Details

analyze2.7s (23.6%)

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)

sample2.8s (25.2%)

Symmetry

(sort x y)

(sort z t)

Results

1.4s	8256×	body	128	valid
1.3s	7387×	body	128	invalid

Compiler

Compiled 83 to 56 computations (32.5% saved)

simplify224.0ms (2%)

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)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
✓	0.0b	(fma.f64 x y (*.f64 z t))
✓	0.1b	(*.f64 c (fma.f64 b c a))
✓	9.1b	(.f64 (.f64 c (fma.f64 b c a)) i)

series159.0ms (1.4%)

Counts

4 → 228

Calls

4 calls:

121.0ms	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
19.0ms	(.f64 (.f64 c (fma.f64 b c a)) i)
10.0ms	(fma.f64 x y (*.f64 z t))
9.0ms	(*.f64 c (fma.f64 b c a))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

9.0ms	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
4.0ms	(.f64 (.f64 c (fma.f64 b c a)) i)
3.0ms	(*.f64 c (fma.f64 b c a))
0.0ms	(fma.f64 x y (*.f64 z t))

simplify118.0ms (1%)

Algorithm

1×	egg-herbie

Rules

684×	`distribute-rgt-in_binary64`
657×	`distribute-lft-in_binary64`
522×	`fma-def_binary64`
379×	`cancel-sign-sub-inv_binary64`
224×	`associate-l_binary64`

Counts

314 → 180

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	200	6062
1	427	4741
2	1381	4643
3	4989	4643

prune188.0ms (1.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	170	10	180
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	171	10	181

Error

0.3b

Counts

181 → 10

Alt Table

Status	Error	Program
	6.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (.f64 c (fma.f64 b c a)) (.f64 (cbrt.f64 i) (cbrt.f64 i))) (cbrt.f64 i))))
	16.1b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c a) i)))
	7.5b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (cbrt.f64 (.f64 c (.f64 i (fma.f64 c b a)))) (cbrt.f64 (.f64 c (.f64 i (fma.f64 c b a))))) (cbrt.f64 (.f64 c (.f64 i (fma.f64 c b a)))))))
	15.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))
	7.1b	(.f64 1 (.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (*.f64 i (fma.f64 c b a))))))
	7.8b	(.f64 (sqrt.f64 2) (.f64 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (*.f64 i (fma.f64 c b a)))) (sqrt.f64 2)))
▶	6.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 c (fma.f64 b c a))) (cbrt.f64 (.f64 c (fma.f64 b c a)))) (cbrt.f64 (.f64 c (fma.f64 b c a)))) i)))
	39.5b	(.f64 i (.f64 (*.f64 c -2) (fma.f64 c b a)))
	33.8b	(.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))))
	46.7b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 c c) c) (.f64 (.f64 (fma.f64 b c a) (fma.f64 b c a)) (fma.f64 b c a))) (.f64 (.f64 i i) i)))))

Compiler

Compiled 4897 to 1415 computations (71.1% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 (.f64 c (fma.f64 b c a))) (cbrt.f64 (.f64 c (fma.f64 b c a)))) (cbrt.f64 (*.f64 c (fma.f64 b c a))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 c (fma.f64 b c a))) (cbrt.f64 (*.f64 c (fma.f64 b c a))))
✓	9.1b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 c (fma.f64 b c a))) (cbrt.f64 (.f64 c (fma.f64 b c a)))) (cbrt.f64 (.f64 c (fma.f64 b c a)))) i)
✓	13.3b	(cbrt.f64 (*.f64 c (fma.f64 b c a)))

series289.0ms (2.6%)

Counts

4 → 156

Calls

4 calls:

120.0ms	(.f64 (.f64 (cbrt.f64 (.f64 c (fma.f64 b c a))) (cbrt.f64 (.f64 c (fma.f64 b c a)))) (cbrt.f64 (*.f64 c (fma.f64 b c a))))
82.0ms	(.f64 (cbrt.f64 (.f64 c (fma.f64 b c a))) (cbrt.f64 (*.f64 c (fma.f64 b c a))))
57.0ms	(cbrt.f64 (*.f64 c (fma.f64 b c a)))
30.0ms	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 c (fma.f64 b c a))) (cbrt.f64 (.f64 c (fma.f64 b c a)))) (cbrt.f64 (.f64 c (fma.f64 b c a)))) i)

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`pow1_binary64`
20×	`add-exp-log_binary64`
16×	`pow1/3_binary64`
13×	`pow-prod-down_binary64`
13×	`add-sqr-sqrt_binary64`

Counts

4 → 102

Calls

4 calls:

