Details

analyze290.0ms (3.6%)

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)

sample156.0ms (1.9%)

Algorithm

1×

intervals

Results

29.0ms	30×	body	4096	valid
19.0ms	166×	body	128	valid
19.0ms	25×	body	2048	valid
11.0ms	22×	body	1024	valid
3.0ms	8×	body	512	valid
1.0ms	5×	body	256	valid

Compiler

Compiled 56 to 44 computations (21.4% saved)

simplify65.0ms (0.8%)

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 (0.1%)

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

14.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	14.9b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))
	32.3b	(.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)))

Status

Error

Program

▶

14.9b

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

32.3b

(*.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:

New	Error	Program
✓	0.0b	(*.f64 180 (/.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)
✓	0.0b	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))
✓	0.8b	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))

series191.0ms (2.4%)

Counts

4 → 144

Calls

4 calls:

72.0ms	(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
58.0ms	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))
36.0ms	(*.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))

rewrite40.0ms (0.5%)

Algorithm

1×	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 (-.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))

simplify149.0ms (1.8%)

Algorithm

1×	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)

Iter	Nodes	Cost
0	674	10323
1	1950	9081
2	4971	9081

prune287.0ms (3.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	369	9	378
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	371	9	380

Error

0.3b

Counts

380 → 9

Alt Table

Status	Error	Program
	51.8b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (fma.f64 (sqrt.f64 (-.f64 C A)) (sqrt.f64 (-.f64 C A)) (neg.f64 (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
	47.3b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) (PI.f64)))
	42.3b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A)))) (PI.f64)))
	47.1b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 1/2 (/.f64 (pow.f64 B 2) A)) B)) (PI.f64)))
▶	14.9b	(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
	34.1b	(exp.f64 (log.f64 (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))))
	48.0b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 -1/2 (/.f64 (pow.f64 B 2) C)) B)) (PI.f64)))
	15.2b	(*.f64 180 (log.f64 (exp.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))))
	45.7b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (/.f64 B A))) (PI.f64)))

Compiler

Compiled 13410 to 5273 computations (60.7% saved)

localize9.0ms (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 (atan.f64 (/.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))
	0.8b	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))

series50.0ms (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))
14.0ms	(*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`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))
5.0ms	(*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)))

simplify186.0ms (2.3%)

Algorithm

1×	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)

Iter	Nodes	Cost
0	92	3008
1	189	2775
2	520	2775
3	1776	2775
4	2166	2775
5	2665	2775
6	3523	2775
7	3958	2775
8	4318	2775
9	4960	2775

prune256.0ms (3.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	333	4	337
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	335	11	346

Error

0.3b

Counts

346 → 11

Alt Table

Status	Error	Program
	51.8b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (fma.f64 (sqrt.f64 (-.f64 C A)) (sqrt.f64 (-.f64 C A)) (neg.f64 (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
	47.3b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) (PI.f64)))
	45.7b	(/.f64 (.f64 180 (atan.f64 (.f64 1/2 (/.f64 B A)))) (PI.f64))
✓	14.9b	(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
	42.3b	(/.f64 (.f64 180 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A))))) (PI.f64))
	34.1b	(exp.f64 (log.f64 (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))))
	48.0b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 -1/2 (/.f64 (pow.f64 B 2) C)) B)) (PI.f64)))
▶	15.2b	(*.f64 180 (log.f64 (exp.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))))
	47.9b	(/.f64 (.f64 180 (atan.f64 (/.f64 (.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 B B) C) (.f64 A A)) (/.f64 (.f64 B B) A))) B))) (PI.f64))
	44.3b	(/.f64 (.f64 180 (atan.f64 (.f64 -1/2 (+.f64 (/.f64 B C) (/.f64 A (/.f64 (*.f64 C C) B)))))) (PI.f64))
	45.7b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (/.f64 B A))) (PI.f64)))

Compiler

Compiled 11997 to 5218 computations (56.5% saved)

localize13.0ms (0.2%)

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 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))
	0.8b	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))
✓	0.9b	(log.f64 (exp.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))))

series26.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

25.0ms

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

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`log-pow_binary64`
13×	`exp-prod_binary64`
9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`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))))

simplify119.0ms (1.5%)

Algorithm

1×	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)

Iter	Nodes	Cost
0	84	1601
1	119	1531
2	223	1531
3	383	1531
4	644	1531
5	1130	1531
6	1985	1531
7	3750	1531
8	4729	1531
9	5050	1531

prune278.0ms (3.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	366	0	366
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	366	11	377

Error

0.3b

Counts

377 → 11

Alt Table

Status	Error	Program
	51.8b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (fma.f64 (sqrt.f64 (-.f64 C A)) (sqrt.f64 (-.f64 C A)) (neg.f64 (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
	47.3b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) (PI.f64)))
	45.7b	(/.f64 (.f64 180 (atan.f64 (.f64 1/2 (/.f64 B A)))) (PI.f64))
✓	14.9b	(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
	42.3b	(/.f64 (.f64 180 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A))))) (PI.f64))
▶	34.1b	(exp.f64 (log.f64 (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))))
	48.0b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 -1/2 (/.f64 (pow.f64 B 2) C)) B)) (PI.f64)))
✓	15.2b	(*.f64 180 (log.f64 (exp.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))))
	47.9b	(/.f64 (.f64 180 (atan.f64 (/.f64 (.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 B B) C) (.f64 A A)) (/.f64 (.f64 B B) A))) B))) (PI.f64))
	44.3b	(/.f64 (.f64 180 (atan.f64 (.f64 -1/2 (+.f64 (/.f64 B C) (/.f64 A (/.f64 (*.f64 C C) B)))))) (PI.f64))
	45.7b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (/.f64 B A))) (PI.f64)))

