Details

analyze160.0ms (3.2%)

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
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
56.2%	43.7%	0.1%	7
56.2%	43.7%	0.1%	8
56.2%	43.7%	0.1%	9
76.5%	23.4%	0.1%	10
76.5%	23.4%	0.1%	11
76.5%	23.4%	0.1%	12
87.8%	12.1%	0.1%	13
87.8%	12.1%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample813.0ms (16.4%)

Infinites

0% of outputs are infinite.

Results

656.0ms	8254×	body	128	valid
0.0ms	2×	body	512	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify215.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

2674×	`fma-neg_binary64`
2270×	`div-sub_binary64`
1877×	`fma-def_binary64`
968×	`associate-/l/_binary64`
705×	`associate-/r/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	14	13
2	20	13
3	28	13
4	41	13
5	55	13
6	72	13
7	85	13
8	102	13
9	127	13
10	155	13
11	215	13
12	356	13
13	666	13
14	1204	13
15	1746	13
16	1897	13
17	2006	13
18	2246	13
19	2452	13
20	1993	13
21	2354	13
22	2400	13
23	2609	13
24	2737	13
25	2812	13
26	2982	13
27	2984	13
28	3004	13
29	3004	13
30	3850	13
31	5135	13

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

9.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	9.0b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (/.f64 y z))
✓	9.0b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

series30.0ms (0.6%)

Counts

2 → 42

Calls

2 calls:

24.0ms	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
6.0ms	(-.f64 1 (/.f64 y z))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`add-sqr-sqrt_binary64`
100×	`*-un-lft-identity_binary64`
80×	`times-frac_binary64`
58×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`

Counts

2 → 135

Calls

2 calls:

8.0ms	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
7.0ms	(-.f64 1 (/.f64 y z))

simplify129.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

549×	`times-frac_binary64`
305×	`distribute-rgt-in_binary64`
243×	`fma-neg_binary64`
226×	`distribute-lft-in_binary64`
175×	`cancel-sign-sub-inv_binary64`

Counts

177 → 200

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	292	4046
1	754	3571
2	2276	3190
3	4701	3187
4	4818	3187

prune215.0ms (4.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	194	6	200
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	194	7	201

Error

0.0b

Counts

201 → 7

Alt Table

Status	Error	Program
✓	9.0b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
▶	9.4b	(/.f64 (+.f64 x y) (+.f64 1 (.f64 (neg.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 1)) (/.f64 (cbrt.f64 y) z))))
	10.0b	(.f64 (.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x))) (/.f64 (cbrt.f64 (+.f64 y x)) (-.f64 1 (/.f64 y z))))
	33.0b	(neg.f64 (+.f64 (/.f64 (.f64 (pow.f64 z 2) x) (pow.f64 y 2)) (+.f64 (/.f64 (pow.f64 z 2) y) (+.f64 (/.f64 (.f64 z x) y) z))))
	25.4b	(.f64 (/.f64 (+.f64 y x) (-.f64 1 (pow.f64 (/.f64 y z) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (/.f64 y z) (/.f64 y z)) (.f64 1 (/.f64 y z)))))
	23.1b	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 1 (/.f64 y z)))) (/.f64 (+.f64 x y) (sqrt.f64 (-.f64 1 (/.f64 y z)))))
	20.3b	(.f64 (/.f64 (+.f64 x y) (-.f64 (.f64 1 1) (*.f64 (/.f64 y z) (/.f64 y z)))) (+.f64 1 (/.f64 y z)))

Compiler

Compiled 5215 to 2065 computations (60.4% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (cbrt.f64 y) z)
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.5b	(cbrt.f64 y)
✓	9.0b	(/.f64 (+.f64 x y) (+.f64 1 (.f64 (neg.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 1)) (/.f64 (cbrt.f64 y) z))))

series349.0ms (7%)

Counts

4 → 84

Calls

4 calls:

238.0ms	(/.f64 (cbrt.f64 y) z)
42.0ms	(cbrt.f64 y)
38.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
30.0ms	(/.f64 (+.f64 x y) (+.f64 1 (.f64 (neg.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 1)) (/.f64 (cbrt.f64 y) z))))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64`
45×	`add-sqr-sqrt_binary64`
37×	`add-cube-cbrt_binary64`
31×	`cbrt-prod_binary64`
30×	`times-frac_binary64`

Counts

4 → 133

Calls

4 calls:

9.0ms	(/.f64 (+.f64 x y) (+.f64 1 (.f64 (neg.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 1)) (/.f64 (cbrt.f64 y) z))))
4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
2.0ms	(/.f64 (cbrt.f64 y) z)
1.0ms	(cbrt.f64 y)

simplify193.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

475×	`fma-neg_binary64`
316×	`distribute-rgt-in_binary64`
244×	`unswap-sqr_binary64`
179×	`distribute-rgt-neg-in_binary64`
176×	`cancel-sign-sub-inv_binary64`

