Details

analyze2.4s (20.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.6%	0.4%	0
0%	99.6%	0.4%	1
0%	99.6%	0.4%	2
0%	99.6%	0.4%	3
0%	99.6%	0.4%	4
0%	99.6%	0.4%	5
0%	99.6%	0.4%	6
0%	99.6%	0.4%	7
0%	99.6%	0.4%	8
0%	99.6%	0.4%	9
0%	99.6%	0.4%	10
0%	99.6%	0.4%	11
0%	99.6%	0.4%	12
0%	99.6%	0.4%	13
0%	99.6%	0.4%	14

Compiler

Compiled 28 to 19 computations (32.1% saved)

sample138.0ms (1.2%)

Algorithm

1×

intervals

Symmetry

(sort x y)

(sort z t)

Results

25.0ms	244×	body	128	invalid
18.0ms	256×	body	128	valid

Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify222.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1133×	`distribute-rgt-in_binary64`
1066×	`distribute-lft-in_binary64`
969×	`unsub-neg_binary64`
583×	`fma-def_binary64`
461×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	26
1	37	24
2	97	24
3	277	24
4	797	24
5	1809	24
6	2532	24
7	2783	24
8	3128	24
9	3409	24
10	3319	24
11	3327	24
12	3331	24
13	3461	24
14	3620	24
15	3621	24
16	3623	24
17	3623	24
18	5071	24

prune4.0ms (0%)

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

6.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.5b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))

Compiler

Compiled 94 to 57 computations (39.4% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x y (*.f64 z t))
✓	0.0b	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i))
✓	0.1b	(*.f64 c (fma.f64 b c a))
✓	7.8b	(.f64 (.f64 c (fma.f64 b c a)) i)

series101.0ms (0.9%)

Counts

4 → 228

Calls

4 calls:

61.0ms	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i))
20.0ms	(.f64 (.f64 c (fma.f64 b c a)) i)
11.0ms	(*.f64 c (fma.f64 b c a))
8.0ms	(fma.f64 x y (*.f64 z t))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
11×	`pow1_binary64`
9×	`*-un-lft-identity_binary64`

Counts

4 → 73

Calls

4 calls:

5.0ms	(.f64 (.f64 c (fma.f64 b c a)) i)
3.0ms	(*.f64 c (fma.f64 b c a))
3.0ms	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i))
0.0ms	(fma.f64 x y (*.f64 z t))

simplify126.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

578×	`fma-neg_binary64`
563×	`distribute-rgt-in_binary64`
556×	`distribute-lft-in_binary64`
505×	`fma-def_binary64`
242×	`cancel-sign-sub-inv_binary64`

Counts

301 → 160

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	4992
1	327	4027
2	1091	3988
3	4531	3988
4	4933	3988

prune213.0ms (1.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	152	8	160
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	153	8	161

Error

0.0b

Counts

161 → 8

Alt Table

Status	Error	Program
	9.0b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (+.f64 (.f64 (pow.f64 c 2) b) (*.f64 c a)) i)))
	34.0b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (*.f64 (fma.f64 c b a) (sqrt.f64 i))) (sqrt.f64 i))))
	11.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))
	28.7b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (sqrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)) (sqrt.f64 (.f64 (*.f64 c (fma.f64 b c a)) i)))))
▶	4.7b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (.f64 (fma.f64 c b a) (.f64 (cbrt.f64 i) (cbrt.f64 i)))) (cbrt.f64 i))))
	5.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (.f64 i (fma.f64 c b a)))))
	6.8b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (.f64 (cbrt.f64 c) (cbrt.f64 c)) (.f64 (cbrt.f64 c) (fma.f64 b c a))) i)))
	7.2b	(.f64 2 (-.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 x y (.f64 z t))) (cbrt.f64 (fma.f64 x y (.f64 z t)))) (cbrt.f64 (fma.f64 x y (.f64 z t)))) (.f64 (.f64 c (fma.f64 b c a)) i)))