10.0ms	(.f64 (cbrt.f64 (.f64 c (fma.f64 b c a))) (cbrt.f64 (*.f64 c (fma.f64 b c a))))
8.0ms	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 c (fma.f64 b c a))) (cbrt.f64 (.f64 c (fma.f64 b c a)))) (cbrt.f64 (.f64 c (fma.f64 b c a)))) i)
6.0ms	(.f64 (.f64 (cbrt.f64 (.f64 c (fma.f64 b c a))) (cbrt.f64 (.f64 c (fma.f64 b c a)))) (cbrt.f64 (*.f64 c (fma.f64 b c a))))
2.0ms	(cbrt.f64 (*.f64 c (fma.f64 b c a)))

simplify188.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

486×	`associate-l_binary64`
474×	`times-frac_binary64`
361×	`associate-/l*_binary64`
343×	`associate-/r*_binary64`
236×	`fma-def_binary64`

Counts

258 → 297

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	531	7708
1	1652	6777
2	4975	6777
3	4936	6777

prune552.0ms (4.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	469	0	469
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	469	10	479

Error

0.3b

Counts

479 → 10

Alt Table

Status	Error	Program
▶	6.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (.f64 c (fma.f64 b c a)) (.f64 (cbrt.f64 i) (cbrt.f64 i))) (cbrt.f64 i))))
	16.1b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c a) i)))
	7.5b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (cbrt.f64 (.f64 c (.f64 i (fma.f64 c b a)))) (cbrt.f64 (.f64 c (.f64 i (fma.f64 c b a))))) (cbrt.f64 (.f64 c (.f64 i (fma.f64 c b a)))))))
	15.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))
	7.1b	(.f64 1 (.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (*.f64 i (fma.f64 c b a))))))
	7.8b	(.f64 (sqrt.f64 2) (.f64 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (*.f64 i (fma.f64 c b a)))) (sqrt.f64 2)))
✓	6.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 c (fma.f64 b c a))) (cbrt.f64 (.f64 c (fma.f64 b c a)))) (cbrt.f64 (.f64 c (fma.f64 b c a)))) i)))
	39.5b	(.f64 i (.f64 (*.f64 c -2) (fma.f64 c b a)))
	33.8b	(.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))))
	46.7b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 c c) c) (.f64 (.f64 (fma.f64 b c a) (fma.f64 b c a)) (fma.f64 b c a))) (.f64 (.f64 i i) i)))))

Compiler

Compiled 26381 to 11222 computations (57.5% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(*.f64 (cbrt.f64 i) (cbrt.f64 i))
✓	0.6b	(cbrt.f64 i)
✓	3.0b	(.f64 (.f64 (.f64 c (fma.f64 b c a)) (.f64 (cbrt.f64 i) (cbrt.f64 i))) (cbrt.f64 i))
✓	6.2b	(.f64 (.f64 c (fma.f64 b c a)) (*.f64 (cbrt.f64 i) (cbrt.f64 i)))

series411.0ms (3.7%)

Counts

4 → 120

Calls

4 calls:

305.0ms	(.f64 (.f64 c (fma.f64 b c a)) (*.f64 (cbrt.f64 i) (cbrt.f64 i)))
38.0ms	(.f64 (.f64 (.f64 c (fma.f64 b c a)) (.f64 (cbrt.f64 i) (cbrt.f64 i))) (cbrt.f64 i))
36.0ms	(*.f64 (cbrt.f64 i) (cbrt.f64 i))
31.0ms	(cbrt.f64 i)

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`pow1_binary64`
36×	`add-exp-log_binary64`
23×	`add-sqr-sqrt_binary64`
23×	`pow-prod-down_binary64`
22×	`cbrt-prod_binary64`

Counts

4 → 111

Calls

4 calls:

9.0ms	(.f64 (.f64 (.f64 c (fma.f64 b c a)) (.f64 (cbrt.f64 i) (cbrt.f64 i))) (cbrt.f64 i))
6.0ms	(.f64 (.f64 c (fma.f64 b c a)) (*.f64 (cbrt.f64 i) (cbrt.f64 i)))
4.0ms	(*.f64 (cbrt.f64 i) (cbrt.f64 i))
1.0ms	(cbrt.f64 i)

simplify105.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

758×	`unswap-sqr_binary64`
541×	`distribute-rgt-in_binary64`
536×	`distribute-lft-in_binary64`
327×	`associate-l_binary64`
279×	`associate-r_binary64`

Counts

231 → 167

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	145	3551
1	322	2709
2	1298	2550
3	3915	2522
4	5268	2522

prune235.0ms (2.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	200	3	203
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	202	11	213

