Details

analyze514.0ms (8.5%)

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
12.5%	87.4%	0.1%	6
18.7%	81.1%	0.1%	7
35.9%	64%	0.1%	8
47.2%	52.7%	0.1%	9
52.1%	47.8%	0.1%	10
65.3%	34.5%	0.1%	11
71.4%	28.4%	0.1%	12
74.2%	25.6%	0.1%	13
81.7%	18.1%	0.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample2.2s (35.8%)

Results

2.0s

8256×

body

128

valid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify139.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

2495×	`fma-neg_binary64`
1241×	`fma-def_binary64`
1051×	`div-sub_binary64`
520×	`unswap-sqr_binary64`
430×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 9 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	20	18
2	31	18
3	48	18
4	71	18
5	103	18
6	155	18
7	209	18
8	270	18
9	300	16
10	389	16
11	599	16
12	934	16
13	1583	16
14	1525	16
15	1839	16
16	1745	16
17	1773	16
18	1933	16
19	2758	16
20	3102	16
21	4012	16
22	4885	16
23	4851	16

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.8b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
▶	0.1b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))

Compiler

Compiled 84 to 56 computations (33.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
✓	0.0b	(fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)
✓	0.1b	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
✓	0.2b	(/.f64 -5641895835477563/5000000000000000 y)

series111.0ms (1.8%)

Counts

4 → 108

Calls

4 calls:

49.0ms	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
47.0ms	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
13.0ms	(fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)
2.0ms	(/.f64 -5641895835477563/5000000000000000 y)

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
21×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
8×	`add-cbrt-cube_binary64`

Counts

4 → 85

Calls

4 calls:

4.0ms	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
3.0ms	(/.f64 -5641895835477563/5000000000000000 y)
2.0ms	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
0.0ms	(fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)

simplify130.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

759×	`associate-/l*_binary64`
549×	`fma-def_binary64`
209×	`distribute-rgt-in_binary64`
152×	`associate-/l/_binary64`
149×	`distribute-lft-in_binary64`

Counts

193 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	263	4154
1	654	3971
2	1995	3895
3	5228	3895

prune176.0ms (2.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	158	3	161
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	159	4	163

Error

Counts

163 → 4

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 x (/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y)))))
	2.8b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
	13.2b	(+.f64 x (cbrt.f64 (/.f64 (.f64 (.f64 -1 -1) -1) (.f64 (.f64 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x) (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)) (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))))
	25.2b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)

Compiler

Compiled 3855 to 2411 computations (37.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y)))
✓	0.0b	(+.f64 x (/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y)))))
✓	0.1b	(/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y))))
✓	0.2b	(*.f64 5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y))

series155.0ms (2.6%)

Counts

4 → 78

Calls

4 calls:

71.0ms	(+.f64 x (/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y)))))
47.0ms	(/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y))))
29.0ms	(-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y)))
8.0ms	(*.f64 5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y))

rewrite75.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

29.0ms	(*.f64 5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y))
22.0ms	(/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y))))
6.0ms	(+.f64 x (/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y)))))
2.0ms	(-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y)))

simplify191.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

723×	`fma-def_binary64`
399×	`fma-neg_binary64`
224×	`distribute-rgt-in_binary64`
191×	`cancel-sign-sub-inv_binary64`
167×	`distribute-lft-in_binary64`

Counts

180 → 223

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	296	4370
1	776	4169
2	2422	3938
3	4790	3930
4	4979	3930
5	4961	3930

prune256.0ms (4.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	223	0	223
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	223	4	227

Error

Counts

227 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 x (/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y)))))
▶	2.8b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
	13.2b	(+.f64 x (cbrt.f64 (/.f64 (.f64 (.f64 -1 -1) -1) (.f64 (.f64 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x) (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)) (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))))
	25.2b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)

Compiler

Compiled 5381 to 3066 computations (43% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))
✓	0.0b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
✓	0.2b	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
✓	7.7b	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))

series101.0ms (1.7%)

Counts

4 → 112

Calls

4 calls:

46.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
43.0ms	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))
10.0ms	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
2.0ms	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
8×	`add-cbrt-cube_binary64`

Counts

4 → 84

Calls

4 calls:

8.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
6.0ms	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))
3.0ms	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
3.0ms	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))

simplify140.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

853×	`fma-def_binary64`
270×	`fma-neg_binary64`
253×	`associate-/r/_binary64`
229×	`cancel-sign-sub-inv_binary64`
155×	`associate-/l/_binary64`

Counts

196 → 208

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	252	4366
1	671	4279
2	2246	4156
3	4858	4146
4	4953	4146

prune224.0ms (3.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	208	0	208
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	208	4	212

Error

Counts

212 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 x (/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y)))))
✓	2.8b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
▶	13.2b	(+.f64 x (cbrt.f64 (/.f64 (.f64 (.f64 -1 -1) -1) (.f64 (.f64 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x) (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)) (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))))
	25.2b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)

Compiler

Compiled 4868 to 2510 computations (48.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x) (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
✓	0.2b	(/.f64 (.f64 (.f64 -1 -1) -1) (.f64 (.f64 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x) (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)) (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
	0.2b	(/.f64 -5641895835477563/5000000000000000 y)
✓	33.9b	(cbrt.f64 (/.f64 (.f64 (.f64 -1 -1) -1) (.f64 (.f64 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x) (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)) (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))))

series314.0ms (5.2%)

Counts

3 → 108

Calls

3 calls:

144.0ms

(/.f64 (*.f64 (*.f64 -1 -1) -1) (*.f64 (*.f64 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x) (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)) (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))

144.0ms

(cbrt.f64 (/.f64 (*.f64 (*.f64 -1 -1) -1) (*.f64 (*.f64 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x) (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)) (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))))

25.0ms

(*.f64 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x) (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-cbrt-cube_binary64`
41×	`add-exp-log_binary64`
19×	`cbrt-unprod_binary64`
19×	`prod-exp_binary64`
10×	`add-sqr-sqrt_binary64`

Counts

3 → 79

Calls

3 calls:

11.0ms

(/.f64 (*.f64 (*.f64 -1 -1) -1) (*.f64 (*.f64 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x) (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)) (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))

8.0ms

(cbrt.f64 (/.f64 (*.f64 (*.f64 -1 -1) -1) (*.f64 (*.f64 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x) (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)) (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))))

3.0ms

(*.f64 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x) (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))

simplify144.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

492×	`times-frac_binary64`
401×	`associate-/r*_binary64`
391×	`associate-/l*_binary64`
295×	`fma-def_binary64`
233×	`associate-l_binary64`

Counts

187 → 172

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	453	8245
1	1373	6265
2	4992	6265

prune343.0ms (5.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	271	0	271
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	271	4	275

Error

Counts

275 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 x (/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y)))))
✓	2.8b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
✓	13.2b	(+.f64 x (cbrt.f64 (/.f64 (.f64 (.f64 -1 -1) -1) (.f64 (.f64 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x) (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)) (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))))
	25.2b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)

Compiler

Compiled 11909 to 7657 computations (35.7% saved)

regimes678.0ms (11.2%)

Accuracy

Total 0.0b remaining (92.6%)

Threshold costs 0.0b (92.6%)

Counts

100 → 1

Compiler

Compiled 14109 to 9866 computations (30.1% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	12	16
2	12	16

end87.0ms (1.4%)

Compiler: Compiled 103 to 71 computations (31.1% saved)

Details

analyze514.0ms (8.5%)

sample2.2s (35.8%)

simplify139.0ms (2.3%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series111.0ms (1.8%)

rewrite13.0ms (0.2%)

simplify130.0ms (2.1%)

prune176.0ms (2.9%)

localize8.0ms (0.1%)

series155.0ms (2.6%)

rewrite75.0ms (1.2%)

simplify191.0ms (3.1%)

prune256.0ms (4.2%)

localize8.0ms (0.1%)

series101.0ms (1.7%)

rewrite24.0ms (0.4%)

simplify140.0ms (2.3%)

prune224.0ms (3.7%)

localize14.0ms (0.2%)

series314.0ms (5.2%)

rewrite31.0ms (0.5%)

simplify144.0ms (2.4%)

prune343.0ms (5.7%)

regimes678.0ms (11.2%)

simplify5.0ms (0.1%)

end87.0ms (1.4%)

Profiling