Details

analyze15.0ms (0.7%)

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
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
93.7%	6.2%	0.1%	7
96.8%	3.1%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 22 to 13 computations (40.9% saved)

sample158.0ms (6.9%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

128

valid

Compiler

Compiled 45 to 27 computations (40% saved)

simplify107.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
549×	`sub-neg_binary64`
460×	`distribute-neg-frac_binary64`
455×	`cancel-sign-sub-inv_binary64`
430×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	23	24
2	52	24
3	105	24
4	199	24
5	330	24
6	442	24
7	603	24
8	901	24
9	2304	24
10	3386	24
11	3956	24
12	4454	24
13	4735	24
14	5238	24

prune3.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

31.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	31.9b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

Compiler

Compiled 80 to 44 computations (45% saved)

localize8.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.7b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
✓	31.3b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

series30.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

22.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
8.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))

rewrite19.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 50

Calls

2 calls:

12.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
3.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))

simplify85.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

499×	`associate-l_binary64`
433×	`fma-def_binary64`
328×	`times-frac_binary64`
299×	`associate-/l*_binary64`
248×	`associate-/r*_binary64`

Counts

98 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	129	2360
1	338	2193
2	1191	2164
3	4702	2164
4	4914	2164

prune82.0ms (3.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	104	5	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	5	110

Error

0.6b

Counts

110 → 5

Alt Table

Status	Error	Program
	31.9b	(log.f64 (exp.f64 (/.f64 (fma.f64 x x (.f64 (.f64 y y) -4)) (fma.f64 x x (.f64 (.f64 y y) 4)))))
▶	31.5b	1
	35.9b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
	32.6b	-1
	31.9b	(/.f64 1 (/.f64 (fma.f64 x x (.f64 (.f64 y y) 4)) (fma.f64 x x (.f64 (.f64 y y) -4))))

Compiler

Compiled 3315 to 1744 computations (47.4% saved)

localize0.0ms (0%)

prune4.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	0	0
Total	5	5

Error

0.6b

Counts

5 → 5

Alt Table

Status	Error	Program
	31.9b	(log.f64 (exp.f64 (/.f64 (fma.f64 x x (.f64 (.f64 y y) -4)) (fma.f64 x x (.f64 (.f64 y y) 4)))))
✓	31.5b	1
	35.9b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
	32.6b	-1
▶	31.9b	(/.f64 1 (/.f64 (fma.f64 x x (.f64 (.f64 y y) 4)) (fma.f64 x x (.f64 (.f64 y y) -4))))

Compiler

Compiled 117 to 73 computations (37.6% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 y y) 4)
✓	0.0b	(/.f64 1 (/.f64 (fma.f64 x x (.f64 (.f64 y y) 4)) (fma.f64 x x (.f64 (.f64 y y) -4))))
✓	1.8b	(fma.f64 x x (.f64 (.f64 y y) -4))
✓	31.3b	(/.f64 (fma.f64 x x (.f64 (.f64 y y) 4)) (fma.f64 x x (.f64 (.f64 y y) -4)))

series54.0ms (2.3%)

Counts

4 → 84

Calls

4 calls:

17.0ms	(/.f64 (fma.f64 x x (.f64 (.f64 y y) 4)) (fma.f64 x x (.f64 (.f64 y y) -4)))
17.0ms	(/.f64 1 (/.f64 (fma.f64 x x (.f64 (.f64 y y) 4)) (fma.f64 x x (.f64 (.f64 y y) -4))))
15.0ms	(fma.f64 x x (.f64 (.f64 y y) -4))
4.0ms	(.f64 (.f64 y y) 4)

rewrite22.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
56×	`add-sqr-sqrt_binary64`
55×	`*-un-lft-identity_binary64`
55×	`add-cube-cbrt_binary64`
22×	`add-exp-log_binary64`

Counts

4 → 138

Calls

4 calls:

4.0ms	(.f64 (.f64 y y) 4)
4.0ms	(/.f64 1 (/.f64 (fma.f64 x x (.f64 (.f64 y y) 4)) (fma.f64 x x (.f64 (.f64 y y) -4))))
2.0ms	(/.f64 (fma.f64 x x (.f64 (.f64 y y) 4)) (fma.f64 x x (.f64 (.f64 y y) -4)))
0.0ms	(fma.f64 x x (.f64 (.f64 y y) -4))

simplify183.0ms (8%)

Algorithm

1×	egg-herbie

Rules

469×	`associate-l_binary64`
451×	`times-frac_binary64`
409×	`associate-r_binary64`
359×	`fma-neg_binary64`
265×	`associate-/r*_binary64`

Counts

222 → 203

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	6284
1	405	5810
2	1215	5756
3	4264	5756
4	4948	5756
5	4953	5756

prune157.0ms (6.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	203	0	203
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	203	5	208

