Details

analyze653.0ms (9.8%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.5s (38.1%)

Results

784.0ms	5366×	body	128	valid
663.0ms	1160×	body	2048	valid
320.0ms	695×	body	1024	valid
295.0ms	447×	body	4096	valid
134.0ms	1023×	body	128	invalid
121.0ms	375×	body	512	valid
58.0ms	213×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify140.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

2079×	`fma-neg_binary64`
1006×	`fma-def_binary64`
919×	`div-sub_binary64`
626×	`distribute-rgt-in_binary64`
435×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	38	24
2	95	24
3	227	22
4	357	22
5	614	22
6	1103	22
7	1373	22
8	1636	22
9	2330	22
10	3187	22
11	2880	22
12	2827	22
13	2896	22
14	2922	22
15	3797	22
16	4824	22
17	5240	22

prune4.0ms (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

34.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	35.2b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))
▶	35.0b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
✓	0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
✓	1.4b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
✓	22.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series185.0ms (2.8%)

Counts

4 → 96

Calls

4 calls:

78.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
55.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
42.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
10.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

rewrite100.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

283×	`expm1-udef_binary64`
283×	`log1p-udef_binary64`
169×	`add-sqr-sqrt_binary64`
165×	`log1p-expm1-u_binary64`
165×	`expm1-log1p-u_binary64`

Counts

4 → 160

Calls

4 calls:

96.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
96.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
96.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
96.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	74
1	342	62
2	4355	62
3	5034	62
0	0	0
1	0	0

simplify75.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

743×	`times-frac_binary64`
469×	`associate-/l*_binary64`
436×	`fma-def_binary64`
429×	`associate-/r*_binary64`
158×	`fma-neg_binary64`

Counts

256 → 235

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	2060
1	411	1984
2	1398	1904
3	5097	1904

prune167.0ms (2.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	225	10	235
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	226	11	237

Error

4.0b

Counts

237 → 11

Alt Table

Status	Error	Program
	43.7b	(/.f64 (-.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 3/2))) (*.f64 2 a))
✓	35.0b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
▶	36.1b	(/.f64 (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4) 2)) (*.f64 2 a))
	45.0b	(-.f64 (/.f64 c b) (/.f64 b a))
	48.0b	(pow.f64 (/.f64 (.f64 a 2) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4))))) -1)
	48.2b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) 2) (pow.f64 (cbrt.f64 (.f64 a 2)) 2)) (cbrt.f64 (.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a))))
	36.5b	(neg.f64 (/.f64 c b))
	48.0b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a))
	44.9b	(/.f64 (neg.f64 b) a)
	55.5b	(/.f64 (-.f64 (neg.f64 b) (neg.f64 b)) (*.f64 2 a))
	44.7b	(.f64 -1/2 (/.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) a))

Compiler

Compiled 6297 to 3646 computations (42.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(pow.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4) 2)
✓	1.0b	(fma.f64 b b (.f64 (.f64 a c) -4))
✓	14.3b	(-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4) 2))
✓	22.7b	(pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4)

series197.0ms (2.9%)

Counts

4 → 128

Calls

4 calls:

83.0ms	(pow.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4) 2)
54.0ms	(-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4) 2))
49.0ms	(pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4)
11.0ms	(fma.f64 b b (.f64 (.f64 a c) -4))

rewrite124.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

812×	`prod-diff_binary64`
249×	`egg-rr`
235×	`log1p-udef_binary64`
143×	`add-sqr-sqrt_binary64`
143×	`log1p-expm1-u_binary64`

Counts

4 → 249

Calls

4 calls:

109.0ms	(pow.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4) 2)
109.0ms	(fma.f64 b b (.f64 (.f64 a c) -4))
109.0ms	(-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4) 2))
109.0ms	(pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	58
1	307	52
2	3166	52
3	4940	52
0	0	0
1	0	0

simplify115.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

301×	`times-frac_binary64`
277×	`sub-neg_binary64`
272×	`associate-/r*_binary64`
238×	`fma-neg_binary64`
233×	`associate-/l*_binary64`

Counts

377 → 383

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	320	4810
1	1101	4654
2	4363	4654
3	5027	4654

prune460.0ms (6.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	381	2	383
Fresh	3	6	9
Picked	0	1	1
Done	0	1	1
Total	384	10	394

Error

0.5b

Counts

394 → 10

Alt Table

Status	Error	Program
	43.7b	(/.f64 (-.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 3/2))) (*.f64 2 a))
✓	35.0b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
✓	36.1b	(/.f64 (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4) 2)) (*.f64 2 a))
	45.0b	(-.f64 (/.f64 c b) (/.f64 b a))
	48.0b	(pow.f64 (/.f64 (.f64 a 2) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4))))) -1)
	48.2b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) 2) (pow.f64 (cbrt.f64 (.f64 a 2)) 2)) (cbrt.f64 (.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a))))
▶	36.5b	(neg.f64 (/.f64 c b))
	48.0b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a))
	53.3b	(/.f64 (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 4 a)) (log.f64 (/.f64 -1 c))))) 2)) (*.f64 2 a))
	54.6b	(/.f64 (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 4 c)) (log.f64 (/.f64 -1 a))))) 2)) (*.f64 2 a))

