Details

analyze1.6s (25.7%)

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
22.6%	77.2%	0.2%	14

Compiler

Compiled 19 to 14 computations (26.3% saved)

sample1.2s (20.1%)

Results

1.1s	8112×	body	128	valid
81.0ms	661×	body	128	invalid
22.0ms	59×	body	1024	valid
17.0ms	27×	body	2048	valid
14.0ms	33×	body	512	valid
5.0ms	23×	body	256	valid
1.0ms	2×	body	4096	valid

Compiler

Compiled 38 to 28 computations (26.3% saved)

preprocess46.0ms (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)

simplify23.0ms (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

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.4b	(+.f64 (/.f64 (.f64 60 (-.f64 x y)) (-.f64 z t)) (.f64 a 120))
▶	0.2b	(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%)

Counts

2 → 108

Calls

27 calls:

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

rewrite57.0ms (0.9%)

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

simplify70.0ms (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

prune125.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	117	7	124
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	118	8	126

Error

0.0b

Counts

126 → 8

Alt Table

Status	Error	Program
	0.2b	(+.f64 (*.f64 a 120) (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
	0.4b	(+.f64 (/.f64 (.f64 60 (-.f64 x y)) (-.f64 z t)) (.f64 a 120))
▶	0.1b	(fma.f64 120 a (*.f64 60 (-.f64 (/.f64 x (-.f64 z t)) (/.f64 y (-.f64 z t)))))
	29.9b	(fma.f64 60 (.f64 (/.f64 (sqrt.f64 (-.f64 x y)) 1) (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z t))) (.f64 a 120))
	0.3b	(fma.f64 60 (.f64 (-.f64 x y) (/.f64 1 (-.f64 z t))) (.f64 a 120))
	1.4b	(pow.f64 (cbrt.f64 (fma.f64 60 (/.f64 (-.f64 x y) (-.f64 z t)) (*.f64 a 120))) 3)
	37.6b	(/.f64 (+.f64 (pow.f64 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))) 3) (pow.f64 (.f64 a 120) 3)) (+.f64 (.f64 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))) (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y)))) (-.f64 (.f64 14400 (.f64 a a)) (.f64 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))) (.f64 a 120)))))
	0.2b	(.f64 (fma.f64 60 (/.f64 (-.f64 x y) (-.f64 z t)) (.f64 a 120)) 1)

Compiler

Compiled 3463 to 1696 computations (51% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 z t))
✓	0.0b	(/.f64 y (-.f64 z t))
✓	0.0b	(fma.f64 120 a (*.f64 60 (-.f64 (/.f64 x (-.f64 z t)) (/.f64 y (-.f64 z t)))))
✓	0.2b	(*.f64 60 (-.f64 (/.f64 x (-.f64 z t)) (/.f64 y (-.f64 z t))))

series129.0ms (2.1%)

Counts

4 → 156

Calls

45 calls:

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

rewrite75.0ms (1.2%)

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	44
1	317	44
2	4672	44

Stop Event

1×	node limit

Counts

4 → 114

simplify93.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

723×	`times-frac_binary64`
578×	`cancel-sign-sub-inv_binary64`
307×	`sub-neg_binary64`
200×	`fma-def_binary64`
183×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	4823
1	674	4647
2	2432	4200

Stop Event

1×	node limit

Counts

270 → 195

prune200.0ms (3.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	192	3	195
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	197	6	203

Error

0.0b

Counts

203 → 6

Alt Table

Status	Error	Program
	0.2b	(+.f64 (*.f64 a 120) (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
	26.9b	(/.f64 (-.f64 (.f64 (.f64 120 a) (.f64 120 a)) (.f64 3600 (pow.f64 (/.f64 (-.f64 x y) (-.f64 z t)) 2))) (-.f64 (.f64 120 a) (/.f64 (.f64 60 (-.f64 x y)) (-.f64 z t))))
	33.1b	(fma.f64 120 a (/.f64 (.f64 (-.f64 (pow.f64 (/.f64 x (-.f64 z t)) 3) (pow.f64 (/.f64 y (-.f64 z t)) 3)) 60) (+.f64 (pow.f64 (/.f64 x (-.f64 z t)) 2) (.f64 (/.f64 y (-.f64 z t)) (*.f64 (/.f64 1 (-.f64 z t)) (+.f64 x y))))))
	0.4b	(fma.f64 120 a (/.f64 (*.f64 (-.f64 x y) 60) (-.f64 z t)))
	29.9b	(fma.f64 60 (.f64 (/.f64 (sqrt.f64 (-.f64 x y)) 1) (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z t))) (.f64 a 120))
▶	0.2b	(.f64 (fma.f64 60 (/.f64 (-.f64 x y) (-.f64 z t)) (.f64 a 120)) 1)

