Details

analyze1.5s (26%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
7.8%	92%	0.2%	11
11.7%	88.1%	0.2%	12
17.9%	81.8%	0.2%	13
18.5%	81.2%	0.2%	14

Compiler

Compiled 19 to 14 computations (26.3% saved)

sample1.3s (21.8%)

Results

1.1s	8123×	body	128	valid
95.0ms	741×	body	128	invalid
20.0ms	42×	body	2048	valid
15.0ms	42×	body	1024	valid
10.0ms	32×	body	512	valid
4.0ms	16×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 38 to 28 computations (26.3% saved)

preprocess39.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

856×	`div-sub_binary64`
529×	`fma-def_binary64`
285×	`fma-neg_binary64`
240×	`times-frac_binary64`
194×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	209
1	122	187
2	272	187
3	587	187
4	1425	187
5	3618	187
0	5	5

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 18 to 13 computations (27.8% saved)

simplify25.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

681×	`fma-def_binary64`
523×	`div-sub_binary64`
520×	`fma-neg_binary64`
422×	`times-frac_binary64`
190×	`associate-/l/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	19
1	23	17
2	46	17
3	93	17
4	200	17
5	408	17
6	869	17
7	2310	17

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.6b	(+.f64 (/.f64 (.f64 60 (-.f64 x y)) (-.f64 z t)) (.f64 a 120))
▶	0.1b	(fma.f64 60 (/.f64 (-.f64 x y) (-.f64 z t)) (*.f64 a 120))

Compiler

Compiled 100 to 68 computations (32% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 z t))
✓	0.1b	(fma.f64 60 (/.f64 (-.f64 x y) (-.f64 z t)) (*.f64 a 120))

series64.0ms (1.1%)

Counts

2 → 108

Calls

27 calls:

7.0ms	(fma.f64 60 (/.f64 (-.f64 x y) (-.f64 z t)) (*.f64 a 120))	y	0
4.0ms	(fma.f64 60 (/.f64 (-.f64 x y) (-.f64 z t)) (*.f64 a 120))	z	0
4.0ms	(fma.f64 60 (/.f64 (-.f64 x y) (-.f64 z t)) (*.f64 a 120))	t	0
3.0ms	(fma.f64 60 (/.f64 (-.f64 x y) (-.f64 z t)) (*.f64 a 120))	y	-inf
3.0ms	(fma.f64 60 (/.f64 (-.f64 x y) (-.f64 z t)) (*.f64 a 120))	y	inf

rewrite63.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

272×	`expm1-udef_binary64`
272×	`log1p-udef_binary64`
212×	`fma-neg_binary64`
150×	`add-sqr-sqrt_binary64`
144×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	27
1	290	27
2	4023	27

Stop Event

1×	node limit

Counts

2 → 74

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

711×	`times-frac_binary64`
462×	`associate-/l*_binary64`
458×	`cancel-sign-sub-inv_binary64`
275×	`sub-neg_binary64`
149×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	153	3389
1	558	3270
2	2053	3006

Stop Event

1×	node limit

Counts

182 → 124

prune115.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	121	5	126

Error

0.0b

Counts

126 → 5

Alt Table

Status	Error	Program
	0.6b	(+.f64 (/.f64 (.f64 60 (-.f64 x y)) (-.f64 z t)) (.f64 a 120))
	29.8b	(pow.f64 (sqrt.f64 (fma.f64 60 (/.f64 (-.f64 x y) (-.f64 z t)) (*.f64 a 120))) 2)
	0.1b	(+.f64 (*.f64 a 120) (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
▶	0.1b	(fma.f64 120 a (*.f64 60 (-.f64 (/.f64 x (-.f64 z t)) (/.f64 y (-.f64 z t)))))
✓	0.1b	(fma.f64 60 (/.f64 (-.f64 x y) (-.f64 z t)) (*.f64 a 120))

Compiler

Compiled 3230 to 1554 computations (51.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 z t))
✓	0.0b	(fma.f64 120 a (*.f64 60 (-.f64 (/.f64 x (-.f64 z t)) (/.f64 y (-.f64 z t)))))
✓	0.0b	(-.f64 (/.f64 x (-.f64 z t)) (/.f64 y (-.f64 z t)))
✓	0.3b	(*.f64 60 (-.f64 (/.f64 x (-.f64 z t)) (/.f64 y (-.f64 z t))))

series130.0ms (2.3%)

