Details

analyze295.0ms (6.1%)

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
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
49.9%	49.9%	0.2%	8
49.9%	49.9%	0.2%	9
49.9%	49.9%	0.2%	10
74.8%	24.9%	0.2%	11
74.8%	24.9%	0.2%	12
74.8%	24.9%	0.2%	13
74.8%	24.9%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample834.0ms (17.1%)

Infinites

8.3% of outputs are infinite.

Results

759.0ms

8256×

body

128

valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify110.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1691×	`fma-neg_binary64`
841×	`div-sub_binary64`
807×	`distribute-rgt-in_binary64`
769×	`fma-def_binary64`
504×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	19	16
2	40	14
3	82	14
4	166	14
5	297	14
6	643	14
7	1551	14
8	3111	14
9	3064	14
10	3153	14
11	3152	14
12	3170	14
13	3201	14
14	5494	14

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
▶	1.1b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	9.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))

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 (-.f64 z t) (-.f64 z a))
✓	1.1b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

series59.0ms (1.2%)

Counts

2 → 96

Calls

2 calls:

39.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
19.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

2 → 64

Calls

2 calls:

6.0ms	(/.f64 (-.f64 z t) (-.f64 z a))
0.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

simplify84.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

878×	`fma-def_binary64`
685×	`times-frac_binary64`
505×	`cancel-sign-sub-inv_binary64`
356×	`sub-neg_binary64`
161×	`+-commutative_binary64`

Counts

160 → 135

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	271	4135
1	699	4064
2	2396	3758
3	5075	3758

prune121.0ms (2.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	127	8	135
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	128	9	137

Error

0.0b

Counts

137 → 9

Alt Table

Status	Error	Program
	28.0b	(fma.f64 y (/.f64 (-.f64 (.f64 z z) (.f64 t t)) (*.f64 (-.f64 z a) (+.f64 z t))) x)
	2.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))
▶	1.1b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
	23.9b	(fma.f64 (/.f64 y a) t x)
✓	1.1b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	9.6b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
	40.1b	(-.f64 (+.f64 (fma.f64 (/.f64 a (/.f64 z a)) (/.f64 y z) (fma.f64 (/.f64 a z) y y)) x) (fma.f64 (/.f64 (.f64 y a) z) (/.f64 t z) (fma.f64 (/.f64 y z) t (/.f64 (.f64 y (.f64 a (.f64 a t))) (pow.f64 z 3)))))
	1.4b	(fma.f64 y (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z a)))) x)
	21.3b	(fma.f64 y (*.f64 (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) x)

Compiler

Compiled 3636 to 1213 computations (66.6% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z a) (-.f64 z t))
✓	0.2b	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
✓	1.1b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

series78.0ms (1.6%)

Counts

3 → 132

Calls

3 calls:

39.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
20.0ms	(/.f64 (-.f64 z a) (-.f64 z t))
19.0ms	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))

rewrite40.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
195×	`*-un-lft-identity_binary64`
195×	`add-sqr-sqrt_binary64`
91×	`add-cube-cbrt_binary64`
52×	`distribute-lft-out--_binary64`

Counts

3 → 214

Calls

3 calls:

9.0ms	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
8.0ms	(/.f64 (-.f64 z a) (-.f64 z t))
0.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

simplify169.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

709×	`cancel-sign-sub-inv_binary64`
528×	`sub-neg_binary64`
232×	`fma-neg_binary64`
224×	`associate--l+_binary64`
221×	`+-commutative_binary64`

Counts

346 → 336

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	403	8765
1	1010	8314
2	3667	8134
3	5378	8134

prune307.0ms (6.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	334	2	336
Fresh	2	5	7
Picked	1	0	1
Done	1	0	1
Total	338	7	345

Error

0.0b

Counts

345 → 7

Alt Table

Status	Error	Program
	40.1b	(-.f64 (+.f64 (fma.f64 (/.f64 a (/.f64 z a)) (/.f64 y z) (fma.f64 (/.f64 a z) y y)) x) (fma.f64 (/.f64 (.f64 y a) z) (/.f64 t z) (fma.f64 (/.f64 y z) t (/.f64 (.f64 y (.f64 a (.f64 a t))) (pow.f64 z 3)))))
▶	1.1b	(fma.f64 y (*.f64 (/.f64 1 (-.f64 z a)) (-.f64 z t)) x)
	1.4b	(fma.f64 y (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z a)))) x)
	1.3b	(fma.f64 y (/.f64 1 (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t)))) x)
	2.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))
	23.9b	(fma.f64 (/.f64 y a) t x)
	9.6b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))

Compiler

Compiled 8804 to 2851 computations (67.6% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 z a))
✓	0.2b	(*.f64 (/.f64 1 (-.f64 z a)) (-.f64 z t))
✓	1.1b	(fma.f64 y (*.f64 (/.f64 1 (-.f64 z a)) (-.f64 z t)) x)

series67.0ms (1.4%)

Counts

3 → 120

Calls

3 calls:

38.0ms	(fma.f64 y (*.f64 (/.f64 1 (-.f64 z a)) (-.f64 z t)) x)
19.0ms	(*.f64 (/.f64 1 (-.f64 z a)) (-.f64 z t))
10.0ms	(/.f64 1 (-.f64 z a))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`add-sqr-sqrt_binary64`
54×	`*-un-lft-identity_binary64`
37×	`add-cube-cbrt_binary64`
32×	`times-frac_binary64`
21×	`associate-l_binary64`

Counts

3 → 130

Calls

3 calls:

11.0ms	(*.f64 (/.f64 1 (-.f64 z a)) (-.f64 z t))
4.0ms	(/.f64 1 (-.f64 z a))
0.0ms	(fma.f64 y (*.f64 (/.f64 1 (-.f64 z a)) (-.f64 z t)) x)

simplify141.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

555×	`cancel-sign-sub-inv_binary64`
363×	`sub-neg_binary64`
269×	`fma-neg_binary64`
203×	`associate-r_binary64`
190×	`associate-l_binary64`

Counts

250 → 257

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	368	5646
1	863	5179
2	3351	4969
3	4847	4968
4	4962	4968

prune236.0ms (4.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	257	0	257
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	257	7	264

Error

0.0b

Counts

264 → 7

Alt Table

Status	Error	Program
	40.1b	(-.f64 (+.f64 (fma.f64 (/.f64 a (/.f64 z a)) (/.f64 y z) (fma.f64 (/.f64 a z) y y)) x) (fma.f64 (/.f64 (.f64 y a) z) (/.f64 t z) (fma.f64 (/.f64 y z) t (/.f64 (.f64 y (.f64 a (.f64 a t))) (pow.f64 z 3)))))
✓	1.1b	(fma.f64 y (*.f64 (/.f64 1 (-.f64 z a)) (-.f64 z t)) x)
	1.4b	(fma.f64 y (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z a)))) x)
▶	1.3b	(fma.f64 y (/.f64 1 (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t)))) x)
	2.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))
	23.9b	(fma.f64 (/.f64 y a) t x)
	9.6b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))

Compiler

Compiled 6455 to 2369 computations (63.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 a (-.f64 z t))
✓	0.0b	(/.f64 z (-.f64 z t))
✓	0.2b	(/.f64 1 (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t))))
✓	1.1b	(fma.f64 y (/.f64 1 (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t)))) x)

series251.0ms (5.1%)

Counts

4 → 144

Calls

4 calls:

150.0ms	(fma.f64 y (/.f64 1 (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t)))) x)
75.0ms	(/.f64 1 (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t))))
17.0ms	(/.f64 a (-.f64 z t))
9.0ms	(/.f64 z (-.f64 z t))

rewrite53.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

175×	`*-un-lft-identity_binary64`
156×	`times-frac_binary64`
135×	`add-sqr-sqrt_binary64`
56×	`distribute-lft-out--_binary64`
55×	`add-cube-cbrt_binary64`

Counts

4 → 185

Calls

4 calls:

24.0ms	(/.f64 1 (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t))))
4.0ms	(/.f64 z (-.f64 z t))
4.0ms	(/.f64 a (-.f64 z t))
0.0ms	(fma.f64 y (/.f64 1 (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t)))) x)

simplify165.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

907×	`associate-/l*_binary64`
309×	`fma-def_binary64`
227×	`+-commutative_binary64`
195×	`associate-/r/_binary64`
182×	`sub-neg_binary64`

Counts

329 → 332

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	804	11377
1	2483	11043
2	5105	11043

prune296.0ms (6.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	331	1	332
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	334	5	339

Error

0.0b

Counts

339 → 5

Alt Table

Status	Error	Program
	2.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))
	1.3b	(+.f64 (/.f64 y (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t)))) x)
	23.9b	(fma.f64 (/.f64 y a) t x)
	9.6b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
✓	1.1b	(fma.f64 y (*.f64 (/.f64 1 (-.f64 z a)) (-.f64 z t)) x)

Compiler

Compiled 13175 to 5309 computations (59.7% saved)

regimes1.4s (29.3%)

Accuracy

Total 1.1b remaining (99.1%)

Threshold costs 0b (0%)

Counts

193 → 1

Compiler

Compiled 30872 to 17901 computations (42% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	15	20
2	25	20
3	31	20
4	35	20
5	36	20
6	36	20

end69.0ms (1.4%)

Compiler: Compiled 147 to 72 computations (51% saved)

Details

analyze295.0ms (6.1%)

sample834.0ms (17.1%)

simplify110.0ms (2.2%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series59.0ms (1.2%)

rewrite11.0ms (0.2%)

simplify84.0ms (1.7%)

prune121.0ms (2.5%)

localize8.0ms (0.2%)

series78.0ms (1.6%)

rewrite40.0ms (0.8%)

simplify169.0ms (3.5%)

prune307.0ms (6.3%)

localize9.0ms (0.2%)

series67.0ms (1.4%)

rewrite24.0ms (0.5%)

simplify141.0ms (2.9%)

prune236.0ms (4.8%)

localize10.0ms (0.2%)

series251.0ms (5.1%)

rewrite53.0ms (1.1%)

simplify165.0ms (3.4%)

prune296.0ms (6.1%)

regimes1.4s (29.3%)

simplify3.0ms (0.1%)

end69.0ms (1.4%)

Profiling