Compiler

Compiled 5191 to 2527 computations (51.3% saved)

localize10.0ms (0.2%)

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))

prune122.0ms (2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	124	6	130

Error

0.0b

Counts

130 → 6

Alt Table

Status	Error	Program
▶	0.2b	(+.f64 (*.f64 a 120) (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
	26.9b	(/.f64 (-.f64 (.f64 (.f64 120 a) (.f64 120 a)) (.f64 3600 (pow.f64 (/.f64 (-.f64 x y) (-.f64 z t)) 2))) (-.f64 (.f64 120 a) (/.f64 (.f64 60 (-.f64 x y)) (-.f64 z t))))
	33.1b	(fma.f64 120 a (/.f64 (.f64 (-.f64 (pow.f64 (/.f64 x (-.f64 z t)) 3) (pow.f64 (/.f64 y (-.f64 z t)) 3)) 60) (+.f64 (pow.f64 (/.f64 x (-.f64 z t)) 2) (.f64 (/.f64 y (-.f64 z t)) (*.f64 (/.f64 1 (-.f64 z t)) (+.f64 x y))))))
	0.4b	(fma.f64 120 a (/.f64 (*.f64 (-.f64 x y) 60) (-.f64 z t)))
	29.9b	(fma.f64 60 (.f64 (/.f64 (sqrt.f64 (-.f64 x y)) 1) (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z t))) (.f64 a 120))
✓	0.2b	(.f64 (fma.f64 60 (/.f64 (-.f64 x y) (-.f64 z t)) (.f64 a 120)) 1)

Compiler

Compiled 3620 to 1880 computations (48.1% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 x y))
✓	0.0b	(+.f64 (*.f64 a 120) (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
✓	0.5b	(/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y)))

series128.0ms (2.1%)

Counts

3 → 156

Calls

39 calls:

12.0ms	(/.f64 (-.f64 z t) (-.f64 x y))	x	inf
6.0ms	(+.f64 (*.f64 a 120) (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))	t	-inf
6.0ms	(+.f64 (*.f64 a 120) (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))	z	0
6.0ms	(/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y)))	t	0
6.0ms	(+.f64 (*.f64 a 120) (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))	a	inf

rewrite75.0ms (1.2%)

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

simplify93.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	206	5147
1	757	4968
2	2928	4707

Stop Event

1×	node limit

Counts

262 → 171

prune162.0ms (2.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	172	5	177

Error

Counts

177 → 5

Alt Table

Status	Error	Program
	0.2b	(fma.f64 (/.f64 60 (-.f64 z t)) (-.f64 x y) (*.f64 a 120))
	26.9b	(/.f64 (-.f64 (.f64 (.f64 120 a) (.f64 120 a)) (.f64 3600 (pow.f64 (/.f64 (-.f64 x y) (-.f64 z t)) 2))) (-.f64 (.f64 120 a) (/.f64 (.f64 60 (-.f64 x y)) (-.f64 z t))))
	0.4b	(fma.f64 120 a (/.f64 (*.f64 (-.f64 x y) 60) (-.f64 z t)))
	0.2b	(+.f64 (.f64 a 120) (pow.f64 (.f64 (/.f64 (-.f64 z t) (-.f64 x y)) 1/60) -1))
✓	0.2b	(.f64 (fma.f64 60 (/.f64 (-.f64 x y) (-.f64 z t)) (.f64 a 120)) 1)

Compiler

Compiled 4578 to 2435 computations (46.8% saved)

regimes1.7s (28.1%)

Accuracy

Total 0.1b remaining (93.7%)

Threshold costs 0.1b (93.7%)

Counts

114 → 1

Compiler

Compiled 30400 to 21052 computations (30.8% saved)

simplify3.0ms (0.1%)

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

end90.0ms (1.5%)

Stop Event

1×

fuel

Compiler

Compiled 153 to 104 computations (32% saved)

Details

analyze1.6s (25.7%)

sample1.2s (20.1%)

preprocess46.0ms (0.7%)

simplify23.0ms (0.4%)

prune5.0ms (0.1%)

localize8.0ms (0.1%)

series64.0ms (1%)

rewrite57.0ms (0.9%)

simplify70.0ms (1.1%)

prune125.0ms (2%)

localize9.0ms (0.1%)

series129.0ms (2.1%)

rewrite75.0ms (1.2%)

simplify93.0ms (1.5%)

prune200.0ms (3.3%)

localize10.0ms (0.2%)

prune122.0ms (2%)

localize10.0ms (0.2%)

series128.0ms (2.1%)

rewrite75.0ms (1.2%)

simplify93.0ms (1.5%)

prune162.0ms (2.6%)

regimes1.7s (28.1%)

simplify3.0ms (0.1%)

end90.0ms (1.5%)

Profiling