Details

analyze1.0s (32.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
9.4%	90.4%	0.2%	8
9.4%	90.4%	0.2%	9
10.9%	88.9%	0.2%	10
25.9%	73.9%	0.2%	11
47.1%	52.7%	0.2%	12
55.3%	44.5%	0.2%	13
59.2%	40.6%	0.2%	14

Compiler

Compiled 22 to 15 computations (31.8% saved)

sample84.0ms (2.6%)

Algorithm

1×

intervals

Results

18.0ms

256×

body

128

valid

Compiler

Compiled 47 to 33 computations (29.8% saved)

simplify55.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

508×	`fma-neg_binary64`
504×	`associate-*l/_binary64`
466×	`div-sub_binary64`
450×	`cancel-sign-sub-inv_binary64`
403×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	30	25
2	70	25
3	177	22
4	486	19
5	1087	19
6	2534	19
7	4434	19
8	5156	19

prune4.0ms (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

3.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	3.4b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
	14.5b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))

Compiler

Compiled 110 to 70 computations (36.4% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.1b	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
✓	6.0b	(/.f64 (.f64 y t) (.f64 2 z))

series45.0ms (1.4%)

Counts

2 → 72

Calls

2 calls:

31.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
14.0ms	(/.f64 (.f64 y t) (.f64 2 z))

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
16×	`times-frac_binary64`
16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`

Counts

2 → 62

Calls

2 calls:

5.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
4.0ms	(/.f64 (.f64 y t) (.f64 2 z))

simplify93.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

873×	`fma-def_binary64`
636×	`associate-*l/_binary64`
486×	`associate-/l/_binary64`
282×	`associate-/r/_binary64`
213×	`times-frac_binary64`

Counts

134 → 114

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	175	2886
1	443	2809
2	1770	2787
3	4920	2776
4	5630	2776

prune110.0ms (3.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	113	3	116

Error

Counts

116 → 3

Alt Table

Status	Error	Program
	3.4b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))
▶	0.0b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
	25.3b	(-.f64 x (*.f64 -2 (/.f64 z t)))

Compiler

Compiled 2776 to 1446 computations (47.9% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.1b	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))
✓	4.6b	(*.f64 (/.f64 y 2) (/.f64 t z))

series49.0ms (1.5%)

Counts

2 → 72

Calls

2 calls:

30.0ms	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))
19.0ms	(*.f64 (/.f64 y 2) (/.f64 t z))

rewrite18.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
31×	`times-frac_binary64`
24×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`

Counts

2 → 83

Calls

2 calls:

9.0ms	(*.f64 (/.f64 y 2) (/.f64 t z))
3.0ms	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))

simplify103.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

899×	`times-frac_binary64`
405×	`associate-/l/_binary64`
192×	`fma-def_binary64`
144×	`associate-/l*_binary64`
142×	`associate-*l/_binary64`

Counts

155 → 153

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	217	3106
1	574	3031
2	1921	3007
3	4843	3007
4	4957	3007

prune102.0ms (3.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	153	3	156

Error

Counts

156 → 3

Alt Table

Status	Error	Program
▶	3.4b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))
✓	0.0b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
	25.3b	(-.f64 x (*.f64 -2 (/.f64 z t)))

Compiler

Compiled 3526 to 1775 computations (49.7% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
✓	2.9b	(.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z)))))
	6.0b	(/.f64 (.f64 y t) (.f64 2 z))

series58.0ms (1.8%)

Counts

2 → 72

Calls

2 calls:

29.0ms	(/.f64 1 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
29.0ms	(.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z)))))

rewrite22.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

2 → 89

Calls

2 calls:

9.0ms	(.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z)))))
7.0ms	(/.f64 1 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))

simplify94.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

768×	`associate-/r*_binary64`
520×	`associate-*l/_binary64`
347×	`fma-def_binary64`
216×	`associate-/r/_binary64`
174×	`associate-/l/_binary64`

Counts

161 → 155

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	173	4402
1	458	4169
2	1716	4122
3	5191	4122

prune150.0ms (4.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	191	3	194

Error

Counts

194 → 3

Alt Table

Status	Error	Program
✓	3.4b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))
✓	0.0b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
▶	25.3b	(-.f64 x (*.f64 -2 (/.f64 z t)))

Compiler

Compiled 5005 to 2863 computations (42.8% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 -2 (/.f64 z t)))
✓	0.0b	(*.f64 -2 (/.f64 z t))

series19.0ms (0.6%)

Counts

2 → 36

Calls

2 calls:

12.0ms	(-.f64 x (*.f64 -2 (/.f64 z t)))
6.0ms	(*.f64 -2 (/.f64 z t))

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
10×	`times-frac_binary64`

Counts

2 → 54

Calls

2 calls:

5.0ms	(*.f64 -2 (/.f64 z t))
2.0ms	(-.f64 x (*.f64 -2 (/.f64 z t)))

simplify62.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

569×	`fma-def_binary64`
566×	`associate-/l*_binary64`
275×	`associate-/l/_binary64`
241×	`distribute-rgt-in_binary64`
221×	`times-frac_binary64`

Counts

90 → 88

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	110	899
1	244	849
2	640	829
3	1931	829
4	4657	829
5	4959	829

prune45.0ms (1.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	88	3	91

Error

Counts

91 → 3

Alt Table

Status	Error	Program
✓	3.4b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))
✓	0.0b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
✓	25.3b	(-.f64 x (*.f64 -2 (/.f64 z t)))

Compiler

Compiled 1185 to 597 computations (49.6% saved)

regimes115.0ms (3.6%)

Accuracy

Total 1.0b remaining (99.4%)

Threshold costs 1.0b (99.4%)

Counts

17 → 1

Compiler

Compiled 1870 to 1276 computations (31.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
7×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	20	19
2	36	19
3	48	19
4	57	19
5	61	19
6	62	19
7	62	19

end0.0ms (0%)

Compiler: Compiled 17 to 11 computations (35.3% saved)

sample877.0ms (27.3%)

Algorithm

1×

intervals

Results

554.0ms

8000×

body

128

valid

Compiler

Compiled 90 to 62 computations (31.1% saved)

Details

analyze1.0s (32.7%)

sample84.0ms (2.6%)

simplify55.0ms (1.7%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series45.0ms (1.4%)

rewrite13.0ms (0.4%)

simplify93.0ms (2.9%)

prune110.0ms (3.4%)

localize9.0ms (0.3%)

series49.0ms (1.5%)

rewrite18.0ms (0.6%)

simplify103.0ms (3.2%)

prune102.0ms (3.2%)

localize9.0ms (0.3%)

series58.0ms (1.8%)

rewrite22.0ms (0.7%)

simplify94.0ms (2.9%)

prune150.0ms (4.7%)

localize4.0ms (0.1%)

series19.0ms (0.6%)

rewrite10.0ms (0.3%)

simplify62.0ms (1.9%)

prune45.0ms (1.4%)

regimes115.0ms (3.6%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample877.0ms (27.3%)

Profiling