Compiler

Compiled 19644 to 12080 computations (38.5% saved)

localize5.0ms (0.1%)

prune10.0ms (0.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	7	7
Picked	1	1
Done	2	2
Total	10	10

Error

0.5b

Counts

10 → 10

Alt Table

Status	Error	Program
▶	43.7b	(/.f64 (-.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 3/2))) (*.f64 2 a))
✓	35.0b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
✓	36.1b	(/.f64 (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4) 2)) (*.f64 2 a))
	45.0b	(-.f64 (/.f64 c b) (/.f64 b a))
	48.0b	(pow.f64 (/.f64 (.f64 a 2) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4))))) -1)
	48.2b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) 2) (pow.f64 (cbrt.f64 (.f64 a 2)) 2)) (cbrt.f64 (.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a))))
✓	36.5b	(neg.f64 (/.f64 c b))
	48.0b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a))
	53.3b	(/.f64 (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 4 a)) (log.f64 (/.f64 -1 c))))) 2)) (*.f64 2 a))
	54.6b	(/.f64 (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 4 c)) (log.f64 (/.f64 -1 a))))) 2)) (*.f64 2 a))

Compiler

Compiled 365 to 265 computations (27.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 3/2)
	1.0b	(fma.f64 b b (.f64 (.f64 a c) -4))
✓	1.4b	(-.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 3/2)))
✓	32.2b	(cbrt.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 3/2))

series148.0ms (2.2%)

Counts

3 → 76

Calls

3 calls:

55.0ms	(-.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 3/2)))
50.0ms	(pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 3/2)
43.0ms	(cbrt.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 3/2))

rewrite81.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

769×	`prod-diff_binary64`
221×	`expm1-udef_binary64`
221×	`log1p-udef_binary64`
167×	`egg-rr`
136×	`add-sqr-sqrt_binary64`

Counts

3 → 167

Calls

3 calls:

76.0ms	(pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 3/2)
76.0ms	(-.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 3/2)))
76.0ms	(cbrt.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 3/2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	51
1	279	41
2	3005	41
3	4992	41
0	0	0
1	0	0

simplify99.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

555×	`fma-neg_binary64`
372×	`cancel-sign-sub-inv_binary64`
345×	`associate-/r/_binary64`
217×	`associate-/l/_binary64`
178×	`distribute-rgt-neg-in_binary64`

Counts

243 → 263

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	225	2925
1	734	2860
2	2633	2852
3	4928	2852
4	5197	2852

prune233.0ms (3.5%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	297	0	297
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	297	10	307

Error

0.5b

Counts

307 → 10

Alt Table

Status	Error	Program
✓	43.7b	(/.f64 (-.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 3/2))) (*.f64 2 a))
✓	35.0b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
✓	36.1b	(/.f64 (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4) 2)) (*.f64 2 a))
	45.0b	(-.f64 (/.f64 c b) (/.f64 b a))
	48.0b	(pow.f64 (/.f64 (.f64 a 2) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4))))) -1)
	48.2b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) 2) (pow.f64 (cbrt.f64 (.f64 a 2)) 2)) (cbrt.f64 (.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a))))
✓	36.5b	(neg.f64 (/.f64 c b))
	48.0b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a))
	53.3b	(/.f64 (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 4 a)) (log.f64 (/.f64 -1 c))))) 2)) (*.f64 2 a))
	54.6b	(/.f64 (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 4 c)) (log.f64 (/.f64 -1 a))))) 2)) (*.f64 2 a))

Compiler

Compiled 10975 to 6663 computations (39.3% saved)

regimes1.1s (16%)

Accuracy

Total 9.4b remaining (91.3%)

Threshold costs 0b (0%)

Counts

69 → 3

Compiler

Compiled 5556 to 3986 computations (28.3% saved)

bsearch74.0ms (1.1%)

Steps

Iters	Range		Point
8	6.605804912973952e+76	2.501177248826239e+80	2.4459965781085926e+80
8	-6.9824393472563535e-59	-5.804463573999287e-63	-1.0210080657580689e-59

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	52
1	39	52
2	54	52
3	68	52
4	75	52
5	78	52
6	79	52
7	79	52

end152.0ms (2.3%)

Compiler: Compiled 283 to 196 computations (30.7% saved)

Details

analyze653.0ms (9.8%)

sample2.5s (38.1%)

simplify140.0ms (2.1%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

series185.0ms (2.8%)

rewrite100.0ms (1.5%)

simplify75.0ms (1.1%)

prune167.0ms (2.5%)

localize14.0ms (0.2%)

series197.0ms (2.9%)

rewrite124.0ms (1.9%)

simplify115.0ms (1.7%)

prune460.0ms (6.9%)

localize5.0ms (0.1%)

prune10.0ms (0.1%)

localize16.0ms (0.2%)

series148.0ms (2.2%)

rewrite81.0ms (1.2%)

simplify99.0ms (1.5%)

prune233.0ms (3.5%)

regimes1.1s (16%)

bsearch74.0ms (1.1%)

simplify4.0ms (0.1%)

end152.0ms (2.3%)

Profiling