Details

analyze1.2s (13.5%)

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
4.7%	95.1%	0.2%	10
12.7%	87.1%	0.2%	11
15.9%	83.9%	0.2%	12
18.4%	81.3%	0.2%	13
29.5%	70.3%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample28.0ms (0.3%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
1.0ms	23×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify121.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1893×	`fma-neg_binary64`
867×	`div-sub_binary64`
749×	`fma-def_binary64`
696×	`distribute-rgt-in_binary64`
535×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	40	14
3	81	14
4	160	14
5	302	14
6	620	14
7	1528	14
8	2624	14
9	2858	14
10	3205	14
11	3392	14
12	3498	14
13	3533	14
14	5398	14

prune4.0ms (0%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	3.4b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	7.9b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 a z))
✓	3.3b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`associate-/r*_binary64`

Counts

2 → 49

Calls

2 calls:

4.0ms	(/.f64 t (-.f64 a z))
0.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

series97.0ms (1.1%)

Counts

2 → 84

Calls

2 calls:

69.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
28.0ms	(/.f64 t (-.f64 a z))

simplify84.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

690×	`times-frac_binary64`
633×	`fma-def_binary64`
620×	`associate-/l*_binary64`
272×	`cancel-sign-sub-inv_binary64`
175×	`associate-/l/_binary64`

Counts

133 → 222

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	198	3215
1	492	3156
2	1711	2520
3	5110	2520

prune81.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	219	3	222
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	220	4	224

Error

0.0b

Counts

224 → 4

Alt Table

Status	Error	Program
✓	3.4b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
▶	1.6b	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
	7.9b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
	3.7b	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) t)) x)

Compiler

Compiled 2369 to 743 computations (68.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 z (-.f64 a z))
✓	0.0b	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
✓	0.0b	(/.f64 y (-.f64 a z))
✓	2.7b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))

rewrite355.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Rules

2048×	`*-un-lft-identity_binary64`
2030×	`add-sqr-sqrt_binary64`
2016×	`times-frac_binary64`
1323×	`prod-diff_binary64`
1200×	`add-cube-cbrt_binary64`

Counts

4 → 1556

Calls

4 calls:

53.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
35.0ms	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
4.0ms	(/.f64 y (-.f64 a z))
4.0ms	(/.f64 z (-.f64 a z))

series152.0ms (1.7%)

Counts

4 → 111

Calls

4 calls:

84.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
32.0ms	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
28.0ms	(/.f64 y (-.f64 a z))
7.0ms	(/.f64 z (-.f64 a z))

simplify2.2s (23.7%)

Algorithm

1×	egg-herbie

Rules

422×	`*-commutative_binary64`
357×	`distribute-rgt-in_binary64`
306×	`fma-udef_binary64`
263×	`unsub-neg_binary64`
251×	`distribute-lft-in_binary64`

Counts

1667 → 3207

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1400	120634
1	2426	87989
2	4585	87650
3	5024	87650

prune1.4s (15.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	3206	1	3207
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	3206	5	3211

Error

Counts

3211 → 5

Alt Table

Status	Error	Program
✓	3.4b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
✓	1.6b	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
	7.9b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
	11.3b	(+.f64 (/.f64 (.f64 t (-.f64 (.f64 (/.f64 y (-.f64 a z)) (/.f64 y (-.f64 a z))) (*.f64 (/.f64 z (-.f64 a z)) (/.f64 z (-.f64 a z))))) (+.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
▶	3.7b	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) t)) x)

Compiler

Compiled 96324 to 16692 computations (82.7% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 a z) t)
✓	0.6b	(/.f64 1 (/.f64 (-.f64 a z) t))
✓	3.3b	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) t)) x)

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

132×	`times-frac_binary64`
101×	`*-un-lft-identity_binary64`
101×	`add-sqr-sqrt_binary64`
69×	`add-cube-cbrt_binary64`
22×	`associate-/r*_binary64`

Counts

3 → 152

Calls

3 calls:

7.0ms	(/.f64 1 (/.f64 (-.f64 a z) t))
5.0ms	(/.f64 (-.f64 a z) t)
0.0ms	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) t)) x)

series119.0ms (1.3%)

Counts

3 → 124

Calls

3 calls:

66.0ms	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) t)) x)
27.0ms	(/.f64 (-.f64 a z) t)
26.0ms	(/.f64 1 (/.f64 (-.f64 a z) t))

simplify283.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

748×	`fma-def_binary64`
289×	`cancel-sign-sub-inv_binary64`
249×	`associate-/l/_binary64`
217×	`fma-neg_binary64`
206×	`distribute-rgt-in_binary64`

