Details

analyze795.0ms (17.9%)

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
16.4%	83.4%	0.2%	9
21.4%	78.4%	0.2%	10
25.1%	74.7%	0.2%	11
28%	70.2%	1.9%	12
39.6%	55.8%	4.6%	13
43.9%	50.4%	5.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample133.0ms (3%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
3.0ms	73×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify71.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

973×	`fma-def_binary64`
752×	`fma-neg_binary64`
239×	`cancel-sign-sub-inv_binary64`
193×	`distribute-rgt-in_binary64`
133×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	33	11
3	64	11
4	125	11
5	238	11
6	414	11
7	791	11
8	1182	11
9	1373	11
10	1483	11
11	1532	11
12	1538	11
13	1543	11
14	1543	11
15	1458	11

prune3.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	8.1b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.3b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series16.0ms (0.4%)

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 (1.4%)

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 (0.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	27	4	31
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	28	5	33

Error

0.0b

Counts

33 → 5

Alt Table

Status	Error	Program
	30.9b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
▶	2.6b	(.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)))
	8.4b	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
	8.1b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

Compiler

Compiled 538 to 160 computations (70.3% saved)

localize9.0ms (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)))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
✓	0.5b	(cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))
	1.3b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series526.0ms (11.8%)

Counts

3 → 144

Calls

3 calls:

376.0ms

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

130.0ms

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

19.0ms

(*.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)))

rewrite20.0ms (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))

simplify328.0ms (7.4%)

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 → 277

Iterations

Useful iterations: 1 (0.0ms)

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

prune627.0ms (14.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	553	1	554
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	553	6	559

Error

0.0b

Counts

559 → 6

Alt Table

Status	Error	Program
	30.9b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
✓	2.6b	(.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)))
	8.4b	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
	31.4b	(.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)))
▶	8.1b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

Compiler

Compiled 45006 to 18395 computations (59.1% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
✓	6.4b	(/.f64 (*.f64 z x) t)
✓	7.2b	(/.f64 (*.f64 y z) t)

series54.0ms (1.2%)

Counts

3 → 12

Calls

3 calls:

23.0ms	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
16.0ms	(/.f64 (*.f64 y z) t)
15.0ms	(/.f64 (*.f64 z x) t)

rewrite27.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64`
28×	`prod-diff_binary64`
27×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
21×	`times-frac_binary64`

Counts

3 → 105

Calls

3 calls:

9.0ms	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
4.0ms	(/.f64 (*.f64 y z) t)
3.0ms	(/.f64 (*.f64 z x) t)

simplify96.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

619×	`fma-def_binary64`
419×	`associate-/l/_binary64`
303×	`distribute-rgt-in_binary64`
285×	`distribute-lft-in_binary64`
167×	`cancel-sign-sub-inv_binary64`

Counts

117 → 155

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	3276
1	532	1947
2	1876	1634
3	4800	1634
4	4901	1634

prune104.0ms (2.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	152	3	155
Fresh	2	1	3
Picked	1	0	1
Done	1	1	2
Total	156	5	161

Error

Counts

161 → 5

Alt Table

Status	Error	Program
	7.0b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (.f64 (/.f64 z (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 x (cbrt.f64 t))))
	8.4b	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
▶	6.2b	(-.f64 (+.f64 (/.f64 y (/.f64 t z)) x) (/.f64 (*.f64 z x) t))
	9.0b	(-.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (/.f64 z (/.f64 t x)))
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

Compiler

Compiled 3799 to 740 computations (80.5% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (/.f64 y (/.f64 t z)) x) (/.f64 (*.f64 z x) t))
✓	4.9b	(/.f64 y (/.f64 t z))
	6.4b	(/.f64 (*.f64 z x) t)

series34.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

23.0ms	(-.f64 (+.f64 (/.f64 y (/.f64 t z)) x) (/.f64 (*.f64 z x) t))
12.0ms	(/.f64 y (/.f64 t z))

rewrite32.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`times-frac_binary64`
83×	`*-un-lft-identity_binary64`
64×	`add-sqr-sqrt_binary64`
62×	`add-cube-cbrt_binary64`
28×	`prod-diff_binary64`

Counts

2 → 131

Calls

2 calls:

18.0ms	(-.f64 (+.f64 (/.f64 y (/.f64 t z)) x) (/.f64 (*.f64 z x) t))
4.0ms	(/.f64 y (/.f64 t z))

simplify139.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

648×	`fma-def_binary64`
380×	`times-frac_binary64`
357×	`fma-neg_binary64`
302×	`distribute-rgt-in_binary64`
178×	`exp-prod_binary64`

Counts

215 → 188

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	290	4335
1	670	3398
2	2153	3116
3	4218	3111
4	4704	3109
5	4783	3109

prune123.0ms (2.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	224	0	224
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	224	5	229

Error

Counts

229 → 5

Alt Table

Status	Error	Program
	7.0b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (.f64 (/.f64 z (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 x (cbrt.f64 t))))
	8.4b	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
✓	6.2b	(-.f64 (+.f64 (/.f64 y (/.f64 t z)) x) (/.f64 (*.f64 z x) t))
	9.0b	(-.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (/.f64 z (/.f64 t x)))
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

Compiler

Compiled 5373 to 1109 computations (79.4% saved)

regimes268.0ms (6%)

Accuracy

Total 2.1b remaining (99.3%)

Threshold costs 0b (0%)

Counts

53 → 1

Compiler

Compiled 5216 to 2798 computations (46.4% 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)

sample935.0ms (21%)

Algorithm

1×

intervals

Results

336.0ms	8000×	body	128	valid
163.0ms	2205×	body	128	invalid

Compiler

Compiled 113 to 68 computations (39.8% saved)

Details

analyze795.0ms (17.9%)

sample133.0ms (3%)

simplify71.0ms (1.6%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series16.0ms (0.4%)

rewrite1.0ms (0%)

simplify63.0ms (1.4%)

prune22.0ms (0.5%)

localize9.0ms (0.2%)

series526.0ms (11.8%)

rewrite20.0ms (0.4%)

simplify328.0ms (7.4%)

prune627.0ms (14.1%)

localize8.0ms (0.2%)

series54.0ms (1.2%)

rewrite27.0ms (0.6%)

simplify96.0ms (2.2%)

prune104.0ms (2.3%)

localize8.0ms (0.2%)

series34.0ms (0.8%)

rewrite32.0ms (0.7%)

simplify139.0ms (3.1%)

prune123.0ms (2.8%)

regimes268.0ms (6%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample935.0ms (21%)

Profiling