Error

0.6b

Counts

208 → 5

Alt Table

Status	Error	Program
▶	31.9b	(log.f64 (exp.f64 (/.f64 (fma.f64 x x (.f64 (.f64 y y) -4)) (fma.f64 x x (.f64 (.f64 y y) 4)))))
✓	31.5b	1
	35.9b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
	32.6b	-1
✓	31.9b	(/.f64 1 (/.f64 (fma.f64 x x (.f64 (.f64 y y) 4)) (fma.f64 x x (.f64 (.f64 y y) -4))))

Compiler

Compiled 6484 to 3513 computations (45.8% saved)

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(.f64 (.f64 y y) 4)
✓	0.0b	(log.f64 (exp.f64 (/.f64 (fma.f64 x x (.f64 (.f64 y y) -4)) (fma.f64 x x (.f64 (.f64 y y) 4)))))
	1.8b	(fma.f64 x x (.f64 (.f64 y y) -4))
✓	31.3b	(/.f64 (fma.f64 x x (.f64 (.f64 y y) -4)) (fma.f64 x x (.f64 (.f64 y y) 4)))

series42.0ms (1.8%)

Counts

2 → 48

Calls

2 calls:

24.0ms	(log.f64 (exp.f64 (/.f64 (fma.f64 x x (.f64 (.f64 y y) -4)) (fma.f64 x x (.f64 (.f64 y y) 4)))))
18.0ms	(/.f64 (fma.f64 x x (.f64 (.f64 y y) -4)) (fma.f64 x x (.f64 (.f64 y y) 4)))

rewrite11.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
18×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
14×	`log-pow_binary64`

Counts

2 → 56

Calls

2 calls:

3.0ms	(log.f64 (exp.f64 (/.f64 (fma.f64 x x (.f64 (.f64 y y) -4)) (fma.f64 x x (.f64 (.f64 y y) 4)))))
2.0ms	(/.f64 (fma.f64 x x (.f64 (.f64 y y) -4)) (fma.f64 x x (.f64 (.f64 y y) 4)))

simplify106.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

680×	`fma-neg_binary64`
571×	`fma-def_binary64`
381×	`associate-/r/_binary64`
354×	`cancel-sign-sub-inv_binary64`
282×	`associate-/l/_binary64`

Counts

104 → 84

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	138	3077
1	242	2867
2	589	2843
3	1956	2807
4	4890	2807
5	5237	2807

prune88.0ms (3.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	125	5	130

Error

0.6b

Counts

130 → 5

Alt Table

Status	Error	Program
✓	31.9b	(log.f64 (exp.f64 (/.f64 (fma.f64 x x (.f64 (.f64 y y) -4)) (fma.f64 x x (.f64 (.f64 y y) 4)))))
✓	31.5b	1
	35.9b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
	32.6b	-1
✓	31.9b	(/.f64 1 (/.f64 (fma.f64 x x (.f64 (.f64 y y) 4)) (fma.f64 x x (.f64 (.f64 y y) -4))))

Compiler

Compiled 3731 to 1977 computations (47% saved)

regimes278.0ms (12.2%)

Accuracy

Total 12.7b remaining (97.4%)

Threshold costs 0b (0%)

Counts

17 → 5

Compiler

Compiled 2983 to 1724 computations (42.2% saved)

bsearch67.0ms (2.9%)

Steps

Iters	Range		Point
8	2.1033317706404465e+98	1.1432126425379692e+101	1.1059142702918062e+101
8	5.2457540392618654e-141	6.862235276571588e-138	1.2000096904552647e-140
11	-1.6972043026141638e-7	-3.8186533484311395e-28	-1.6627280741517615e-25
7	-2.2243175699992136e+106	-1.3285854952512314e+105	-4.783857141098266e+105

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
5×	`+-commutative_binary64`
4×	`distribute-rgt-neg-in_binary64`
4×	`sub-neg_binary64`
3×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	86
1	47	86
2	60	86
3	66	86
4	70	86
5	71	86
6	69	86

end1.0ms (0%)

Compiler: Compiled 61 to 39 computations (36.1% saved)

sample740.0ms (32.4%)

Algorithm

1×

intervals

Results

447.0ms

8000×

body

128

valid

Compiler

Compiled 145 to 92 computations (36.6% saved)

Details

analyze15.0ms (0.7%)

sample158.0ms (6.9%)

simplify107.0ms (4.7%)

prune3.0ms (0.2%)

localize8.0ms (0.4%)

series30.0ms (1.3%)

rewrite19.0ms (0.8%)

simplify85.0ms (3.7%)

prune82.0ms (3.6%)

localize0.0ms (0%)

prune4.0ms (0.2%)

localize11.0ms (0.5%)

series54.0ms (2.3%)

rewrite22.0ms (0.9%)

simplify183.0ms (8%)

prune157.0ms (6.9%)

localize12.0ms (0.5%)

series42.0ms (1.8%)

rewrite11.0ms (0.5%)

simplify106.0ms (4.6%)

prune88.0ms (3.8%)

regimes278.0ms (12.2%)

bsearch67.0ms (2.9%)

simplify5.0ms (0.2%)

end1.0ms (0%)

sample740.0ms (32.4%)

Profiling