Counts

276 → 492

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	257	5419
1	622	5057
2	2193	4377
3	4627	4377
4	5157	4377

prune185.0ms (2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	492	0	492
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	492	5	497

Error

Counts

497 → 5

Alt Table

Status	Error	Program
✓	3.4b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
✓	1.6b	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
▶	7.9b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
	11.3b	(+.f64 (/.f64 (.f64 t (-.f64 (.f64 (/.f64 y (-.f64 a z)) (/.f64 y (-.f64 a z))) (*.f64 (/.f64 z (-.f64 a z)) (/.f64 z (-.f64 a z))))) (+.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
✓	3.7b	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) t)) x)

Compiler

Compiled 5502 to 1728 computations (68.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (*.f64 y t) (-.f64 a z)) x)
✓	0.0b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
✓	3.6b	(/.f64 (*.f64 y t) (-.f64 a z))
✓	9.0b	(/.f64 (*.f64 t z) (-.f64 a z))

rewrite48.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

83×	`*-un-lft-identity_binary64`
54×	`add-sqr-sqrt_binary64`
44×	`prod-diff_binary64`
40×	`times-frac_binary64`
32×	`add-cube-cbrt_binary64`

Counts

4 → 162

Calls

4 calls:

15.0ms	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
10.0ms	(+.f64 (/.f64 (*.f64 y t) (-.f64 a z)) x)
6.0ms	(/.f64 (*.f64 t z) (-.f64 a z))
5.0ms	(/.f64 (*.f64 y t) (-.f64 a z))

series273.0ms (3%)

Counts

4 → 144

Calls

4 calls:

91.0ms	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
84.0ms	(+.f64 (/.f64 (*.f64 y t) (-.f64 a z)) x)
65.0ms	(/.f64 (*.f64 y t) (-.f64 a z))
33.0ms	(/.f64 (*.f64 t z) (-.f64 a z))

simplify236.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

373×	`fma-neg_binary64`
296×	`sub-neg_binary64`
224×	`associate-/l*_binary64`
191×	`times-frac_binary64`
174×	`associate-l_binary64`

Counts

306 → 552

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	382	8802
1	1080	7597
2	3913	7022
3	4564	7021
4	4834	7021

prune213.0ms (2.3%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	552	0	552
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	552	5	557

Error

Counts

557 → 5

Alt Table

Status	Error	Program
✓	3.4b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
✓	1.6b	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
✓	7.9b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
	11.3b	(+.f64 (/.f64 (.f64 t (-.f64 (.f64 (/.f64 y (-.f64 a z)) (/.f64 y (-.f64 a z))) (*.f64 (/.f64 z (-.f64 a z)) (/.f64 z (-.f64 a z))))) (+.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
✓	3.7b	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) t)) x)

Compiler

Compiled 9478 to 1774 computations (81.3% saved)

regimes1.1s (12.1%)

Accuracy

Total 0.6b remaining (98.2%)

Threshold costs 0.6b (98.2%)

Compiler

Compiled 13302 to 7940 computations (40.3% saved)

bsearch35.0ms (0.4%)

Steps

Iters	Range		Point
6	2.0482063190407343e-140	7.583359324609944e-139	6.335412352147459e-139
7	-3.55999717036573e-76	-1.4269412657846431e-77	-1.6302512175718477e-77

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
9×	`*-commutative_binary64`
9×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	75
1	43	75
2	58	75
3	71	75
4	78	75
5	81	75
6	82	75
7	82	75

end1.0ms (0%)

Compiler: Compiled 56 to 27 computations (51.8% saved)

sample852.0ms (9.4%)

Algorithm

1×

intervals

Results

372.0ms	7998×	body	128	valid
34.0ms	737×	body	128	invalid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 196 to 101 computations (48.5% saved)

Details

analyze1.2s (13.5%)

sample28.0ms (0.3%)

simplify121.0ms (1.3%)

prune4.0ms (0%)

localize8.0ms (0.1%)

rewrite6.0ms (0.1%)

series97.0ms (1.1%)

simplify84.0ms (0.9%)

prune81.0ms (0.9%)

localize9.0ms (0.1%)

rewrite355.0ms (3.9%)

series152.0ms (1.7%)

simplify2.2s (23.7%)

prune1.4s (15.2%)

localize9.0ms (0.1%)

rewrite22.0ms (0.2%)

series119.0ms (1.3%)

simplify283.0ms (3.1%)

prune185.0ms (2%)

localize10.0ms (0.1%)

rewrite48.0ms (0.5%)

series273.0ms (3%)

simplify236.0ms (2.6%)

prune213.0ms (2.3%)

regimes1.1s (12.1%)

bsearch35.0ms (0.4%)

simplify8.0ms (0.1%)

end1.0ms (0%)

sample852.0ms (9.4%)

Profiling