Counts

217 → 225

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	262	4155
1	612	3195
2	2325	3019
3	4060	3004
4	4902	3004
5	4956	3004

prune188.0ms (3.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	260	1	261
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	261	7	268

Error

0.0b

Counts

268 → 7

Alt Table

Status	Error	Program
✓	9.0b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
✓	9.4b	(/.f64 (+.f64 x y) (+.f64 1 (.f64 (neg.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 1)) (/.f64 (cbrt.f64 y) z))))
	25.4b	(.f64 (/.f64 (+.f64 y x) (-.f64 1 (pow.f64 (/.f64 y z) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (/.f64 y z) (/.f64 y z)) (.f64 1 (/.f64 y z)))))
▶	19.2b	(/.f64 (+.f64 x y) (+.f64 1 (.f64 (neg.f64 (/.f64 (cbrt.f64 (.f64 y y)) 1)) (/.f64 (cbrt.f64 y) z))))
	33.0b	(neg.f64 (+.f64 (/.f64 (.f64 (pow.f64 z 2) x) (pow.f64 y 2)) (+.f64 (/.f64 (pow.f64 z 2) y) (+.f64 (/.f64 (.f64 z x) y) z))))
	23.1b	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 1 (/.f64 y z)))) (/.f64 (+.f64 x y) (sqrt.f64 (-.f64 1 (/.f64 y z)))))
	20.3b	(.f64 (/.f64 (+.f64 x y) (-.f64 (.f64 1 1) (*.f64 (/.f64 y z) (/.f64 y z)))) (+.f64 1 (/.f64 y z)))

Compiler

Compiled 6892 to 2999 computations (56.5% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 (cbrt.f64 y) z)
	0.5b	(cbrt.f64 y)
✓	9.0b	(/.f64 (+.f64 x y) (+.f64 1 (.f64 (neg.f64 (/.f64 (cbrt.f64 (.f64 y y)) 1)) (/.f64 (cbrt.f64 y) z))))
✓	29.4b	(cbrt.f64 (*.f64 y y))

series63.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

37.0ms	(/.f64 (+.f64 x y) (+.f64 1 (.f64 (neg.f64 (/.f64 (cbrt.f64 (.f64 y y)) 1)) (/.f64 (cbrt.f64 y) z))))
25.0ms	(cbrt.f64 (*.f64 y y))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
4×	`associate-/l*_binary64`

Counts

2 → 48

Calls

2 calls:

6.0ms	(/.f64 (+.f64 x y) (+.f64 1 (.f64 (neg.f64 (/.f64 (cbrt.f64 (.f64 y y)) 1)) (/.f64 (cbrt.f64 y) z))))
2.0ms	(cbrt.f64 (*.f64 y y))

simplify117.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

955×	`times-frac_binary64`
790×	`fma-def_binary64`
171×	`cancel-sign-sub-inv_binary64`
159×	`associate-+r+_binary64`
138×	`fma-neg_binary64`

Counts

96 → 115

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	195	2853
1	535	2630
2	1930	2552
3	4826	2531
4	4896	2522
5	4960	2522

prune147.0ms (3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	186	1	187
Fresh	0	4	4
Picked	1	0	1
Done	1	1	2
Total	188	6	194

Error

Counts

194 → 6

Alt Table

Status	Error	Program
	25.4b	(.f64 (/.f64 (+.f64 y x) (-.f64 1 (pow.f64 (/.f64 y z) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (/.f64 y z) (/.f64 y z)) (.f64 1 (/.f64 y z)))))
	30.4b	(-.f64 (fma.f64 (/.f64 z (cbrt.f64 -1)) (/.f64 x y) (/.f64 z (cbrt.f64 -1))) (/.f64 (.f64 z z) (.f64 y (pow.f64 (cbrt.f64 -1) 2))))
✓	9.0b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
	33.0b	(neg.f64 (+.f64 (/.f64 (.f64 (pow.f64 z 2) x) (pow.f64 y 2)) (+.f64 (/.f64 (pow.f64 z 2) y) (+.f64 (/.f64 (.f64 z x) y) z))))
	23.1b	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 1 (/.f64 y z)))) (/.f64 (+.f64 x y) (sqrt.f64 (-.f64 1 (/.f64 y z)))))
▶	20.3b	(.f64 (/.f64 (+.f64 x y) (-.f64 (.f64 1 1) (*.f64 (/.f64 y z) (/.f64 y z)))) (+.f64 1 (/.f64 y z)))

Compiler

Compiled 5350 to 2344 computations (56.2% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (/.f64 y z))
✓	0.3b	(*.f64 (/.f64 y z) (/.f64 y z))
✓	4.3b	(/.f64 (+.f64 x y) (-.f64 (.f64 1 1) (.f64 (/.f64 y z) (/.f64 y z))))
✓	15.8b	(.f64 (/.f64 (+.f64 x y) (-.f64 (.f64 1 1) (*.f64 (/.f64 y z) (/.f64 y z)))) (+.f64 1 (/.f64 y z)))

series189.0ms (3.8%)