Counts

4 → 162

Calls

48 calls:

7.0ms	(fma.f64 120 a (*.f64 60 (-.f64 (/.f64 x (-.f64 z t)) (/.f64 y (-.f64 z t)))))	z	0
6.0ms	(fma.f64 120 a (*.f64 60 (-.f64 (/.f64 x (-.f64 z t)) (/.f64 y (-.f64 z t)))))	y	-inf
5.0ms	(*.f64 60 (-.f64 (/.f64 x (-.f64 z t)) (/.f64 y (-.f64 z t))))	y	0
4.0ms	(*.f64 60 (-.f64 (/.f64 x (-.f64 z t)) (/.f64 y (-.f64 z t))))	x	-inf
4.0ms	(-.f64 (/.f64 x (-.f64 z t)) (/.f64 y (-.f64 z t)))	t	-inf

rewrite77.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

298×	`log1p-udef_binary64`
164×	`add-sqr-sqrt_binary64`
157×	`log1p-expm1-u_binary64`
157×	`expm1-log1p-u_binary64`
156×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	47
1	317	47
2	4672	47

Stop Event

1×	node limit

Counts

4 → 143

simplify94.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

725×	`times-frac_binary64`
698×	`cancel-sign-sub-inv_binary64`
406×	`sub-neg_binary64`
236×	`fma-neg_binary64`
200×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	187	5463
1	708	5245
2	2623	5245

Stop Event

1×	node limit

Counts

305 → 234

prune262.0ms (4.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	232	2	234
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	233	6	239

Error

0.0b

Counts

239 → 6

Alt Table

Status	Error	Program
	29.8b	(pow.f64 (sqrt.f64 (fma.f64 60 (/.f64 (-.f64 x y) (-.f64 z t)) (*.f64 a 120))) 2)
	0.6b	(fma.f64 120 a (/.f64 (*.f64 (-.f64 x y) 60) (-.f64 z t)))
	29.5b	(fma.f64 120 a (/.f64 (.f64 (-.f64 (.f64 x (-.f64 z t)) (*.f64 (-.f64 z t) y)) 60) (pow.f64 (-.f64 z t) 2)))
▶	0.1b	(+.f64 (*.f64 a 120) (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
✓	0.1b	(fma.f64 120 a (*.f64 60 (-.f64 (/.f64 x (-.f64 z t)) (/.f64 y (-.f64 z t)))))
✓	0.1b	(fma.f64 60 (/.f64 (-.f64 x y) (-.f64 z t)) (*.f64 a 120))

Compiler

Compiled 6210 to 2867 computations (53.8% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 a 120) (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 x y))
✓	0.6b	(/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y)))

series136.0ms (2.4%)

Counts

3 → 156

Calls

39 calls:

34.0ms	(/.f64 (-.f64 z t) (-.f64 x y))	z	-inf
5.0ms	(/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y)))	t	0
5.0ms	(+.f64 (*.f64 a 120) (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))	y	-inf
4.0ms	(+.f64 (*.f64 a 120) (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))	a	0
4.0ms	(+.f64 (*.f64 a 120) (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))	y	inf

rewrite78.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

307×	`log1p-udef_binary64`
170×	`add-sqr-sqrt_binary64`
165×	`log1p-expm1-u_binary64`
165×	`expm1-log1p-u_binary64`
164×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	40
1	329	40
2	4891	40

Stop Event

1×	node limit

Counts

3 → 106

simplify90.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

829×	`cancel-sign-sub-inv_binary64`
401×	`sub-neg_binary64`
260×	`fma-neg_binary64`
203×	`fma-def_binary64`
169×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	206	5147
1	758	4968
2	2930	4707

Stop Event

1×	node limit

Counts

262 → 171

prune177.0ms (3.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	1	2	3
Picked	0	1	1
Done	1	1	2
Total	171	6	177

Error

Counts

177 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 60 (/.f64 (-.f64 x y) (-.f64 z t)) (*.f64 a 120))
▶	0.2b	(fma.f64 a 120 (*.f64 (-.f64 x y) (/.f64 60 (-.f64 z t))))
	29.8b	(pow.f64 (sqrt.f64 (fma.f64 60 (/.f64 (-.f64 x y) (-.f64 z t)) (*.f64 a 120))) 2)
	0.6b	(fma.f64 120 a (/.f64 (*.f64 (-.f64 x y) 60) (-.f64 z t)))
✓	0.1b	(+.f64 (*.f64 a 120) (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
	0.7b	(+.f64 (*.f64 a 120) (/.f64 60 (pow.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 x y))) 3)))