Compiler

Compiled 4115 to 1175 computations (71.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 i)
✓	1.6b	(.f64 c (.f64 (fma.f64 c b a) (*.f64 (cbrt.f64 i) (cbrt.f64 i))))
✓	1.7b	(.f64 (fma.f64 c b a) (.f64 (cbrt.f64 i) (cbrt.f64 i)))
✓	2.8b	(.f64 (.f64 c (.f64 (fma.f64 c b a) (.f64 (cbrt.f64 i) (cbrt.f64 i)))) (cbrt.f64 i))

series711.0ms (6.1%)

Counts

4 → 156

Calls

4 calls:

346.0ms	(.f64 c (.f64 (fma.f64 c b a) (*.f64 (cbrt.f64 i) (cbrt.f64 i))))
299.0ms	(.f64 (fma.f64 c b a) (.f64 (cbrt.f64 i) (cbrt.f64 i)))
35.0ms	(.f64 (.f64 c (.f64 (fma.f64 c b a) (.f64 (cbrt.f64 i) (cbrt.f64 i)))) (cbrt.f64 i))
31.0ms	(cbrt.f64 i)

rewrite29.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64`
32×	`pow1_binary64`
22×	`add-cbrt-cube_binary64`
19×	`cbrt-unprod_binary64`
19×	`prod-exp_binary64`

Counts

4 → 86

Calls

4 calls:

9.0ms	(.f64 (.f64 c (.f64 (fma.f64 c b a) (.f64 (cbrt.f64 i) (cbrt.f64 i)))) (cbrt.f64 i))
6.0ms	(.f64 c (.f64 (fma.f64 c b a) (*.f64 (cbrt.f64 i) (cbrt.f64 i))))
5.0ms	(.f64 (fma.f64 c b a) (.f64 (cbrt.f64 i) (cbrt.f64 i)))
1.0ms	(cbrt.f64 i)

simplify110.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

937×	`fma-def_binary64`
720×	`*-commutative_binary64`
594×	`unswap-sqr_binary64`
569×	`distribute-rgt-in_binary64`
568×	`distribute-lft-in_binary64`

Counts

242 → 146

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	142	3940
1	320	3127
2	1276	2914
3	3374	2912
4	5331	2912

prune352.0ms (3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	182	8	190

Error

0.0b

Counts

190 → 8

Alt Table

Status	Error	Program
	11.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))
	28.7b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (sqrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)) (sqrt.f64 (.f64 (*.f64 c (fma.f64 b c a)) i)))))
▶	4.8b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (.f64 (fma.f64 c b a) (.f64 (cbrt.f64 i) (.f64 (cbrt.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i))) (cbrt.f64 (cbrt.f64 i)))))) (cbrt.f64 i))))
	34.0b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (*.f64 (fma.f64 c b a) (sqrt.f64 i))) (sqrt.f64 i))))
✓	4.7b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (.f64 (fma.f64 c b a) (.f64 (cbrt.f64 i) (cbrt.f64 i)))) (cbrt.f64 i))))
	5.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (.f64 i (fma.f64 c b a)))))
	6.8b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (.f64 (cbrt.f64 c) (cbrt.f64 c)) (.f64 (cbrt.f64 c) (fma.f64 b c a))) i)))
	7.2b	(.f64 2 (-.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 x y (.f64 z t))) (cbrt.f64 (fma.f64 x y (.f64 z t)))) (cbrt.f64 (fma.f64 x y (.f64 z t)))) (.f64 (.f64 c (fma.f64 b c a)) i)))

Compiler

Compiled 5698 to 1742 computations (69.4% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 i)
✓	1.6b	(.f64 c (.f64 (fma.f64 c b a) (.f64 (cbrt.f64 i) (.f64 (cbrt.f64 (*.f64 (cbrt.f64 i) (cbrt.f64 i))) (cbrt.f64 (cbrt.f64 i))))))
✓	1.7b	(.f64 (fma.f64 c b a) (.f64 (cbrt.f64 i) (.f64 (cbrt.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i))) (cbrt.f64 (cbrt.f64 i)))))
✓	2.8b	(.f64 (.f64 c (.f64 (fma.f64 c b a) (.f64 (cbrt.f64 i) (.f64 (cbrt.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i))) (cbrt.f64 (cbrt.f64 i)))))) (cbrt.f64 i))

series702.0ms (6%)

