Details

analyze2.2s (21%)

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)

sample3.0s (28.6%)

Symmetry

(sort x y)

(sort z t)

Results

1.5s	7530×	body	128	invalid
1.4s	8256×	body	128	valid

Compiler

Compiled 83 to 56 computations (32.5% saved)

simplify217.0ms (2.1%)

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

7.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	7.1b	(.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)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x y (*.f64 z t))
✓	0.1b	(*.f64 c (fma.f64 b c a))
✓	9.2b	(.f64 (.f64 c (fma.f64 b c a)) i)

series36.0ms (0.3%)

Counts

3 → 132

Calls

3 calls:

18.0ms	(.f64 (.f64 c (fma.f64 b c a)) i)
9.0ms	(*.f64 c (fma.f64 b c a))
8.0ms	(fma.f64 x y (*.f64 z t))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`

Counts

3 → 52

Calls

3 calls:

5.0ms	(.f64 (.f64 c (fma.f64 b c a)) i)
2.0ms	(*.f64 c (fma.f64 b c a))
0.0ms	(fma.f64 x y (*.f64 z t))

simplify85.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

861×	`fma-def_binary64`
825×	`unswap-sqr_binary64`
416×	`*-commutative_binary64`
318×	`distribute-lft-in_binary64`
318×	`distribute-rgt-in_binary64`

Counts

184 → 103

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	103	2165
1	192	1709
2	631	1709
3	1674	1709
4	2256	1709
5	3170	1709
6	5045	1709

prune119.0ms (1.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	94	9	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	9	104

Error

0.0b

Counts

104 → 9

Alt Table

Status	Error	Program
	5.2b	(.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)))))))
	4.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (.f64 i (fma.f64 c b a)))))
	7.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)) (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i))) (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)))))
	13.7b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))
	32.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (sqrt.f64 (.f64 c (fma.f64 b c a))) (sqrt.f64 (.f64 c (fma.f64 b c a)))) i)))
	7.1b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	10.1b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (+.f64 (.f64 (pow.f64 c 2) b) (*.f64 c a)) i)))
▶	4.3b	(.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))))
	31.1b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (sqrt.f64 (.f64 c (.f64 i (fma.f64 c b a)))) (sqrt.f64 (.f64 c (*.f64 i (fma.f64 c b a)))))))

Compiler

Compiled 2846 to 939 computations (67% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(cbrt.f64 i)
✓	1.2b	(.f64 (fma.f64 c b a) (.f64 (cbrt.f64 i) (cbrt.f64 i)))
✓	1.4b	(.f64 c (.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))

series595.0ms (5.7%)

Counts

4 → 156

Calls

4 calls:

275.0ms	(.f64 c (.f64 (fma.f64 c b a) (*.f64 (cbrt.f64 i) (cbrt.f64 i))))
256.0ms	(.f64 (fma.f64 c b a) (.f64 (cbrt.f64 i) (cbrt.f64 i)))
33.0ms	(.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 (0.3%)

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:

10.0ms	(.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)

simplify105.0ms (1%)

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

prune226.0ms (2.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	182	9	191

Error

0.0b

Counts

191 → 9

Alt Table

Status	Error	Program
▶	4.3b	(.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 (.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (cbrt.f64 i)))))) (cbrt.f64 i))))
	10.1b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (+.f64 (.f64 (pow.f64 c 2) b) (*.f64 c a)) i)))
	5.2b	(.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)))))))
	4.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (.f64 i (fma.f64 c b a)))))
	7.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)) (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i))) (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)))))
	13.7b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))
	32.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (sqrt.f64 (.f64 c (fma.f64 b c a))) (sqrt.f64 (.f64 c (fma.f64 b c a)))) i)))
	7.1b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	31.1b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (sqrt.f64 (.f64 c (.f64 i (fma.f64 c b a)))) (sqrt.f64 (.f64 c (*.f64 i (fma.f64 c b a)))))))

Compiler

Compiled 5816 to 1774 computations (69.5% saved)

localize115.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(cbrt.f64 (.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (cbrt.f64 i)))
✓	1.2b	(.f64 (fma.f64 c b a) (.f64 (cbrt.f64 i) (cbrt.f64 (.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (cbrt.f64 i)))))
✓	1.4b	(.f64 c (.f64 (fma.f64 c b a) (.f64 (cbrt.f64 i) (cbrt.f64 (.f64 (*.f64 (cbrt.f64 i) (cbrt.f64 i)) (cbrt.f64 i))))))
✓	2.8b	(.f64 (.f64 c (.f64 (fma.f64 c b a) (.f64 (cbrt.f64 i) (cbrt.f64 (.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (cbrt.f64 i)))))) (cbrt.f64 i))

series653.0ms (6.2%)

Counts

4 → 156

Calls

4 calls:

307.0ms	(.f64 c (.f64 (fma.f64 c b a) (.f64 (cbrt.f64 i) (cbrt.f64 (.f64 (*.f64 (cbrt.f64 i) (cbrt.f64 i)) (cbrt.f64 i))))))
259.0ms	(.f64 (fma.f64 c b a) (.f64 (cbrt.f64 i) (cbrt.f64 (.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (cbrt.f64 i)))))
52.0ms	(cbrt.f64 (.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (cbrt.f64 i)))
33.0ms	(.f64 (.f64 c (.f64 (fma.f64 c b a) (.f64 (cbrt.f64 i) (cbrt.f64 (.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (cbrt.f64 i)))))) (cbrt.f64 i))

rewrite33.0ms (0.3%)

