Details

analyze669.0ms (9.2%)

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
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
37.4%	62.4%	0.1%	6
46.8%	53%	0.1%	7
52.3%	47.6%	0.1%	8
65.5%	34.3%	0.1%	9
71%	28.9%	0.1%	10
75%	24.9%	0.1%	11
81.6%	18.2%	0.1%	12
84.5%	15.4%	0.1%	13
86.9%	13%	0.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample42.0ms (0.6%)

Algorithm

1×

intervals

Results

24.0ms

256×

body

128

valid

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify158.0ms (2.2%)

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

prune7.0ms (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
▶	0.1b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
	2.6b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 84 to 56 computations (33.3% saved)

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series201.0ms (2.8%)

Counts

3 → 72

Calls

3 calls:

99.0ms

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

98.0ms

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

3.0ms

(/.f64 -5641895835477563/5000000000000000 y)

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
7×	`add-cbrt-cube_binary64`

Counts

3 → 75

Calls

3 calls:

9.0ms

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

6.0ms

(/.f64 -5641895835477563/5000000000000000 y)

4.0ms

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

simplify227.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

753×	`associate-/l*_binary64`
483×	`fma-def_binary64`
213×	`fma-neg_binary64`
189×	`distribute-rgt-in_binary64`
149×	`associate-/l/_binary64`

Counts

147 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	3584
1	599	3514
2	1868	3402
3	4874	3394
4	4971	3394

prune223.0ms (3.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	134	3	137
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	134	5	139

Error

Counts

139 → 5

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
▶	2.6b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
	24.2b	(+.f64 x (*.f64 (sqrt.f64 (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))) (sqrt.f64 (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))))
	9.6b	(+.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)))))
	24.9b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)

Compiler

Compiled 3490 to 2197 computations (37% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
✓	0.0b	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))
✓	1.2b	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
✓	8.9b	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))

series190.0ms (2.6%)

Counts

4 → 112

Calls

4 calls:

85.0ms	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))
81.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
20.0ms	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
4.0ms	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))

rewrite46.0ms (0.6%)

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:

14.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
9.0ms	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))
8.0ms	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
7.0ms	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))

simplify249.0ms (3.4%)

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

prune350.0ms (4.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	207	1	208
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	209	4	213

Error

Counts

213 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
▶	2.6b	(+.f64 x (/.f64 y (-.f64 (exp.f64 (+.f64 (log.f64 5641895835477563/5000000000000000) z)) (*.f64 x y))))
	9.6b	(+.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)))))
	24.9b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)

Compiler

Compiled 4884 to 2521 computations (48.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (+.f64 (log.f64 5641895835477563/5000000000000000) z))
✓	1.2b	(-.f64 (exp.f64 (+.f64 (log.f64 5641895835477563/5000000000000000) z)) (*.f64 x y))
✓	2.0b	(log.f64 5641895835477563/5000000000000000)
✓	8.9b	(/.f64 y (-.f64 (exp.f64 (+.f64 (log.f64 5641895835477563/5000000000000000) z)) (*.f64 x y)))

series137.0ms (1.9%)

Counts

4 → 76

Calls

4 calls:

78.0ms	(/.f64 y (-.f64 (exp.f64 (+.f64 (log.f64 5641895835477563/5000000000000000) z)) (*.f64 x y)))
55.0ms	(-.f64 (exp.f64 (+.f64 (log.f64 5641895835477563/5000000000000000) z)) (*.f64 x y))
4.0ms	(exp.f64 (+.f64 (log.f64 5641895835477563/5000000000000000) z))
0.0ms	(log.f64 5641895835477563/5000000000000000)

rewrite43.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
8×	`add-log-exp_binary64`

Counts

4 → 84

Calls

4 calls:

14.0ms	(/.f64 y (-.f64 (exp.f64 (+.f64 (log.f64 5641895835477563/5000000000000000) z)) (*.f64 x y)))
11.0ms	(exp.f64 (+.f64 (log.f64 5641895835477563/5000000000000000) z))
10.0ms	(-.f64 (exp.f64 (+.f64 (log.f64 5641895835477563/5000000000000000) z)) (*.f64 x y))
1.0ms	(log.f64 5641895835477563/5000000000000000)

simplify198.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

823×	`associate-/l*_binary64`
509×	`fma-def_binary64`
209×	`fma-neg_binary64`
194×	`associate-/r/_binary64`
153×	`associate-/l/_binary64`

