Details

analyze102.0ms (1.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
49.9%	49.9%	0.1%	4
49.9%	49.9%	0.1%	5
49.9%	49.9%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
74.9%	25%	0.1%	9
87.4%	12.5%	0.1%	10
87.4%	12.5%	0.1%	11
87.4%	12.5%	0.1%	12
93.6%	6.2%	0.1%	13
93.6%	6.2%	0.1%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample822.0ms (13.8%)

Infinites

83.1% of outputs are infinite.

Results

605.0ms

8256×

body

128

valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify170.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

907×	`associate-/l*_binary64`
740×	`associate-/l/_binary64`
677×	`fma-def_binary64`
607×	`associate-/r/_binary64`
557×	`associate-*l/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	17	10
2	23	10
3	36	10
4	41	10
5	47	10
6	51	8
7	61	8
8	228	8
9	761	8
10	851	8
11	964	8
12	975	8
13	980	8
14	985	8
15	2231	8
16	2288	8
17	2637	8
18	2689	8
19	2901	8
20	3031	8
21	3278	8
22	3700	8
23	4109	8
24	4157	8
25	4872	8
26	4997	8
27	4889	8

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
▶	3.2b	(fma.f64 x (/.f64 y z) x)
	7.7b	(/.f64 (*.f64 x (+.f64 y z)) z)

Compiler

Compiled 54 to 30 computations (44.4% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.2b	(fma.f64 x (/.f64 y z) x)

series14.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

14.0ms

(fma.f64 x (/.f64 y z) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 x (/.f64 y z) x)

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

635×	`fma-def_binary64`
449×	`associate-/l/_binary64`
410×	`distribute-rgt-in_binary64`
404×	`distribute-rgt-out_binary64`
400×	`unswap-sqr_binary64`

Counts

46 → 24

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	451
1	32	374
2	63	374
3	171	374
4	650	374
5	2482	374
6	3613	374
7	3881	374
8	4329	374
9	5248	374

prune15.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	22	2	24
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	22	4	26

Error

0.0b

Counts

26 → 4

Alt Table

Status	Error	Program
	36.1b	(*.f64 (sqrt.f64 (fma.f64 x (/.f64 y z) x)) (sqrt.f64 (fma.f64 x (/.f64 y z) x)))
▶	4.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x))) (cbrt.f64 (fma.f64 x (/.f64 y z) x)))
✓	3.2b	(fma.f64 x (/.f64 y z) x)
	7.7b	(/.f64 (*.f64 x (+.f64 y z)) z)

Compiler

Compiled 351 to 99 computations (71.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x))) (cbrt.f64 (fma.f64 x (/.f64 y z) x)))
✓	0.4b	(*.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x)))
	3.2b	(fma.f64 x (/.f64 y z) x)
✓	9.6b	(cbrt.f64 (fma.f64 x (/.f64 y z) x))

series813.0ms (13.6%)

Counts

3 → 108

Calls

3 calls:

423.0ms

(*.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x)))

376.0ms

(cbrt.f64 (fma.f64 x (/.f64 y z) x))

14.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x))) (cbrt.f64 (fma.f64 x (/.f64 y z) x)))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

8.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x))) (cbrt.f64 (fma.f64 x (/.f64 y z) x)))

5.0ms

(*.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x)))

1.0ms

(cbrt.f64 (fma.f64 x (/.f64 y z) x))

simplify129.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

884×	`times-frac_binary64`
509×	`fma-def_binary64`
305×	`fma-neg_binary64`
168×	`cancel-sign-sub-inv_binary64`
153×	`associate-r_binary64`

Counts

201 → 188

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	267	5248
1	697	4885
2	1919	4145
3	4758	4117
4	5006	4117

prune195.0ms (3.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	353	3	356
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	353	7	360

Error

0.0b

Counts

360 → 7

Alt Table

Status	Error	Program
	4.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x))) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x))) 6)) (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)))))
	36.1b	(*.f64 (sqrt.f64 (fma.f64 x (/.f64 y z) x)) (sqrt.f64 (fma.f64 x (/.f64 y z) x)))
▶	4.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)))))
✓	4.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x))) (cbrt.f64 (fma.f64 x (/.f64 y z) x)))
	36.5b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (/.f64 y z) x))) (cbrt.f64 (sqrt.f64 (fma.f64 x (/.f64 y z) x)))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (/.f64 y z) x))) (cbrt.f64 (sqrt.f64 (fma.f64 x (/.f64 y z) x))))) (cbrt.f64 (fma.f64 x (/.f64 y z) x)))
✓	3.2b	(fma.f64 x (/.f64 y z) x)
	7.7b	(/.f64 (*.f64 x (+.f64 y z)) z)

Compiler

Compiled 12693 to 3434 computations (72.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x))))
✓	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)))
	3.2b	(fma.f64 x (/.f64 y z) x)
	9.6b	(cbrt.f64 (fma.f64 x (/.f64 y z) x))

series773.0ms (13%)

Counts

2 → 72

Calls

2 calls:

426.0ms	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x))))
346.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`cbrt-prod_binary64`
34×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
9×	`associate-r_binary64`

Counts

2 → 72

Calls

2 calls:

6.0ms	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x))))
1.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)))

simplify135.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

884×	`times-frac_binary64`
515×	`fma-def_binary64`
365×	`fma-neg_binary64`
176×	`cancel-sign-sub-inv_binary64`
173×	`associate-/r/_binary64`

Counts

144 → 155

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	264	5374
1	691	5014
2	1862	4354
3	4871	4345
4	5086	4345

prune383.0ms (6.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	612	1	613
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	614	6	620

Error

0.0b

Counts

620 → 6

Alt Table

Status	Error	Program
▶	4.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x))))) (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)))) 4)) (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)))))
	36.5b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (/.f64 y z) x))) (cbrt.f64 (sqrt.f64 (fma.f64 x (/.f64 y z) x)))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (/.f64 y z) x))) (cbrt.f64 (sqrt.f64 (fma.f64 x (/.f64 y z) x))))) (cbrt.f64 (fma.f64 x (/.f64 y z) x)))
	36.1b	(*.f64 (sqrt.f64 (fma.f64 x (/.f64 y z) x)) (sqrt.f64 (fma.f64 x (/.f64 y z) x)))
✓	4.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x))) (cbrt.f64 (fma.f64 x (/.f64 y z) x)))
✓	3.2b	(fma.f64 x (/.f64 y z) x)
	7.7b	(/.f64 (*.f64 x (+.f64 y z)) z)

Compiler

Compiled 35186 to 7315 computations (79.2% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)))) 4)
	3.2b	(fma.f64 x (/.f64 y z) x)
✓	5.1b	(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x))))
	9.6b	(cbrt.f64 (fma.f64 x (/.f64 y z) x))

series848.0ms (14.2%)

Counts

2 → 72

Calls

2 calls:

425.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x))))
423.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)))) 4)

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`cbrt-prod_binary64`
12×	`unpow-prod-down_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`

Counts

2 → 40

Calls

2 calls:

3.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)))) 4)
3.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x))))

simplify117.0ms (2%)

Algorithm

1×	egg-herbie

Rules

687×	`associate-/l*_binary64`
522×	`fma-def_binary64`
263×	`fma-neg_binary64`
224×	`associate-/r/_binary64`
178×	`cancel-sign-sub-inv_binary64`

Counts

112 → 113

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	281	4439
1	730	4116
2	1962	3715
3	4919	3712
4	5000	3712

prune382.0ms (6.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	543	2	545
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	543	8	551

Error

0.0b

Counts

551 → 8

Alt Table

Status	Error	Program
✓	4.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x))))) (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)))) 4)) (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)))))
	36.5b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (/.f64 y z) x))) (cbrt.f64 (sqrt.f64 (fma.f64 x (/.f64 y z) x)))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (/.f64 y z) x))) (cbrt.f64 (sqrt.f64 (fma.f64 x (/.f64 y z) x))))) (cbrt.f64 (fma.f64 x (/.f64 y z) x)))
	36.1b	(*.f64 (sqrt.f64 (fma.f64 x (/.f64 y z) x)) (sqrt.f64 (fma.f64 x (/.f64 y z) x)))
✓	4.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x))) (cbrt.f64 (fma.f64 x (/.f64 y z) x)))
	36.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (pow.f64 (fma.f64 x (/.f64 y z) x) 1/3)))) (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)))) 4)) (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)))))
	57.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x))) (.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 1/9) (fma.f64 (log.f64 (/.f64 -1 y)) -2 (*.f64 2 (log.f64 (/.f64 x z)))))) (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)))) 4)) (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)))))
✓	3.2b	(fma.f64 x (/.f64 y z) x)
	7.7b	(/.f64 (*.f64 x (+.f64 y z)) z)

Compiler

Compiled 37632 to 8576 computations (77.2% saved)

regimes727.0ms (12.2%)

Accuracy

Total 0.8b remaining (96.2%)

Threshold costs 0.8b (96.2%)

Counts

127 → 5

Compiler

Compiled 20752 to 7014 computations (66.2% saved)

bsearch7.0ms (0.1%)

Compiler: Compiled 10 to 6 computations (40% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`if-not_binary64`
3×	`if-if-or-not_binary64`
3×	`not-not_bool`
3×	`not-or_bool`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	98
1	27	90
2	30	84
3	36	82
4	39	82
5	42	82
6	42	82
7	43	82
8	43	82

end153.0ms (2.6%)

Compiler: Compiled 396 to 143 computations (63.9% saved)

Details

analyze102.0ms (1.7%)

sample822.0ms (13.8%)

simplify170.0ms (2.9%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series14.0ms (0.2%)

rewrite1.0ms (0%)

simplify79.0ms (1.3%)

prune15.0ms (0.2%)

localize10.0ms (0.2%)

series813.0ms (13.6%)

rewrite20.0ms (0.3%)

simplify129.0ms (2.2%)

prune195.0ms (3.3%)

localize13.0ms (0.2%)

series773.0ms (13%)

rewrite15.0ms (0.3%)

simplify135.0ms (2.3%)

prune383.0ms (6.4%)

localize17.0ms (0.3%)

series848.0ms (14.2%)

rewrite8.0ms (0.1%)

simplify117.0ms (2%)

prune382.0ms (6.4%)

regimes727.0ms (12.2%)

bsearch7.0ms (0.1%)

simplify5.0ms (0.1%)

end153.0ms (2.6%)

Profiling