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 → 84

Calls

4 calls:

9.0ms	(.f64 (.f64 c (.f64 (fma.f64 c b a) (.f64 (cbrt.f64 i) (cbrt.f64 (.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (cbrt.f64 i)))))) (cbrt.f64 i))
8.0ms	(.f64 c (.f64 (fma.f64 c b a) (.f64 (cbrt.f64 i) (cbrt.f64 (.f64 (*.f64 (cbrt.f64 i) (cbrt.f64 i)) (cbrt.f64 i))))))
5.0ms	(cbrt.f64 (.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (cbrt.f64 i)))
5.0ms	(.f64 (fma.f64 c b a) (.f64 (cbrt.f64 i) (cbrt.f64 (.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (cbrt.f64 i)))))

simplify111.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

240 → 148

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	149	3902
1	337	3089
2	1276	2876
3	3369	2874
4	5331	2874

prune174.0ms (1.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	148	9	157

Error

0.0b

Counts

157 → 9

Alt Table

Status	Error	Program
✓	4.3b	(.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 (.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (cbrt.f64 i)))))) (cbrt.f64 i))))
	10.1b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (+.f64 (.f64 (pow.f64 c 2) b) (*.f64 c a)) i)))
	5.2b	(.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)))))))
▶	4.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (.f64 i (fma.f64 c b a)))))
	7.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)) (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i))) (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)))))
	13.7b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))
	32.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (sqrt.f64 (.f64 c (fma.f64 b c a))) (sqrt.f64 (.f64 c (fma.f64 b c a)))) i)))
	7.1b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	31.1b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (sqrt.f64 (.f64 c (.f64 i (fma.f64 c b a)))) (sqrt.f64 (.f64 c (*.f64 i (fma.f64 c b a)))))))

Compiler

Compiled 5536 to 1536 computations (72.3% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x y (*.f64 z t))
✓	1.0b	(*.f64 i (fma.f64 c b a))
✓	4.0b	(.f64 c (.f64 i (fma.f64 c b a)))

series30.0ms (0.3%)

Counts

2 → 96

Calls

2 calls:

19.0ms	(.f64 c (.f64 i (fma.f64 c b a)))
10.0ms	(*.f64 i (fma.f64 c b a))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`

Counts

2 → 46

Calls

2 calls:

4.0ms	(.f64 c (.f64 i (fma.f64 c b a)))
2.0ms	(*.f64 i (fma.f64 c b a))

simplify86.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

779×	`fma-def_binary64`
427×	`*-commutative_binary64`
379×	`distribute-rgt-in_binary64`
377×	`distribute-lft-in_binary64`
285×	`sqr-pow_binary64`

Counts

142 → 69

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	89	1779
1	173	1424
2	608	1424
3	1693	1424
4	2357	1424
5	3563	1424
6	4984	1424

prune112.0ms (1.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	88	3	91
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	92	8	100

Error

0.0b

Counts

100 → 8

Alt Table

Status	Error	Program
✓	4.3b	(.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 (.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (cbrt.f64 i)))))) (cbrt.f64 i))))
	10.1b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (+.f64 (.f64 (pow.f64 c 2) b) (*.f64 c a)) i)))
	32.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (sqrt.f64 (.f64 c (fma.f64 b c a))) (sqrt.f64 (.f64 c (fma.f64 b c a)))) i)))
	7.1b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	34.1b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (sqrt.f64 c) (.f64 (sqrt.f64 c) (*.f64 i (fma.f64 c b a))))))
	5.2b	(.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)))))))
	2.0b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c i) (fma.f64 c b a))))
	7.7b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))))

Compiler

Compiled 2223 to 663 computations (70.2% saved)

regimes2.3s (22.1%)

Accuracy

Total 0.9b remaining (96.6%)

Threshold costs 0.9b (96.6%)

Counts

114 → 3

Compiler

Compiled 53928 to 33335 computations (38.2% saved)

bsearch5.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

24×	`*-commutative_binary64`
16×	`+-commutative_binary64`
14×	`sub-neg_binary64`
12×	`distribute-rgt-neg-in_binary64`
12×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	85
1	63	85
2	86	85
3	104	85
4	130	85
5	146	85
6	154	85
7	158	85
8	159	85
9	159	85

end163.0ms (1.6%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 650 to 362 computations (44.3% saved)

Details

analyze2.2s (21%)

sample3.0s (28.6%)

simplify217.0ms (2.1%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series36.0ms (0.3%)

rewrite9.0ms (0.1%)

simplify85.0ms (0.8%)

prune119.0ms (1.1%)

localize19.0ms (0.2%)

series595.0ms (5.7%)

rewrite29.0ms (0.3%)

simplify105.0ms (1%)

prune226.0ms (2.2%)

localize115.0ms (1.1%)

series653.0ms (6.2%)

rewrite33.0ms (0.3%)

simplify111.0ms (1.1%)

prune174.0ms (1.7%)

localize11.0ms (0.1%)

series30.0ms (0.3%)

rewrite10.0ms (0.1%)

simplify86.0ms (0.8%)

prune112.0ms (1.1%)

regimes2.3s (22.1%)

bsearch5.0ms (0%)

simplify6.0ms (0.1%)

end163.0ms (1.6%)

Profiling