Details

analyze764.0ms (14.3%)

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
0%	99.8%	0.2%	8
17.2%	82.7%	0.2%	9
22.6%	77.2%	0.2%	10
25.7%	74.1%	0.2%	11
28.3%	69.9%	1.9%	12
40.1%	55.3%	4.6%	13
44.4%	49.9%	5.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample184.0ms (3.5%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
3.0ms	79×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify64.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

775×	`fma-def_binary64`
730×	`fma-neg_binary64`
228×	`cancel-sign-sub-inv_binary64`
138×	`distribute-rgt-in_binary64`
97×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	11
2	31	11
3	72	11
4	146	11
5	255	11
6	409	11
7	668	11
8	1099	11
9	1352	11
10	1478	11
11	1525	11
12	1531	11
13	1536	11
14	1536	11
15	1451	11

prune3.0ms (0.1%)

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

0.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.9b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

Compiler

Compiled 45 to 23 computations (48.9% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.8b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series16.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

16.0ms

(fma.f64 (-.f64 y x) (/.f64 z t) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (-.f64 y x) (/.f64 z t) x)

simplify63.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

539×	`distribute-rgt-neg-out_binary64`
515×	`distribute-lft-neg-out_binary64`
375×	`distribute-rgt-in_binary64`
373×	`distribute-lft-in_binary64`
270×	`times-frac_binary64`

Counts

58 → 31

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	946
1	88	635
2	194	623
3	469	623
4	2305	623
5	4632	623
6	5238	623

prune22.0ms (0.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	27	4	31
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	5	32

Error

0.0b

Counts

32 → 5

Alt Table

Status	Error	Program
	8.0b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
✓	0.9b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
▶	2.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	41.2b	(cbrt.f64 (.f64 (.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x) (fma.f64 (-.f64 y x) (/.f64 z t) x)) (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	36.8b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)

Compiler

Compiled 554 to 162 computations (70.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
✓	0.6b	(cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))
✓	0.6b	(*.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	0.8b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series496.0ms (9.3%)

Counts

3 → 144

Calls

3 calls:

356.0ms

(*.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))

121.0ms

(cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))

18.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

7.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))

4.0ms

(*.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))

1.0ms

(cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))

simplify269.0ms (5%)

Algorithm

1×	egg-herbie

Rules

938×	`fma-def_binary64`
540×	`*-commutative_binary64`
218×	`+-commutative_binary64`
210×	`associate-r_binary64`
141×	`associate-+r+_binary64`

Counts

237 → 276

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1216	19471
1	4389	19186
2	5141	19186

prune732.0ms (13.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	551	2	553
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	551	7	558

Error

0.0b

Counts

558 → 7

Alt Table

Status	Error	Program
▶	8.0b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
	30.7b	(.f64 (cbrt.f64 (.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x) (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	33.2b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
✓	0.9b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	2.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	41.2b	(cbrt.f64 (.f64 (.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x) (fma.f64 (-.f64 y x) (/.f64 z t) x)) (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	36.8b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)

Compiler

Compiled 45055 to 18416 computations (59.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (*.f64 y z) t) x)
✓	0.0b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
✓	7.3b	(/.f64 (*.f64 z x) t)
✓	7.6b	(/.f64 (*.f64 y z) t)

series64.0ms (1.2%)

Counts

4 → 24

Calls

4 calls:

23.0ms	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
14.0ms	(+.f64 (/.f64 (*.f64 y z) t) x)
14.0ms	(/.f64 (*.f64 y z) t)
13.0ms	(/.f64 (*.f64 z x) t)

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
28×	`prod-diff_binary64`
28×	`add-cube-cbrt_binary64`
24×	`times-frac_binary64`

Counts

4 → 126

Calls

4 calls:

11.0ms	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
5.0ms	(+.f64 (/.f64 (*.f64 y z) t) x)
5.0ms	(/.f64 (*.f64 y z) t)
4.0ms	(/.f64 (*.f64 z x) t)

simplify99.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

634×	`fma-def_binary64`
419×	`associate-/l/_binary64`
316×	`distribute-rgt-in_binary64`
298×	`distribute-lft-in_binary64`
193×	`cancel-sign-sub-inv_binary64`

Counts

150 → 185

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	213	3546
1	541	2217
2	1901	1872
3	4868	1872
4	4866	1872

prune131.0ms (2.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	182	3	185
Fresh	3	1	4
Picked	1	0	1
Done	0	2	2
Total	186	6	192

