Details

analyze341.0ms (6.4%)

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)

sample880.0ms (16.6%)

Infinites

8.3% of outputs are infinite.

Results

798.0ms

8256×

body

128

valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify112.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1405×	`fma-def_binary64`
906×	`div-sub_binary64`
613×	`distribute-rgt-in_binary64`
583×	`fma-neg_binary64`
525×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	22	14
2	43	14
3	82	14
4	164	14
5	304	14
6	655	14
7	1590	14
8	3046	14
9	2781	14
10	2954	14
11	3028	14
12	3116	14
13	4289	14
14	5187	14

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

1.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.1b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

Compiler

Compiled 56 to 29 computations (48.2% 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)

series58.0ms (1.1%)

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))

rewrite12.0ms (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:

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

simplify87.0ms (1.6%)

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

prune130.0ms (2.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	127	8	135
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	127	9	136

Error

0.0b

Counts

136 → 9

Alt Table

Status	Error	Program
	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)
	23.9b	(fma.f64 (/.f64 y a) t x)
	28.0b	(fma.f64 y (/.f64 (-.f64 (.f64 z z) (.f64 t t)) (*.f64 (-.f64 z a) (+.f64 z t))) x)
	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 1 (/.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)))
	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)
✓	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)))

Compiler

Compiled 3636 to 1213 computations (66.6% saved)

localize9.0ms (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)

series77.0ms (1.4%)

Counts

3 → 132

Calls

3 calls:

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

10.0ms	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
6.0ms	(/.f64 (-.f64 z a) (-.f64 z t))
0.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

simplify218.0ms (4.1%)

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

prune311.0ms (5.9%)

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
	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)
	23.9b	(fma.f64 (/.f64 y a) 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)))
	1.3b	(fma.f64 y (/.f64 1 (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t)))) x)
▶	1.1b	(fma.f64 y (*.f64 (/.f64 1 (-.f64 z a)) (-.f64 z t)) 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)))))

Compiler

Compiled 8804 to 2851 computations (67.6% saved)

localize8.0ms (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 (1.3%)

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))
9.0ms	(/.f64 1 (-.f64 z a))

rewrite29.0ms (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:

15.0ms	(*.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)

simplify143.0ms (2.7%)

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

prune231.0ms (4.3%)

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
	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)
	23.9b	(fma.f64 (/.f64 y a) 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)))
▶	1.3b	(fma.f64 y (/.f64 1 (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t)))) x)
✓	1.1b	(fma.f64 y (*.f64 (/.f64 1 (-.f64 z a)) (-.f64 z t)) 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)))))

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)

series253.0ms (4.8%)

Counts

4 → 144

Calls

4 calls:

151.0ms	(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))))
18.0ms	(/.f64 a (-.f64 z t))
9.0ms	(/.f64 z (-.f64 z t))

rewrite54.0ms (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))))
5.0ms	(/.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)

simplify167.0ms (3.1%)

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

prune309.0ms (5.8%)

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
	1.3b	(+.f64 (/.f64 y (-.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)
✓	1.1b	(fma.f64 y (*.f64 (/.f64 1 (-.f64 z a)) (-.f64 z t)) x)
	9.6b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))

Compiler

Compiled 13175 to 5309 computations (59.7% saved)

regimes1.7s (31.6%)

Accuracy

Total 1.1b remaining (99.1%)

Threshold costs 0b (0%)

Counts

195 → 1

Compiler

Compiled 35600 to 20644 computations (42% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	14
1	19	14
2	26	14
3	30	14
4	32	14
5	31	14

end74.0ms (1.4%)

Compiler: Compiled 139 to 70 computations (49.6% saved)

Details

analyze341.0ms (6.4%)

sample880.0ms (16.6%)

simplify112.0ms (2.1%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series58.0ms (1.1%)

rewrite12.0ms (0.2%)

simplify87.0ms (1.6%)

prune130.0ms (2.5%)

localize9.0ms (0.2%)

series77.0ms (1.4%)

rewrite40.0ms (0.8%)

simplify218.0ms (4.1%)

prune311.0ms (5.9%)

localize8.0ms (0.2%)

series67.0ms (1.3%)

rewrite29.0ms (0.5%)

simplify143.0ms (2.7%)

prune231.0ms (4.3%)

localize10.0ms (0.2%)

series253.0ms (4.8%)

rewrite54.0ms (1%)

simplify167.0ms (3.1%)

prune309.0ms (5.8%)

regimes1.7s (31.6%)

simplify2.0ms (0%)

end74.0ms (1.4%)

Profiling