Counts

160 → 173

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	209	3093
1	489	2971
2	1634	2874
3	4822	2872
4	4941	2872

prune317.0ms (4.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	173	4	177

Error

Counts

177 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
✓	2.6b	(+.f64 x (/.f64 y (-.f64 (exp.f64 (+.f64 (log.f64 5641895835477563/5000000000000000) z)) (*.f64 x y))))
▶	9.6b	(+.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)))))
	24.9b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)

Compiler

Compiled 3982 to 2295 computations (42.4% saved)

localize35.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.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)))
✓	0.1b	(.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)
✓	29.8b	(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))))

series595.0ms (8.2%)

Counts

3 → 108

Calls

3 calls:

272.0ms

(/.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)))

240.0ms

(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))))

81.0ms

(*.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))

rewrite70.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-cbrt-cube_binary64`
44×	`add-exp-log_binary64`
22×	`pow1_binary64`
21×	`cbrt-unprod_binary64`
21×	`prod-exp_binary64`

Counts

3 → 83

Calls

3 calls:

21.0ms

(/.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)))

17.0ms

(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))))

9.0ms

(*.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))

simplify289.0ms (4%)

Algorithm

1×	egg-herbie

Rules

510×	`times-frac_binary64`
412×	`associate-/r*_binary64`
402×	`associate-/l*_binary64`
348×	`fma-def_binary64`
238×	`associate-l_binary64`

Counts

191 → 176

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	472	8906
1	1464	6618
2	5160	6618

prune654.0ms (9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	275	0	275
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	275	4	279

Error

Counts

279 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
✓	2.6b	(+.f64 x (/.f64 y (-.f64 (exp.f64 (+.f64 (log.f64 5641895835477563/5000000000000000) z)) (*.f64 x y))))
✓	9.6b	(+.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)))))
	24.9b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)

Compiler

Compiled 12068 to 7819 computations (35.2% saved)

regimes955.0ms (13.2%)

Accuracy

Total 0.1b remaining (90.5%)

Threshold costs 0.1b (90.5%)

Counts

63 → 3

Compiler

Compiled 7302 to 5525 computations (24.3% saved)

bsearch49.0ms (0.7%)

Steps

Iters	Range		Point
1	1.1284088629419693	1.2268051383513738	1.2022060694990226
14	0.0	0.0322665064721328	7.106359833159424e-307

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
5×	`*-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	61
1	34	61
2	43	61
3	49	61
4	53	61
5	54	61
6	54	61

end2.0ms (0%)

Compiler: Compiled 43 to 28 computations (34.9% saved)

sample1.4s (20%)

Algorithm

1×

intervals

Results

807.0ms

8000×

body

128

valid

Compiler

Compiled 137 to 93 computations (32.1% saved)

Details

analyze669.0ms (9.2%)

sample42.0ms (0.6%)

simplify158.0ms (2.2%)

prune7.0ms (0.1%)

localize15.0ms (0.2%)

series201.0ms (2.8%)

rewrite25.0ms (0.4%)

simplify227.0ms (3.1%)

prune223.0ms (3.1%)

localize18.0ms (0.3%)

series190.0ms (2.6%)

rewrite46.0ms (0.6%)

simplify249.0ms (3.4%)

prune350.0ms (4.8%)

localize18.0ms (0.2%)

series137.0ms (1.9%)

rewrite43.0ms (0.6%)

simplify198.0ms (2.7%)

prune317.0ms (4.4%)

localize35.0ms (0.5%)

series595.0ms (8.2%)

rewrite70.0ms (1%)

simplify289.0ms (4%)

prune654.0ms (9%)

regimes955.0ms (13.2%)

bsearch49.0ms (0.7%)

simplify9.0ms (0.1%)

end2.0ms (0%)

sample1.4s (20%)

Profiling