Error

Counts

192 → 6

Alt Table

Status	Error	Program
	22.0b	(-.f64 (+.f64 (cbrt.f64 (.f64 (.f64 (/.f64 (.f64 y z) t) (/.f64 (.f64 y z) t)) (/.f64 (.f64 y z) t))) x) (/.f64 (.f64 z x) t))
✓	0.9b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	2.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	8.0b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (.f64 (*.f64 z x) (/.f64 1 t)))
▶	5.6b	(-.f64 (+.f64 (/.f64 y (/.f64 t z)) x) (/.f64 (*.f64 z x) t))
	36.8b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)

Compiler

Compiled 4443 to 845 computations (81% saved)

localize56.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 y (/.f64 t z)) x)
✓	0.0b	(-.f64 (+.f64 (/.f64 y (/.f64 t z)) x) (/.f64 (*.f64 z x) t))
✓	3.2b	(/.f64 y (/.f64 t z))
	7.3b	(/.f64 (*.f64 z x) t)

series54.0ms (1%)

Counts

3 → 132

Calls

3 calls:

26.0ms	(-.f64 (+.f64 (/.f64 y (/.f64 t z)) x) (/.f64 (*.f64 z x) t))
14.0ms	(/.f64 y (/.f64 t z))
13.0ms	(+.f64 (/.f64 y (/.f64 t z)) x)

rewrite52.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`times-frac_binary64`
121×	`*-un-lft-identity_binary64`
100×	`add-sqr-sqrt_binary64`
98×	`add-cube-cbrt_binary64`
44×	`fma-def_binary64`

Counts

3 → 189

Calls

3 calls:

17.0ms	(-.f64 (+.f64 (/.f64 y (/.f64 t z)) x) (/.f64 (*.f64 z x) t))
14.0ms	(+.f64 (/.f64 y (/.f64 t z)) x)
4.0ms	(/.f64 y (/.f64 t z))

simplify167.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-def_binary64`
399×	`fma-neg_binary64`
382×	`times-frac_binary64`
317×	`distribute-rgt-in_binary64`
170×	`cancel-sign-sub-inv_binary64`

Counts

321 → 258

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	294	4967
1	679	3935
2	2182	3647
3	4285	3647
4	4922	3644
5	4954	3644

prune211.0ms (4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	294	0	294
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	294	6	300

Error

Counts

300 → 6

Alt Table

Status	Error	Program
	22.0b	(-.f64 (+.f64 (cbrt.f64 (.f64 (.f64 (/.f64 (.f64 y z) t) (/.f64 (.f64 y z) t)) (/.f64 (.f64 y z) t))) x) (/.f64 (.f64 z x) t))
✓	0.9b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	2.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	8.0b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (.f64 (*.f64 z x) (/.f64 1 t)))
✓	5.6b	(-.f64 (+.f64 (/.f64 y (/.f64 t z)) x) (/.f64 (*.f64 z x) t))
	36.8b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)

Compiler

Compiled 6944 to 1365 computations (80.3% saved)

regimes943.0ms (17.6%)

Accuracy

Total 2.1b remaining (99.3%)

Threshold costs 0b (0%)

Counts

142 → 1

Compiler

Compiled 19052 to 10132 computations (46.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-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	8	11
1	10	11
2	15	11
3	17	11
4	18	11
5	18	11

end0.0ms (0%)

Compiler: Compiled 12 to 7 computations (41.7% saved)

sample870.0ms (16.3%)

Algorithm

1×

intervals

Results

317.0ms	8000×	body	128	valid
86.0ms	2196×	body	128	invalid

Compiler

Compiled 154 to 80 computations (48.1% saved)

Details

analyze764.0ms (14.3%)

sample184.0ms (3.5%)

simplify64.0ms (1.2%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series16.0ms (0.3%)

rewrite1.0ms (0%)

simplify63.0ms (1.2%)

prune22.0ms (0.4%)

localize10.0ms (0.2%)

series496.0ms (9.3%)

rewrite19.0ms (0.4%)

simplify269.0ms (5%)

prune732.0ms (13.7%)

localize10.0ms (0.2%)

series64.0ms (1.2%)

rewrite34.0ms (0.6%)

simplify99.0ms (1.9%)

prune131.0ms (2.5%)

localize56.0ms (1.1%)

series54.0ms (1%)

rewrite52.0ms (1%)

simplify167.0ms (3.1%)

prune211.0ms (4%)

regimes943.0ms (17.6%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample870.0ms (16.3%)

Profiling