Compiler

Compiled 13857 to 5855 computations (57.7% saved)

localize12.0ms (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 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))
✓	0.2b	(exp.f64 (log.f64 (*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))))
	0.8b	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))

series37.0ms (0.5%)

Counts

1 → 36

Calls

1 calls:

37.0ms

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

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`exp-prod_binary64`
4×	`pow1_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`

Counts

1 → 17

Calls

1 calls:

3.0ms

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

simplify75.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

751×	`div-exp_binary64`
493×	`associate-/l*_binary64`
407×	`associate-/l/_binary64`
407×	`fma-def_binary64`
406×	`associate-*l/_binary64`

Counts

53 → 28

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	53	1369
1	88	1318
2	200	1318
3	534	1318
4	1539	1318
5	4026	1318
6	5661	1318

prune252.0ms (3.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	341	2	343
Fresh	1	7	8
Picked	1	0	1
Done	0	2	2
Total	343	11	354

Error

0.3b

Counts

354 → 11

Alt Table

Status	Error	Program
	45.7b	(/.f64 (.f64 180 (atan.f64 (.f64 1/2 (/.f64 B A)))) (PI.f64))
✓	14.9b	(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
	44.3b	(/.f64 (.f64 180 (atan.f64 (.f64 -1/2 (+.f64 (/.f64 B C) (/.f64 A (/.f64 (*.f64 C C) B)))))) (PI.f64))
	57.0b	(exp.f64 (log.f64 (*.f64 180 (/.f64 (atan.f64 (/.f64 (fma.f64 (sqrt.f64 (-.f64 C A)) (sqrt.f64 (-.f64 C A)) (neg.f64 (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))))
	47.3b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) (PI.f64)))
	42.3b	(/.f64 (.f64 180 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A))))) (PI.f64))
	48.0b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 -1/2 (/.f64 (pow.f64 B 2) C)) B)) (PI.f64)))
	53.5b	(exp.f64 (log.f64 (.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 B B) C) (.f64 A A)) (/.f64 (.f64 B B) A))) B)) (PI.f64)))))
✓	15.2b	(*.f64 180 (log.f64 (exp.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))))
	47.9b	(/.f64 (.f64 180 (atan.f64 (/.f64 (.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 B B) C) (.f64 A A)) (/.f64 (.f64 B B) A))) B))) (PI.f64))
	45.7b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (/.f64 B A))) (PI.f64)))

Compiler

Compiled 12893 to 5730 computations (55.6% saved)

regimes1.7s (20.9%)

Accuracy

Total 12.7b remaining (97.7%)

Threshold costs 0b (0%)

Counts

179 → 4

Compiler

Compiled 27512 to 19945 computations (27.5% saved)

bsearch187.0ms (2.3%)

Steps

Iters	Range		Point
10	3.0889970582678576e+146	2.341518551116029e+159	4.9369960185973415e+146
5	-1.2474237140456945e-79	-4.527803310856721e-80	-1.2315399059169273e-79
10	-0.0018270026643440614	-7.8406292298092e-17	-7.961133987601505e-17

Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	116
1	54	116
2	62	116
3	66	116
4	68	116
5	68	116

end1.0ms (0%)

Compiler: Compiled 77 to 44 computations (42.9% saved)

sample3.7s (45.4%)

Algorithm

1×

intervals

Results

1.6s	868×	body	4096	valid
651.0ms	5394×	body	128	valid
584.0ms	852×	body	2048	valid
269.0ms	520×	body	1024	valid
99.0ms	244×	body	512	valid
31.0ms	122×	body	256	valid

Compiler

Compiled 328 to 223 computations (32% saved)

Details

analyze290.0ms (3.6%)

sample156.0ms (1.9%)

simplify65.0ms (0.8%)

prune5.0ms (0.1%)

localize9.0ms (0.1%)

series191.0ms (2.4%)

rewrite40.0ms (0.5%)

simplify149.0ms (1.8%)

prune287.0ms (3.5%)

localize9.0ms (0.1%)

series50.0ms (0.6%)

rewrite12.0ms (0.1%)

simplify186.0ms (2.3%)

prune256.0ms (3.2%)

localize13.0ms (0.2%)

series26.0ms (0.3%)

rewrite10.0ms (0.1%)

simplify119.0ms (1.5%)

prune278.0ms (3.4%)

localize12.0ms (0.1%)

series37.0ms (0.5%)

rewrite4.0ms (0.1%)

simplify75.0ms (0.9%)

prune252.0ms (3.1%)

regimes1.7s (20.9%)

bsearch187.0ms (2.3%)

simplify7.0ms (0.1%)

end1.0ms (0%)

sample3.7s (45.4%)

Profiling