Details

analyze298.0ms (4.5%)

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
0%	99.9%	0.1%	5
0%	74.9%	25.1%	6
6.2%	68.6%	25.1%	7
10.1%	64.7%	25.1%	8
17.2%	32.8%	50.1%	9
23%	26.9%	50.1%	10
26.8%	23.1%	50.1%	11
31.6%	18.3%	50.1%	12
35.2%	14.7%	50.1%	13
37.5%	12.4%	50.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample165.0ms (2.5%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify155.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

782×	`fma-neg_binary64`
610×	`unsub-neg_binary64`
567×	`distribute-rgt-in_binary64`
442×	`sub-neg_binary64`
412×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	25	18
2	75	16
3	253	16
4	654	16
5	1767	16
6	2167	16
7	2284	16
8	2375	16
9	2374	16
10	2391	16
11	2701	16
12	3417	16
13	4877	16
14	4713	16
15	4967	16

prune3.0ms (0%)

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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))

Compiler

Compiled 54 to 33 computations (38.9% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))
✓	0.1b	(fma.f64 (+.f64 y 1/2) (log.f64 y) z)

series134.0ms (2%)

Counts

2 → 60

Calls

2 calls:

87.0ms	(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))
47.0ms	(fma.f64 (+.f64 y 1/2) (log.f64 y) z)

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
24×	`prod-diff_binary64`
19×	`add-cube-cbrt_binary64`
14×	`associate--r+_binary64`

Counts

2 → 65

Calls

2 calls:

7.0ms	(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))
1.0ms	(fma.f64 (+.f64 y 1/2) (log.f64 y) z)

simplify324.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

667×	`fma-def_binary64`
547×	`distribute-rgt-in_binary64`
508×	`distribute-lft-in_binary64`
456×	`fma-neg_binary64`
232×	`exp-sum_binary64`

Counts

125 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	171	2510
1	373	2200
2	1256	1943
3	4472	1943
4	5111	1943

prune155.0ms (2.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	120	5	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	5	126

Error

0.0b

Counts

126 → 5

Alt Table

Status	Error	Program
	0.1b	(-.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) (-.f64 z x))
	0.9b	(-.f64 y (-.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) x))
	1.4b	(.f64 (.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))
▶	0.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) x))
	27.1b	(-.f64 y (-.f64 (*.f64 (sqrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (sqrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) x))

Compiler

Compiled 3215 to 1624 computations (49.5% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))
✓	0.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) x))
✓	0.3b	(*.f64 y (log.f64 y))

series234.0ms (3.5%)

Counts

3 → 53

Calls

3 calls:

184.0ms	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) x))
34.0ms	(*.f64 y (log.f64 y))
15.0ms	(+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`*-un-lft-identity_binary64`
42×	`add-sqr-sqrt_binary64`
30×	`prod-diff_binary64`
30×	`add-cube-cbrt_binary64`
19×	`add-log-exp_binary64`

Counts

3 → 119

Calls

3 calls:

11.0ms	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) x))
5.0ms	(+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))
4.0ms	(*.f64 y (log.f64 y))

simplify177.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

366×	`associate-+l+_binary64`
326×	`fma-neg_binary64`
266×	`cancel-sign-sub-inv_binary64`
244×	`associate--r+_binary64`
228×	`exp-diff_binary64`

Counts

172 → 182

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	248	2826
1	546	2490
2	1945	2371
3	4415	2358
4	4967	2358
5	4982	2358
6	4842	2358

prune232.0ms (3.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	179	3	182
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	182	5	187

Error

Counts

187 → 5

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) (-.f64 z x))
	0.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 (log.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) y) (fma.f64 y (log.f64 (cbrt.f64 y)) (log.f64 (sqrt.f64 y))))) x))
	0.4b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (log.f64 y))) (cbrt.f64 (.f64 y (log.f64 y)))) (cbrt.f64 (.f64 y (log.f64 y)))) (.f64 1/2 (log.f64 y)))) x))
	1.4b	(.f64 (.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))
	31.0b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 (.f64 y (sqrt.f64 (log.f64 y))) (sqrt.f64 (log.f64 y))) (*.f64 1/2 (log.f64 y)))) x))

Compiler

Compiled 5107 to 2286 computations (55.2% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) (-.f64 z x))
✓	0.2b	(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

series108.0ms (1.6%)

Counts

2 → 48

Calls

2 calls:

95.0ms	(-.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) (-.f64 z x))
13.0ms	(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
24×	`prod-diff_binary64`
19×	`add-cube-cbrt_binary64`
13×	`associate--r+_binary64`

Counts

2 → 65

Calls

2 calls:

7.0ms	(-.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) (-.f64 z x))
1.0ms	(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

simplify113.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

656×	`fma-def_binary64`
608×	`fma-neg_binary64`
469×	`associate-l_binary64`
402×	`associate-r_binary64`
352×	`distribute-rgt-in_binary64`

Counts

113 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	171	2157
1	375	1915
2	1163	1750
3	4304	1750
4	4929	1750

prune107.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	109	5	114

Error

Counts

114 → 5

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) (-.f64 z x))
▶	0.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 (log.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) y) (fma.f64 y (log.f64 (cbrt.f64 y)) (log.f64 (sqrt.f64 y))))) x))
	0.4b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (log.f64 y))) (cbrt.f64 (.f64 y (log.f64 y)))) (cbrt.f64 (.f64 y (log.f64 y)))) (.f64 1/2 (log.f64 y)))) x))
	0.6b	(fma.f64 (*.f64 (cbrt.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y)) (cbrt.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y))) (cbrt.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y)) (-.f64 x z))
	31.0b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 (.f64 y (sqrt.f64 (log.f64 y))) (sqrt.f64 (log.f64 y))) (*.f64 1/2 (log.f64 y)))) x))

Compiler

Compiled 2655 to 1084 computations (59.2% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (log.f64 (cbrt.f64 y)) (log.f64 (sqrt.f64 y)))
✓	0.3b	(.f64 (log.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) y)
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.6b	(cbrt.f64 y)

series1.0s (15.3%)

Counts

4 → 38

Calls

4 calls:

837.0ms	(.f64 (log.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) y)
73.0ms	(cbrt.f64 y)
54.0ms	(fma.f64 y (log.f64 (cbrt.f64 y)) (log.f64 (sqrt.f64 y)))
41.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
21×	`pow1_binary64`
19×	`cbrt-prod_binary64`
18×	`associate-l_binary64`
15×	`*-un-lft-identity_binary64`

Counts

4 → 94

Calls

4 calls:

12.0ms	(.f64 (log.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) y)
5.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)
0.0ms	(fma.f64 y (log.f64 (cbrt.f64 y)) (log.f64 (sqrt.f64 y)))

simplify318.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

593×	`log-prod_binary64`
420×	`fma-neg_binary64`
335×	`*-commutative_binary64`
331×	`exp-prod_binary64`
304×	`distribute-rgt-out_binary64`

Counts

132 → 145

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	115	1363
1	208	1240
2	793	1178
3	2010	1145
4	3727	1133
5	4869	1133

prune274.0ms (4.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	184	4	188

Error

Counts

188 → 4

Alt Table

Status	Error	Program
	0.4b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (log.f64 y))) (cbrt.f64 (.f64 y (log.f64 y)))) (cbrt.f64 (.f64 y (log.f64 y)))) (.f64 1/2 (log.f64 y)))) x))
	0.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 (log.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) y) (fma.f64 y (log.f64 (pow.f64 y 1/3)) (log.f64 (sqrt.f64 y))))) x))
✓	0.1b	(-.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) (-.f64 z x))
	31.0b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 (.f64 y (sqrt.f64 (log.f64 y))) (sqrt.f64 (log.f64 y))) (*.f64 1/2 (log.f64 y)))) x))

Compiler

Compiled 5081 to 1612 computations (68.3% saved)

regimes1.8s (27.6%)

Accuracy

Total 0.1b remaining (79.5%)

Threshold costs 0.1b (79.5%)

Counts

266 → 1

Compiler

Compiled 28987 to 18358 computations (36.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	15	26
2	20	26
3	22	26
4	23	26
5	23	26

end1.0ms (0%)

Compiler: Compiled 20 to 11 computations (45% saved)

sample830.0ms (12.6%)

Algorithm

1×

intervals

Results

476.0ms	7999×	body	128	valid
2.0ms	38×	body	128	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 134 to 78 computations (41.8% saved)

Details

analyze298.0ms (4.5%)

sample165.0ms (2.5%)

simplify155.0ms (2.3%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series134.0ms (2%)

rewrite18.0ms (0.3%)

simplify324.0ms (4.9%)

prune155.0ms (2.3%)

localize11.0ms (0.2%)

series234.0ms (3.5%)

rewrite33.0ms (0.5%)

simplify177.0ms (2.7%)

prune232.0ms (3.5%)

localize8.0ms (0.1%)

series108.0ms (1.6%)

rewrite13.0ms (0.2%)

simplify113.0ms (1.7%)

prune107.0ms (1.6%)

localize18.0ms (0.3%)

series1.0s (15.3%)

rewrite23.0ms (0.4%)

simplify318.0ms (4.8%)

prune274.0ms (4.2%)

regimes1.8s (27.6%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample830.0ms (12.6%)

Profiling