Details

analyze1.3s (24.5%)

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
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
16.5%	83.2%	0.2%	13
25.9%	73.9%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.1s (21.8%)

Results

1.0s	8256×	body	128	valid
90.0ms	785×	body	128	invalid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify27.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

726×	`fma-def_binary64`
585×	`fma-neg_binary64`
512×	`div-sub_binary64`
345×	`times-frac_binary64`
287×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	40	14
3	84	14
4	185	14
5	371	14
6	871	14
7	2142	14

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
▶	4.3b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	11.8b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 a z))
✓	4.3b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

series48.0ms (0.9%)

Counts

2 → 84

Calls

2 calls:

32.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
16.0ms	(/.f64 t (-.f64 a z))

rewrite51.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

805×	`prod-diff_binary64`
218×	`log1p-udef_binary64`
119×	`add-sqr-sqrt_binary64`
113×	`log1p-expm1-u_binary64`
113×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	223	21
2	3231	21

Stop Event

1×	node limit

Counts

2 → 58

Calls

2 calls:

50.0ms	(/.f64 t (-.f64 a z))
50.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

simplify51.0ms (1%)

Algorithm

1×	egg-herbie

Rules

636×	`times-frac_binary64`
600×	`fma-def_binary64`
499×	`associate-/l*_binary64`
262×	`cancel-sign-sub-inv_binary64`
247×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	2438
1	374	2438
2	1413	2037

Stop Event

1×	node limit

Counts

142 → 115

prune92.0ms (1.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	110	5	115
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	111	6	117

Error

Counts

117 → 6

Alt Table

Status	Error	Program
	11.8b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
	27.3b	(-.f64 (fma.f64 (/.f64 y a) t x) (*.f64 (/.f64 t a) z))
	4.6b	(fma.f64 (-.f64 y z) (pow.f64 (/.f64 (-.f64 a z) t) -1) x)
	4.8b	(fma.f64 (-.f64 y z) (.f64 (pow.f64 (cbrt.f64 t) 2) (.f64 (cbrt.f64 t) (/.f64 1 (-.f64 a z)))) x)
	4.4b	(fma.f64 (-.f64 y z) (*.f64 t (/.f64 1 (-.f64 a z))) x)
▶	1.4b	(+.f64 x (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))

Compiler

Compiled 2525 to 846 computations (66.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))
✓	0.0b	(/.f64 z (-.f64 a z))
✓	0.0b	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
✓	2.1b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))

series111.0ms (2.1%)

Counts

4 → 147

Calls

4 calls:

42.0ms	(+.f64 x (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))
40.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
22.0ms	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
7.0ms	(/.f64 z (-.f64 a z))

rewrite82.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

276×	`log1p-udef_binary64`
157×	`egg-rr`
150×	`add-sqr-sqrt_binary64`
145×	`log1p-expm1-u_binary64`
145×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	46
1	283	44
2	4605	44

Stop Event

1×	node limit

Counts

4 → 157

Calls

4 calls:

73.0ms	(+.f64 x (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))
73.0ms	(/.f64 z (-.f64 a z))
73.0ms	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
73.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))

simplify80.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

793×	`cancel-sign-sub-inv_binary64`
756×	`times-frac_binary64`
437×	`sub-neg_binary64`
216×	`associate--l+_binary64`
187×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	212	4678
1	689	4651
2	2447	4462

Stop Event

1×	node limit

Counts

304 → 285

prune228.0ms (4.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	284	1	285
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	286	5	291

Error

Counts

291 → 5

Alt Table

Status	Error	Program
	4.6b	(+.f64 x (-.f64 (/.f64 t (/.f64 (-.f64 a z) y)) (*.f64 (/.f64 t (-.f64 a z)) z)))
	11.8b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
	4.6b	(fma.f64 (-.f64 y z) (pow.f64 (/.f64 (-.f64 a z) t) -1) x)
▶	4.4b	(fma.f64 (-.f64 y z) (*.f64 t (/.f64 1 (-.f64 a z))) x)
✓	1.4b	(+.f64 x (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))

Compiler

Compiled 7289 to 2412 computations (66.9% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 a z))
✓	0.2b	(*.f64 t (/.f64 1 (-.f64 a z)))
✓	4.3b	(fma.f64 (-.f64 y z) (*.f64 t (/.f64 1 (-.f64 a z))) x)

series52.0ms (1%)

Counts

3 → 120

Calls

3 calls:

31.0ms	(fma.f64 (-.f64 y z) (*.f64 t (/.f64 1 (-.f64 a z))) x)
14.0ms	(*.f64 t (/.f64 1 (-.f64 a z)))
6.0ms	(/.f64 1 (-.f64 a z))

rewrite54.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

801×	`prod-diff_binary64`
133×	`add-sqr-sqrt_binary64`
125×	`add-cbrt-cube_binary64`
125×	`log1p-expm1-u_binary64`
125×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	259	28
2	3514	28

Stop Event

1×	node limit

Counts

3 → 74

Calls

3 calls:

53.0ms	(/.f64 1 (-.f64 a z))
53.0ms	(*.f64 t (/.f64 1 (-.f64 a z)))
53.0ms	(fma.f64 (-.f64 y z) (*.f64 t (/.f64 1 (-.f64 a z))) x)

simplify52.0ms (1%)

Algorithm

1×	egg-herbie

Rules

670×	`fma-def_binary64`
662×	`times-frac_binary64`
527×	`associate-/l*_binary64`
274×	`cancel-sign-sub-inv_binary64`
163×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	142	3014
1	426	2996
2	1608	2549

Stop Event

1×	node limit

Counts

194 → 145

prune97.0ms (1.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	145	5	150

Error

Counts

150 → 5

Alt Table

Status	Error	Program
▶	4.6b	(+.f64 x (-.f64 (/.f64 t (/.f64 (-.f64 a z) y)) (*.f64 (/.f64 t (-.f64 a z)) z)))
	11.8b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
	4.6b	(fma.f64 (-.f64 y z) (pow.f64 (/.f64 (-.f64 a z) t) -1) x)
✓	4.4b	(fma.f64 (-.f64 y z) (*.f64 t (/.f64 1 (-.f64 a z))) x)
✓	1.4b	(+.f64 x (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))

Compiler

Compiled 2966 to 1057 computations (64.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (-.f64 (/.f64 t (/.f64 (-.f64 a z) y)) (*.f64 (/.f64 t (-.f64 a z)) z)))
✓	0.0b	(/.f64 (-.f64 a z) y)
✓	7.1b	(/.f64 t (/.f64 (-.f64 a z) y))
✓	10.6b	(*.f64 (/.f64 t (-.f64 a z)) z)

series98.0ms (1.9%)

Counts

4 → 172

Calls

4 calls:

42.0ms	(+.f64 x (-.f64 (/.f64 t (/.f64 (-.f64 a z) y)) (*.f64 (/.f64 t (-.f64 a z)) z)))
25.0ms	(/.f64 t (/.f64 (-.f64 a z) y))
20.0ms	(*.f64 (/.f64 t (-.f64 a z)) z)
11.0ms	(/.f64 (-.f64 a z) y)

rewrite44.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

167×	`add-sqr-sqrt_binary64`
161×	`log1p-expm1-u_binary64`
161×	`expm1-log1p-u_binary64`
160×	`add-cbrt-cube_binary64`
155×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	52
1	315	43

Stop Event

1×	node limit

Counts

4 → 138

Calls

4 calls:

41.0ms	(+.f64 x (-.f64 (/.f64 t (/.f64 (-.f64 a z) y)) (*.f64 (/.f64 t (-.f64 a z)) z)))
41.0ms	(/.f64 (-.f64 a z) y)
41.0ms	(/.f64 t (/.f64 (-.f64 a z) y))
41.0ms	(*.f64 (/.f64 t (-.f64 a z)) z)

simplify63.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

678×	`fma-def_binary64`
631×	`times-frac_binary64`
490×	`associate-/l*_binary64`
376×	`cancel-sign-sub-inv_binary64`
172×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	3836
1	474	3836
2	1817	3154

Stop Event

1×	node limit

Counts

310 → 224

prune160.0ms (3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	224	0	224
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	224	5	229

Error

Counts

229 → 5

Alt Table

Status	Error	Program
✓	4.6b	(+.f64 x (-.f64 (/.f64 t (/.f64 (-.f64 a z) y)) (*.f64 (/.f64 t (-.f64 a z)) z)))
	11.8b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
	4.6b	(fma.f64 (-.f64 y z) (pow.f64 (/.f64 (-.f64 a z) t) -1) x)
✓	4.4b	(fma.f64 (-.f64 y z) (*.f64 t (/.f64 1 (-.f64 a z))) x)
✓	1.4b	(+.f64 x (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))

Compiler

Compiled 5452 to 1496 computations (72.6% saved)

regimes1.3s (24.9%)

Accuracy

Total 0.3b remaining (96.7%)

Threshold costs 0.3b (96.7%)

Counts

147 → 3

Compiler

Compiled 17915 to 11433 computations (36.2% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	80
1	32	80
2	37	80
3	39	80
4	40	80

Stop Event

1×

saturated

end80.0ms (1.5%)

Compiler: Compiled 212 to 95 computations (55.2% saved)

Details

analyze1.3s (24.5%)

sample1.1s (21.8%)

simplify27.0ms (0.5%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series48.0ms (0.9%)

rewrite51.0ms (1%)

simplify51.0ms (1%)

prune92.0ms (1.7%)

localize10.0ms (0.2%)

series111.0ms (2.1%)

rewrite82.0ms (1.5%)

simplify80.0ms (1.5%)

prune228.0ms (4.3%)

localize9.0ms (0.2%)

series52.0ms (1%)

rewrite54.0ms (1%)

simplify52.0ms (1%)

prune97.0ms (1.8%)

localize12.0ms (0.2%)

series98.0ms (1.9%)

rewrite44.0ms (0.8%)

simplify63.0ms (1.2%)

prune160.0ms (3%)

regimes1.3s (24.9%)

bsearch4.0ms (0.1%)

simplify5.0ms (0.1%)

end80.0ms (1.5%)

Profiling