Compiler

Compiled 4652 to 2485 computations (46.6% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 60 (-.f64 z t))
✓	0.0b	(fma.f64 a 120 (*.f64 (-.f64 x y) (/.f64 60 (-.f64 z t))))
✓	0.3b	(*.f64 (-.f64 x y) (/.f64 60 (-.f64 z t)))

series78.0ms (1.3%)

Counts

3 → 132

Calls

33 calls:

5.0ms	(fma.f64 a 120 (*.f64 (-.f64 x y) (/.f64 60 (-.f64 z t))))	z	0
5.0ms	(fma.f64 a 120 (*.f64 (-.f64 x y) (/.f64 60 (-.f64 z t))))	y	-inf
4.0ms	(fma.f64 a 120 (*.f64 (-.f64 x y) (/.f64 60 (-.f64 z t))))	t	0
3.0ms	(*.f64 (-.f64 x y) (/.f64 60 (-.f64 z t)))	z	inf
3.0ms	(*.f64 (-.f64 x y) (/.f64 60 (-.f64 z t)))	t	0

rewrite70.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

907×	`prod-diff_binary64`
149×	`add-sqr-sqrt_binary64`
143×	`log1p-expm1-u_binary64`
143×	`expm1-log1p-u_binary64`
142×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	37
1	290	37
2	3916	37

Stop Event

1×	node limit

Counts

3 → 89

simplify80.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

807×	`times-frac_binary64`
674×	`cancel-sign-sub-inv_binary64`
293×	`sub-neg_binary64`
249×	`fma-def_binary64`
228×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	176	4151
1	673	3969
2	2556	3954

Stop Event

1×	node limit

Counts

221 → 150

prune145.0ms (2.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	150	6	156

Error

Counts

156 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 60 (/.f64 (-.f64 x y) (-.f64 z t)) (*.f64 a 120))
✓	0.2b	(fma.f64 a 120 (*.f64 (-.f64 x y) (/.f64 60 (-.f64 z t))))
	29.8b	(pow.f64 (sqrt.f64 (fma.f64 60 (/.f64 (-.f64 x y) (-.f64 z t)) (*.f64 a 120))) 2)
	0.6b	(fma.f64 120 a (/.f64 (*.f64 (-.f64 x y) 60) (-.f64 z t)))
✓	0.1b	(+.f64 (*.f64 a 120) (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
	0.6b	(fma.f64 a 120 (*.f64 (-.f64 x y) (pow.f64 (cbrt.f64 (/.f64 60 (-.f64 z t))) 3)))

Compiler

Compiled 3771 to 2002 computations (46.9% saved)

regimes1.1s (18.7%)

Accuracy

Total 0.1b remaining (93.8%)

Threshold costs 0.1b (93.8%)

Counts

78 → 1

Compiler

Compiled 16293 to 11819 computations (27.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	23
1	19	23
2	29	23
3	35	23
4	39	23
5	40	23

Stop Event

1×

saturated

end97.0ms (1.7%)

Stop Event

1×

fuel

Compiler

Compiled 151 to 105 computations (30.5% saved)

Details

analyze1.5s (26%)

sample1.3s (21.8%)

preprocess39.0ms (0.7%)

simplify25.0ms (0.4%)

prune3.0ms (0.1%)

localize8.0ms (0.1%)

series64.0ms (1.1%)

rewrite63.0ms (1.1%)

simplify65.0ms (1.1%)

prune115.0ms (2%)

localize9.0ms (0.2%)

series130.0ms (2.3%)

rewrite77.0ms (1.3%)

simplify94.0ms (1.6%)

prune262.0ms (4.6%)

localize9.0ms (0.2%)

series136.0ms (2.4%)

rewrite78.0ms (1.4%)

simplify90.0ms (1.6%)

prune177.0ms (3.1%)

localize11.0ms (0.2%)

series78.0ms (1.3%)

rewrite70.0ms (1.2%)

simplify80.0ms (1.4%)

prune145.0ms (2.5%)

regimes1.1s (18.7%)

simplify3.0ms (0%)

end97.0ms (1.7%)

Profiling