Details

analyze186.0ms (6.4%)

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
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
31.2%	68.7%	0.1%	6
46.8%	53.1%	0.1%	7
60.9%	39%	0.1%	8
67.9%	31.2%	0.9%	9
74.5%	22.2%	3.2%	10
77.9%	17.2%	5%	11
81.1%	11.8%	7.1%	12
82.7%	9%	8.3%	13
84.3%	6.1%	9.7%	14

Compiler

Compiled 14 to 10 computations (28.6% saved)

sample1.0s (35%)

Results

892.0ms	8256×	body	128	valid
23.0ms	251×	body	128	invalid

Compiler

Compiled 41 to 29 computations (29.3% saved)

simplify87.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1151×	`distribute-rgt-in_binary64`
1143×	`distribute-lft-in_binary64`
971×	`fma-def_binary64`
653×	`associate-/l*_binary64`
535×	`associate-/l/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	22	14
2	30	14
3	75	14
4	112	14
5	222	14
6	406	14
7	419	14
8	783	14
9	937	14
10	1259	14
11	1611	14
12	1778	14
13	2015	14
14	2939	14
15	3245	14
16	5075	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

8.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	8.8b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))

Compiler

Compiled 47 to 27 computations (42.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (/.f64 x y) x)
✓	8.2b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))

series19.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))
7.0ms	(fma.f64 x (/.f64 x y) x)

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
4×	`associate-/r*_binary64`

Counts

2 → 45

Calls

2 calls:

4.0ms	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))
0.0ms	(fma.f64 x (/.f64 x y) x)

simplify85.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

1032×	`fma-neg_binary64`
526×	`cancel-sign-sub-inv_binary64`
338×	`sub-neg_binary64`
265×	`distribute-rgt-in_binary64`
240×	`associate-/l/_binary64`

Counts

93 → 74

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1641
1	245	1554
2	714	1484
3	2409	1453
4	4439	1453
5	5061	1453

prune50.0ms (1.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	70	4	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	4	75

Error

0.0b

Counts

75 → 4

Alt Table

Status	Error	Program
	9.8b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))) (cbrt.f64 (/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1)))) (cbrt.f64 (/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))))
	8.8b	(/.f64 (+.f64 (*.f64 x (/.f64 x y)) x) (+.f64 x 1))
	9.0b	(/.f64 1 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))
▶	0.0b	(.f64 1 (.f64 (+.f64 (/.f64 x y) 1) (/.f64 x (+.f64 x 1))))

Compiler

Compiled 1415 to 634 computations (55.2% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (+.f64 x 1))
✓	0.0b	(+.f64 (/.f64 x y) 1)
✓	0.0b	(*.f64 (+.f64 (/.f64 x y) 1) (/.f64 x (+.f64 x 1)))

series17.0ms (0.6%)

Counts

3 → 51

Calls

3 calls:

11.0ms	(*.f64 (+.f64 (/.f64 x y) 1) (/.f64 x (+.f64 x 1)))
4.0ms	(+.f64 (/.f64 x y) 1)
2.0ms	(/.f64 x (+.f64 x 1))

rewrite25.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64`
34×	`times-frac_binary64`
33×	`add-sqr-sqrt_binary64`
28×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64`

Counts

3 → 106

Calls

3 calls:

11.0ms	(*.f64 (+.f64 (/.f64 x y) 1) (/.f64 x (+.f64 x 1)))
5.0ms	(+.f64 (/.f64 x y) 1)
3.0ms	(/.f64 x (+.f64 x 1))

simplify127.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

440×	`fma-def_binary64`
386×	`associate-/l*_binary64`
386×	`times-frac_binary64`
344×	`distribute-rgt-in_binary64`
313×	`fma-neg_binary64`

Counts

157 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	171	2330
1	444	2167
2	1466	2015
3	4449	2015
4	4896	2015
5	4995	2015
6	4966	2015

prune112.0ms (3.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	160	1	161
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	160	5	165

Error

Counts

165 → 5

Alt Table

Status	Error	Program
▶	0.6b	(.f64 1 (.f64 (fma.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (/.f64 (cbrt.f64 x) y) 1) (/.f64 x (+.f64 x 1))))
	9.8b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))) (cbrt.f64 (/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1)))) (cbrt.f64 (/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))))
	8.8b	(/.f64 (+.f64 (*.f64 x (/.f64 x y)) x) (+.f64 x 1))
	9.0b	(/.f64 1 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))
✓	0.0b	(.f64 1 (.f64 (+.f64 (/.f64 x y) 1) (/.f64 x (+.f64 x 1))))

Compiler

Compiled 3433 to 2081 computations (39.4% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (/.f64 (cbrt.f64 x) y) 1)
✓	0.3b	(/.f64 (cbrt.f64 x) y)
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)

series444.0ms (15.1%)

Counts

4 → 72

Calls

4 calls:

213.0ms	(/.f64 (cbrt.f64 x) y)
164.0ms	(fma.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (/.f64 (cbrt.f64 x) y) 1)
33.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
33.0ms	(cbrt.f64 x)

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
31×	`cbrt-prod_binary64`
28×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`

Counts

4 → 106

Calls

4 calls:

5.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
2.0ms	(/.f64 (cbrt.f64 x) y)
1.0ms	(cbrt.f64 x)
0.0ms	(fma.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (/.f64 (cbrt.f64 x) y) 1)

simplify93.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

508×	`unswap-sqr_binary64`
461×	`*-commutative_binary64`
379×	`log-prod_binary64`
375×	`associate-/l*_binary64`
342×	`exp-prod_binary64`

Counts

178 → 155

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	128	1685
1	209	1529
2	673	1472
3	2156	1457
4	4131	1433
5	4988	1433

prune141.0ms (4.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	193	0	193
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	193	5	198

Error

Counts

198 → 5

Alt Table

Status	Error	Program
✓	0.6b	(.f64 1 (.f64 (fma.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (/.f64 (cbrt.f64 x) y) 1) (/.f64 x (+.f64 x 1))))
	9.8b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))) (cbrt.f64 (/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1)))) (cbrt.f64 (/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))))
▶	8.8b	(/.f64 (+.f64 (*.f64 x (/.f64 x y)) x) (+.f64 x 1))
	9.0b	(/.f64 1 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))
✓	0.0b	(.f64 1 (.f64 (+.f64 (/.f64 x y) 1) (/.f64 x (+.f64 x 1))))

Compiler

Compiled 5138 to 2617 computations (49.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 x (/.f64 x y)) x)
✓	0.1b	(*.f64 x (/.f64 x y))
✓	8.2b	(/.f64 (+.f64 (*.f64 x (/.f64 x y)) x) (+.f64 x 1))

series42.0ms (1.4%)

Counts

3 → 72

Calls

3 calls:

22.0ms	(/.f64 (+.f64 (*.f64 x (/.f64 x y)) x) (+.f64 x 1))
13.0ms	(*.f64 x (/.f64 x y))
7.0ms	(+.f64 (*.f64 x (/.f64 x y)) x)

rewrite22.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
22×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`

Counts

3 → 85

Calls

3 calls:

7.0ms	(+.f64 (*.f64 x (/.f64 x y)) x)
6.0ms	(/.f64 (+.f64 (*.f64 x (/.f64 x y)) x) (+.f64 x 1))
4.0ms	(*.f64 x (/.f64 x y))

simplify89.0ms (3%)

Algorithm

1×	egg-herbie

Rules

614×	`fma-neg_binary64`
520×	`fma-def_binary64`
406×	`sub-neg_binary64`
360×	`associate-/l*_binary64`
317×	`times-frac_binary64`

Counts

157 → 154

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	174	2274
1	434	2154
2	1421	2082
3	4190	2074
4	5113	2074

prune102.0ms (3.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	154	5	159

Error

Counts

159 → 5

Alt Table

Status	Error	Program
✓	0.6b	(.f64 1 (.f64 (fma.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (/.f64 (cbrt.f64 x) y) 1) (/.f64 x (+.f64 x 1))))
	23.9b	(/.f64 (+.f64 (cbrt.f64 (pow.f64 (/.f64 (*.f64 x x) y) 3)) x) (+.f64 x 1))
✓	8.8b	(/.f64 (+.f64 (*.f64 x (/.f64 x y)) x) (+.f64 x 1))
	9.0b	(/.f64 1 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))
✓	0.0b	(.f64 1 (.f64 (+.f64 (/.f64 x y) 1) (/.f64 x (+.f64 x 1))))

Compiler

Compiled 2957 to 1190 computations (59.8% saved)

regimes140.0ms (4.8%)

Accuracy

Total 0.0b remaining (48.3%)

Threshold costs 0.0b (48.3%)

Counts

53 → 1

Compiler

Compiled 2648 to 1511 computations (42.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	14	16
2	13	16

end70.0ms (2.4%)

Compiler: Compiled 107 to 72 computations (32.7% saved)

Details

analyze186.0ms (6.4%)

sample1.0s (35%)

simplify87.0ms (3%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series19.0ms (0.6%)

rewrite6.0ms (0.2%)

simplify85.0ms (2.9%)

prune50.0ms (1.7%)

localize7.0ms (0.2%)

series17.0ms (0.6%)

rewrite25.0ms (0.9%)

simplify127.0ms (4.3%)

prune112.0ms (3.8%)

localize11.0ms (0.4%)

series444.0ms (15.1%)

rewrite12.0ms (0.4%)

simplify93.0ms (3.2%)

prune141.0ms (4.8%)

localize6.0ms (0.2%)

series42.0ms (1.4%)

rewrite22.0ms (0.7%)

simplify89.0ms (3%)

prune102.0ms (3.5%)

regimes140.0ms (4.8%)

simplify2.0ms (0.1%)

end70.0ms (2.4%)

Profiling