Counts

3 → 144

Calls

3 calls:

345.0ms

(*.f64 c (*.f64 (fma.f64 c b a) (*.f64 (cbrt.f64 i) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 i) (cbrt.f64 i))) (cbrt.f64 (cbrt.f64 i))))))

319.0ms

(*.f64 (fma.f64 c b a) (*.f64 (cbrt.f64 i) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 i) (cbrt.f64 i))) (cbrt.f64 (cbrt.f64 i)))))

37.0ms

(*.f64 (*.f64 c (*.f64 (fma.f64 c b a) (*.f64 (cbrt.f64 i) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 i) (cbrt.f64 i))) (cbrt.f64 (cbrt.f64 i)))))) (cbrt.f64 i))

rewrite45.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-exp-log_binary64`
46×	`pow1_binary64`
31×	`cbrt-unprod_binary64`
31×	`prod-exp_binary64`
31×	`pow-prod-down_binary64`

Counts

3 → 81

Calls

3 calls:

14.0ms

(*.f64 (*.f64 c (*.f64 (fma.f64 c b a) (*.f64 (cbrt.f64 i) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 i) (cbrt.f64 i))) (cbrt.f64 (cbrt.f64 i)))))) (cbrt.f64 i))

11.0ms

(*.f64 c (*.f64 (fma.f64 c b a) (*.f64 (cbrt.f64 i) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 i) (cbrt.f64 i))) (cbrt.f64 (cbrt.f64 i))))))

9.0ms

(*.f64 (fma.f64 c b a) (*.f64 (cbrt.f64 i) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 i) (cbrt.f64 i))) (cbrt.f64 (cbrt.f64 i)))))

simplify190.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

521×	`distribute-lft-in_binary64`
520×	`distribute-rgt-in_binary64`
411×	`sqr-pow_binary64`
361×	`associate-l_binary64`
360×	`associate-r_binary64`

Counts

225 → 132

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	150	5800
1	366	4399
2	1525	4357
3	4172	3971
4	4681	3154
5	4042	3144
6	4934	3144

prune238.0ms (2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	222	8	230

Error

0.0b

Counts

230 → 8

Alt Table

Status	Error	Program
	11.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))
	28.7b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (sqrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)) (sqrt.f64 (.f64 (*.f64 c (fma.f64 b c a)) i)))))
✓	4.8b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (.f64 (fma.f64 c b a) (.f64 (cbrt.f64 i) (.f64 (cbrt.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i))) (cbrt.f64 (cbrt.f64 i)))))) (cbrt.f64 i))))
	34.0b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (*.f64 (fma.f64 c b a) (sqrt.f64 i))) (sqrt.f64 i))))
✓	4.7b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (.f64 (fma.f64 c b a) (.f64 (cbrt.f64 i) (cbrt.f64 i)))) (cbrt.f64 i))))
▶	5.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (.f64 i (fma.f64 c b a)))))
	6.8b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (.f64 (cbrt.f64 c) (cbrt.f64 c)) (.f64 (cbrt.f64 c) (fma.f64 b c a))) i)))
	7.2b	(.f64 2 (-.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 x y (.f64 z t))) (cbrt.f64 (fma.f64 x y (.f64 z t)))) (cbrt.f64 (fma.f64 x y (.f64 z t)))) (.f64 (.f64 c (fma.f64 b c a)) i)))

Compiler

Compiled 8368 to 2044 computations (75.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x y (*.f64 z t))
✓	0.0b	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (*.f64 i (fma.f64 c b a))))
✓	1.5b	(*.f64 i (fma.f64 c b a))
✓	4.0b	(.f64 c (.f64 i (fma.f64 c b a)))

series94.0ms (0.8%)

Counts

3 → 192

Calls

3 calls:

63.0ms	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (*.f64 i (fma.f64 c b a))))
18.0ms	(.f64 c (.f64 i (fma.f64 c b a)))
13.0ms	(*.f64 i (fma.f64 c b a))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`fma-udef_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`

Counts

3 → 71

Calls

3 calls:

4.0ms	(.f64 c (.f64 i (fma.f64 c b a)))
3.0ms	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (*.f64 i (fma.f64 c b a))))
3.0ms	(*.f64 i (fma.f64 c b a))

simplify143.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

613×	`distribute-rgt-in_binary64`
606×	`distribute-lft-in_binary64`
552×	`fma-def_binary64`
306×	`fma-neg_binary64`
215×	`cancel-sign-sub-inv_binary64`

Counts

263 → 138

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	154	4703
1	332	3822
2	1163	3783
3	4522	3783
4	4977	3783
5	4931	3783

prune154.0ms (1.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	154	2	156
Fresh	2	3	5
Picked	0	1	1
Done	2	0	2
Total	158	6	164

Error

0.0b

Counts

164 → 6

Alt Table

Status	Error	Program
	11.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))
	28.7b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (sqrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)) (sqrt.f64 (.f64 (*.f64 c (fma.f64 b c a)) i)))))
	2.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c i) (fma.f64 c b a))))
✓	5.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (.f64 i (fma.f64 c b a)))))
	7.2b	(.f64 2 (-.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 x y (.f64 z t))) (cbrt.f64 (fma.f64 x y (.f64 z t)))) (cbrt.f64 (fma.f64 x y (.f64 z t)))) (.f64 (.f64 c (fma.f64 b c a)) i)))
	34.7b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (.f64 (sqrt.f64 i) (*.f64 (sqrt.f64 i) (fma.f64 c b a))))))

Compiler

Compiled 3697 to 918 computations (75.2% saved)

regimes3.4s (28.7%)

Accuracy

Total 1.3b remaining (80.4%)

Threshold costs 0b (0%)

Counts

130 → 3

Compiler

Compiled 56097 to 36227 computations (35.4% saved)

bsearch53.0ms (0.4%)

Steps

Iters	Range		Point
6	2.4172271978890414e+25	1.0749186922051812e+26	2.578892516458991e+25
1	-5.4290531299657336e-49	-1.7388498958852213e-49	-3.0819729376635466e-49

Compiler

Compiled 9 to 8 computations (11.1% saved)

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

32×	`*-commutative_binary64`
24×	`+-commutative_binary64`
21×	`sub-neg_binary64`
20×	`distribute-rgt-neg-in_binary64`
18×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	99
1	71	99
2	103	99
3	149	99
4	192	99
5	215	99
6	223	99
7	224	99
8	224	99

end21.0ms (0.2%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 380 to 200 computations (47.4% saved)

sample2.2s (18.4%)

Algorithm

1×

intervals

Results

614.0ms	8000×	body	128	valid
591.0ms	7219×	body	128	invalid

Compiler

Compiled 299 to 174 computations (41.8% saved)

Details

analyze2.4s (20.8%)

sample138.0ms (1.2%)

simplify222.0ms (1.9%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series101.0ms (0.9%)

rewrite14.0ms (0.1%)

simplify126.0ms (1.1%)

prune213.0ms (1.8%)

localize18.0ms (0.2%)

series711.0ms (6.1%)

rewrite29.0ms (0.2%)

simplify110.0ms (0.9%)

prune352.0ms (3%)

localize22.0ms (0.2%)

series702.0ms (6%)

rewrite45.0ms (0.4%)

simplify190.0ms (1.6%)

prune238.0ms (2%)

localize14.0ms (0.1%)

series94.0ms (0.8%)

rewrite14.0ms (0.1%)

simplify143.0ms (1.2%)

prune154.0ms (1.3%)

regimes3.4s (28.7%)

bsearch53.0ms (0.4%)

simplify16.0ms (0.1%)

end21.0ms (0.2%)

sample2.2s (18.4%)

Profiling