Counts

4 → 102

Calls

4 calls:

81.0ms	(.f64 (/.f64 (+.f64 x y) (-.f64 (.f64 1 1) (*.f64 (/.f64 y z) (/.f64 y z)))) (+.f64 1 (/.f64 y z)))
75.0ms	(/.f64 (+.f64 x y) (-.f64 (.f64 1 1) (.f64 (/.f64 y z) (/.f64 y z))))
28.0ms	(*.f64 (/.f64 y z) (/.f64 y z))
5.0ms	(+.f64 1 (/.f64 y z))

rewrite56.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`*-un-lft-identity_binary64`
73×	`times-frac_binary64`
70×	`add-sqr-sqrt_binary64`
53×	`add-cube-cbrt_binary64`
35×	`associate-l_binary64`

Counts

4 → 178

Calls

4 calls:

18.0ms	(.f64 (/.f64 (+.f64 x y) (-.f64 (.f64 1 1) (*.f64 (/.f64 y z) (/.f64 y z)))) (+.f64 1 (/.f64 y z)))
11.0ms	(/.f64 (+.f64 x y) (-.f64 (.f64 1 1) (.f64 (/.f64 y z) (/.f64 y z))))
9.0ms	(*.f64 (/.f64 y z) (/.f64 y z))
4.0ms	(+.f64 1 (/.f64 y z))

simplify199.0ms (4%)

Algorithm

1×	egg-herbie

Rules

268×	`associate-+r+_binary64`
256×	`associate-*l/_binary64`
244×	`associate-/l*_binary64`
222×	`associate-l_binary64`
221×	`associate-*r/_binary64`

Counts

280 → 338

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	400	7478
1	1222	6937
2	4226	6653
3	4841	6653
4	4974	6653

prune280.0ms (5.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	338	0	338
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	338	6	344

Error

Counts

344 → 6

Alt Table

Status	Error	Program
	25.4b	(.f64 (/.f64 (+.f64 y x) (-.f64 1 (pow.f64 (/.f64 y z) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (/.f64 y z) (/.f64 y z)) (.f64 1 (/.f64 y z)))))
	30.4b	(-.f64 (fma.f64 (/.f64 z (cbrt.f64 -1)) (/.f64 x y) (/.f64 z (cbrt.f64 -1))) (/.f64 (.f64 z z) (.f64 y (pow.f64 (cbrt.f64 -1) 2))))
✓	9.0b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
	33.0b	(neg.f64 (+.f64 (/.f64 (.f64 (pow.f64 z 2) x) (pow.f64 y 2)) (+.f64 (/.f64 (pow.f64 z 2) y) (+.f64 (/.f64 (.f64 z x) y) z))))
	23.1b	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 1 (/.f64 y z)))) (/.f64 (+.f64 x y) (sqrt.f64 (-.f64 1 (/.f64 y z)))))
✓	20.3b	(.f64 (/.f64 (+.f64 x y) (-.f64 (.f64 1 1) (*.f64 (/.f64 y z) (/.f64 y z)))) (+.f64 1 (/.f64 y z)))

Compiler

Compiled 10633 to 4759 computations (55.2% saved)

regimes1.4s (27.8%)

Accuracy

Total 0.3b remaining (96%)

Threshold costs 0.3b (96%)

Counts

185 → 3

Compiler

Compiled 17131 to 11031 computations (35.6% saved)

bsearch6.0ms (0.1%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`*-commutative_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	86
1	37	86
2	47	86
3	58	86
4	66	86
5	70	86
6	71	86
7	70	86

end110.0ms (2.2%)

Compiler: Compiled 263 to 167 computations (36.5% saved)

Details

analyze160.0ms (3.2%)

sample813.0ms (16.4%)

simplify215.0ms (4.3%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series30.0ms (0.6%)

rewrite27.0ms (0.5%)

simplify129.0ms (2.6%)

prune215.0ms (4.3%)

localize14.0ms (0.3%)

series349.0ms (7%)

rewrite23.0ms (0.5%)

simplify193.0ms (3.9%)

prune188.0ms (3.8%)

localize14.0ms (0.3%)

series63.0ms (1.3%)

rewrite11.0ms (0.2%)

simplify117.0ms (2.4%)

prune147.0ms (3%)

localize13.0ms (0.3%)

series189.0ms (3.8%)

rewrite56.0ms (1.1%)

simplify199.0ms (4%)

prune280.0ms (5.7%)

regimes1.4s (27.8%)

bsearch6.0ms (0.1%)

simplify5.0ms (0.1%)

end110.0ms (2.2%)

Profiling