Details

analyze964.0ms (17.5%)

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
25.9%	73.3%	0.8%	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)

sample26.0ms (0.5%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
2.0ms	60×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify74.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

799×	`fma-def_binary64`
661×	`fma-neg_binary64`
203×	`cancel-sign-sub-inv_binary64`
145×	`distribute-rgt-in_binary64`
99×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	30	11
3	61	11
4	129	11
5	232	11
6	397	11
7	667	11
8	1062	11
9	1355	11
10	1480	11
11	1529	11
12	1535	11
13	1540	11
14	1540	11
15	1455	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
	7.0b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
▶	4.2b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite50.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-cube-cbrt_binary64`
19×	`pow1_binary64`
16×	`add-exp-log_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cbrt-cube_binary64`

Counts

3 → 136

Calls

3 calls:

16.0ms	(*.f64 y (-.f64 z x))
15.0ms	(/.f64 (*.f64 y (-.f64 z x)) t)
12.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

series174.0ms (3.2%)

Counts

3 → 104

Calls

3 calls:

85.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
65.0ms	(/.f64 (*.f64 y (-.f64 z x)) t)
24.0ms	(*.f64 y (-.f64 z x))

simplify138.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

789×	`fma-def_binary64`
431×	`fma-neg_binary64`
367×	`cancel-sign-sub-inv_binary64`
201×	`exp-prod_binary64`
152×	`associate-l_binary64`

Counts

240 → 403

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	191	3072
1	503	2639
2	2116	2458
3	4551	2448
4	4993	2448

prune129.0ms (2.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	394	9	403
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	396	9	405

Error

Counts

405 → 9

Alt Table

Status	Error	Program
	36.5b	(*.f64 (-.f64 (/.f64 z t) (/.f64 x t)) y)
	1.9b	(+.f64 x (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x))) (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x)))) (cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x)))))
	4.6b	(+.f64 x (/.f64 (pow.f64 (cbrt.f64 (*.f64 y (-.f64 z x))) 3) t))
▶	1.3b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	4.2b	(+.f64 x (pow.f64 (/.f64 t (*.f64 y (-.f64 z x))) -1))
	5.6b	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
	4.2b	(+.f64 x (.f64 (.f64 y (-.f64 z x)) (/.f64 1 t)))
	4.7b	(+.f64 x (/.f64 (.f64 (.f64 y (*.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x)))) (cbrt.f64 (-.f64 z x))) t))
	4.7b	(+.f64 x (/.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (-.f64 z x))) t))

Compiler

Compiled 3742 to 956 computations (74.5% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-cube-cbrt_binary64`
5×	`fma-udef_binary64`
4×	`pow1_binary64`
4×	`add-sqr-sqrt_binary64`
3×	`add-cbrt-cube_binary64`

Counts

1 → 33

Calls

1 calls:

9.0ms

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

series77.0ms (1.4%)

Counts

1 → 48

Calls

1 calls:

77.0ms

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

simplify81.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

760×	`fma-def_binary64`
591×	`fma-neg_binary64`
543×	`associate-*l/_binary64`
522×	`times-frac_binary64`
457×	`associate-*r/_binary64`

Counts

81 → 129

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	1203
1	156	892
2	421	871
3	1351	869
4	4153	869
5	5439	869

prune32.0ms (0.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	129	9	138

Error

Counts

138 → 9

Alt Table

Status	Error	Program
	36.5b	(*.f64 (-.f64 (/.f64 z t) (/.f64 x t)) y)
▶	1.9b	(+.f64 x (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x))) (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x)))) (cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x)))))
	4.6b	(+.f64 x (/.f64 (pow.f64 (cbrt.f64 (*.f64 y (-.f64 z x))) 3) t))
✓	1.3b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	4.2b	(+.f64 x (pow.f64 (/.f64 t (*.f64 y (-.f64 z x))) -1))
	5.6b	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
	4.2b	(+.f64 x (.f64 (.f64 y (-.f64 z x)) (/.f64 1 t)))
	4.7b	(+.f64 x (/.f64 (.f64 (.f64 y (*.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x)))) (cbrt.f64 (-.f64 z x))) t))
	4.7b	(+.f64 x (/.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (-.f64 z x))) t))

Compiler

Compiled 899 to 285 computations (68.3% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.1b	(cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x)))
	6.6b	(*.f64 (/.f64 y t) (-.f64 z x))
	6.6b	(*.f64 (/.f64 y t) (-.f64 z x))
✓	6.6b	(*.f64 (/.f64 y t) (-.f64 z x))

rewrite119.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-cube-cbrt_binary64`
13×	`flip3--_binary64`
13×	`pow1_binary64`
12×	`frac-times_binary64`
12×	`add-sqr-sqrt_binary64`

Counts

2 → 89

Calls

2 calls:

102.0ms	(*.f64 (/.f64 y t) (-.f64 z x))
12.0ms	(cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x)))

series1.1s (20.7%)

Counts

2 → 96

Calls

2 calls:

1.1s	(cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x)))
61.0ms	(*.f64 (/.f64 y t) (-.f64 z x))

simplify152.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

835×	`fma-def_binary64`
364×	`fma-neg_binary64`
210×	`associate-r_binary64`
202×	`sub-neg_binary64`
162×	`associate-l_binary64`

Counts

185 → 316

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	314	3850
1	907	3553
2	3257	3275
3	4865	3274
4	4934	3274

prune291.0ms (5.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	808	0	808
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	808	9	817

Error

Counts

817 → 9

Alt Table

Status	Error	Program
	36.5b	(*.f64 (-.f64 (/.f64 z t) (/.f64 x t)) y)
✓	1.9b	(+.f64 x (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x))) (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x)))) (cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x)))))
	4.6b	(+.f64 x (/.f64 (pow.f64 (cbrt.f64 (*.f64 y (-.f64 z x))) 3) t))
✓	1.3b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
▶	4.2b	(+.f64 x (pow.f64 (/.f64 t (*.f64 y (-.f64 z x))) -1))
	5.6b	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
	4.2b	(+.f64 x (.f64 (.f64 y (-.f64 z x)) (/.f64 1 t)))
	4.7b	(+.f64 x (/.f64 (.f64 (.f64 y (*.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x)))) (cbrt.f64 (-.f64 z x))) t))
	4.7b	(+.f64 x (/.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (-.f64 z x))) t))

Compiler

Compiled 14108 to 3150 computations (77.7% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 y (-.f64 z x))
✓	0.0b	(+.f64 x (pow.f64 (/.f64 t (*.f64 y (-.f64 z x))) -1))
✓	0.3b	(pow.f64 (/.f64 t (*.f64 y (-.f64 z x))) -1)
✓	4.8b	(/.f64 t (*.f64 y (-.f64 z x)))

rewrite44.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`

Counts

3 → 132

Calls

3 calls:

14.0ms	(/.f64 t (*.f64 y (-.f64 z x)))
12.0ms	(+.f64 x (pow.f64 (/.f64 t (*.f64 y (-.f64 z x))) -1))
12.0ms	(pow.f64 (/.f64 t (*.f64 y (-.f64 z x))) -1)

series504.0ms (9.1%)

Counts

3 → 128

Calls

3 calls:

260.0ms	(pow.f64 (/.f64 t (*.f64 y (-.f64 z x))) -1)
167.0ms	(+.f64 x (pow.f64 (/.f64 t (*.f64 y (-.f64 z x))) -1))
77.0ms	(/.f64 t (*.f64 y (-.f64 z x)))

simplify119.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

781×	`fma-def_binary64`
418×	`distribute-rgt-in_binary64`
259×	`cancel-sign-sub-inv_binary64`
170×	`distribute-rgt-neg-in_binary64`
168×	`times-frac_binary64`

Counts

260 → 444

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	206	3944
1	517	3371
2	2303	3172
3	5155	3172

prune182.0ms (3.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	558	2	560
Fresh	3	3	6
Picked	1	0	1
Done	0	2	2
Total	562	7	569

Error

Counts

569 → 7

Alt Table

Status	Error	Program
	1.4b	(+.f64 x (pow.f64 (/.f64 (/.f64 t y) (-.f64 z x)) -1))
✓	1.9b	(+.f64 x (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x))) (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x)))) (cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x)))))
	36.5b	(*.f64 (-.f64 (/.f64 z t) (/.f64 x t)) y)
	4.5b	(+.f64 x (pow.f64 (.f64 t (/.f64 1 (.f64 y (-.f64 z x)))) -1))
✓	1.3b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	4.2b	(+.f64 x (.f64 (.f64 y (-.f64 z x)) (/.f64 1 t)))
	4.7b	(+.f64 x (/.f64 (.f64 (.f64 y (*.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x)))) (cbrt.f64 (-.f64 z x))) t))

Compiler

Compiled 5060 to 1714 computations (66.1% saved)

regimes295.0ms (5.3%)

Accuracy

Total 2.0b remaining (99.4%)

Threshold costs 0b (0%)

Compiler

Compiled 5301 to 3163 computations (40.3% 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)

sample859.0ms (15.6%)

Algorithm

1×

intervals

Results

336.0ms	8000×	body	128	valid
85.0ms	2031×	body	128	invalid

Compiler

Compiled 158 to 89 computations (43.7% saved)

Details

analyze964.0ms (17.5%)

sample26.0ms (0.5%)

simplify74.0ms (1.3%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

rewrite50.0ms (0.9%)

series174.0ms (3.2%)

simplify138.0ms (2.5%)

prune129.0ms (2.3%)

localize6.0ms (0.1%)

rewrite14.0ms (0.2%)

series77.0ms (1.4%)

simplify81.0ms (1.5%)

prune32.0ms (0.6%)

localize18.0ms (0.3%)

rewrite119.0ms (2.2%)

series1.1s (20.7%)

simplify152.0ms (2.8%)

prune291.0ms (5.3%)

localize7.0ms (0.1%)

rewrite44.0ms (0.8%)

series504.0ms (9.1%)

simplify119.0ms (2.2%)

prune182.0ms (3.3%)

regimes295.0ms (5.3%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample859.0ms (15.6%)

Profiling