Error

0.2b

Counts

213 → 11

Alt Table

Status	Error	Program
	22.5b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (.f64 c (fma.f64 b c a)) (cbrt.f64 (.f64 i i))) (cbrt.f64 i))))
▶	7.1b	(.f64 1 (.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (*.f64 i (fma.f64 c b a))))))
	7.7b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (*.f64 (fma.f64 c b a) (pow.f64 (cbrt.f64 (cbrt.f64 i)) 8))) (cbrt.f64 (cbrt.f64 i)))))
✓	6.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 c (fma.f64 b c a))) (cbrt.f64 (.f64 c (fma.f64 b c a)))) (cbrt.f64 (.f64 c (fma.f64 b c a)))) i)))
	7.5b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (cbrt.f64 (.f64 c (.f64 i (fma.f64 c b a)))) (cbrt.f64 (.f64 c (.f64 i (fma.f64 c b a))))) (cbrt.f64 (.f64 c (.f64 i (fma.f64 c b a)))))))
	40.7b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (*.f64 c a) (pow.f64 i 2/3)) (cbrt.f64 i))))
	15.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))
	7.8b	(.f64 (sqrt.f64 2) (.f64 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (*.f64 i (fma.f64 c b a)))) (sqrt.f64 2)))
	39.5b	(.f64 i (.f64 (*.f64 c -2) (fma.f64 c b a)))
	33.8b	(.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))))
✓	6.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (.f64 c (fma.f64 b c a)) (.f64 (cbrt.f64 i) (cbrt.f64 i))) (cbrt.f64 i))))

Compiler

Compiled 6384 to 1874 computations (70.6% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (fma.f64 c b a)))))
✓	0.8b	(*.f64 i (fma.f64 c b a))
✓	6.4b	(.f64 c (.f64 i (fma.f64 c b a)))

series179.0ms (1.6%)

Counts

3 → 192

Calls

3 calls:

103.0ms	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (fma.f64 c b a)))))
61.0ms	(.f64 c (.f64 i (fma.f64 c b a)))
15.0ms	(*.f64 i (fma.f64 c b a))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`add-cbrt-cube_binary64`
12×	`add-exp-log_binary64`
12×	`pow1_binary64`
11×	`distribute-lft-in_binary64`

Counts

3 → 80

Calls

3 calls:

5.0ms	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (fma.f64 c b a)))))
4.0ms	(.f64 c (.f64 i (fma.f64 c b a)))
3.0ms	(*.f64 i (fma.f64 c b a))

simplify163.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

855×	`fma-neg_binary64`
635×	`fma-def_binary64`
567×	`exp-prod_binary64`
455×	`*-commutative_binary64`
432×	`cancel-sign-sub-inv_binary64`

Counts

272 → 146

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	198	5693
1	425	4456
2	1443	4358
3	3115	4355
4	4832	4355
5	4876	4355

prune179.0ms (1.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	4	4	8
Picked	0	1	1
Done	1	1	2
Total	149	8	157

Error

0.0b

Counts

157 → 8

Alt Table

Status	Error	Program
	7.7b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (*.f64 (fma.f64 c b a) (pow.f64 (cbrt.f64 (cbrt.f64 i)) 8))) (cbrt.f64 (cbrt.f64 i)))))
✓	6.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 c (fma.f64 b c a))) (cbrt.f64 (.f64 c (fma.f64 b c a)))) (cbrt.f64 (.f64 c (fma.f64 b c a)))) i)))
	7.5b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (cbrt.f64 (.f64 c (.f64 i (fma.f64 c b a)))) (cbrt.f64 (.f64 c (.f64 i (fma.f64 c b a))))) (cbrt.f64 (.f64 c (.f64 i (fma.f64 c b a)))))))
	1.6b	(.f64 1 (.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (*.f64 c i) (fma.f64 c b a)))))
✓	7.1b	(.f64 1 (.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (*.f64 i (fma.f64 c b a))))))
	7.8b	(.f64 (sqrt.f64 2) (.f64 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (*.f64 i (fma.f64 c b a)))) (sqrt.f64 2)))
	39.5b	(.f64 i (.f64 (*.f64 c -2) (fma.f64 c b a)))
	10.0b	(.f64 1 (.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (*.f64 a i))))))

Compiler

Compiled 4070 to 1295 computations (68.2% saved)

regimes2.4s (21.7%)

Accuracy

Total 1.6b remaining (98.5%)

Threshold costs 0b (0%)

Counts

130 → 1

Compiler

Compiled 59633 to 38044 computations (36.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	24
1	31	24
2	46	24
3	56	24
4	64	24
5	67	24
6	66	24

end155.0ms (1.4%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 402 to 244 computations (39.3% saved)

Details

analyze2.7s (23.6%)

sample2.8s (25.2%)

simplify224.0ms (2%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series159.0ms (1.4%)

rewrite21.0ms (0.2%)

simplify118.0ms (1%)

prune188.0ms (1.7%)

localize20.0ms (0.2%)

series289.0ms (2.6%)

rewrite34.0ms (0.3%)

simplify188.0ms (1.7%)

prune552.0ms (4.9%)

localize16.0ms (0.1%)

series411.0ms (3.7%)

rewrite30.0ms (0.3%)

simplify105.0ms (0.9%)

prune235.0ms (2.1%)

localize14.0ms (0.1%)

series179.0ms (1.6%)

rewrite17.0ms (0.2%)

simplify163.0ms (1.5%)

prune179.0ms (1.6%)

regimes2.4s (21.7%)

simplify3.0ms (0%)

end155.0ms (1.4%)

Profiling