ms (0.1%)

end174.0ms (1.7%)

Profiling