Details

analyze166.0ms (1.5%)

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
49.9%	49.9%	0.1%	4
49.9%	49.9%	0.1%	5
49.9%	49.9%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
74.9%	25%	0.1%	9
87.4%	12.5%	0.1%	10
87.4%	12.5%	0.1%	11
87.4%	12.5%	0.1%	12
93.6%	6.2%	0.1%	13
93.6%	6.2%	0.1%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample1.4s (12.3%)

Results

993.0ms

8256×

body

128

valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify58.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

377×	`fma-neg_binary64`
309×	`fma-def_binary64`
112×	`cancel-sign-sub-inv_binary64`
77×	`distribute-rgt-in_binary64`
56×	`unsub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	42	10
4	80	10
5	138	10
6	302	10
7	420	10
8	581	10
9	647	10
10	718	10
11	740	10
12	744	10
13	699	10

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

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 x (/.f64 (-.f64 y x) z))

Compiler

Compiled 30 to 18 computations (40% saved)

localize19.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series72.0ms (0.6%)

Counts

2 → 64

Calls

2 calls:

44.0ms	(+.f64 x (/.f64 (-.f64 y x) z))
28.0ms	(/.f64 (-.f64 y x) z)

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`
5×	`associate-/l*_binary64`

Counts

2 → 58

Calls

2 calls:

14.0ms	(+.f64 x (/.f64 (-.f64 y x) z))
9.0ms	(/.f64 (-.f64 y x) z)

simplify145.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-neg_binary64`
598×	`times-frac_binary64`
572×	`associate-/l*_binary64`
274×	`div-sub_binary64`
243×	`distribute-rgt-in_binary64`

Counts

122 → 81

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	1378
1	273	1269
2	636	1260
3	1893	1260
4	4435	1260
5	5003	1260

prune55.0ms (0.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	2	82

Error

0.0b

Counts

82 → 2

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 x (/.f64 1 (/.f64 z (-.f64 y x))))
	1.5b	(+.f64 x (-.f64 (/.f64 y z) (/.f64 x z)))

Compiler

Compiled 1125 to 324 computations (71.2% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 1 (/.f64 z (-.f64 y x))))
✓	0.0b	(/.f64 z (-.f64 y x))
✓	0.4b	(/.f64 1 (/.f64 z (-.f64 y x)))

series77.0ms (0.7%)

Counts

3 → 96

Calls

3 calls:

33.0ms	(/.f64 z (-.f64 y x))
27.0ms	(+.f64 x (/.f64 1 (/.f64 z (-.f64 y x))))
17.0ms	(/.f64 1 (/.f64 z (-.f64 y x)))

rewrite78.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
107×	`*-un-lft-identity_binary64`
104×	`add-sqr-sqrt_binary64`
72×	`add-cube-cbrt_binary64`
26×	`associate-/r*_binary64`

Counts

3 → 167

Calls

3 calls:

23.0ms	(+.f64 x (/.f64 1 (/.f64 z (-.f64 y x))))
17.0ms	(/.f64 1 (/.f64 z (-.f64 y x)))
5.0ms	(/.f64 z (-.f64 y x))

simplify337.0ms (3%)

Algorithm

1×	egg-herbie

Rules

492×	`fma-neg_binary64`
390×	`times-frac_binary64`
376×	`fma-def_binary64`
319×	`associate-/l*_binary64`
287×	`distribute-rgt-in_binary64`

Counts

263 → 229

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	201	4146
1	447	3761
2	1281	3568
3	4164	3568
4	4962	3568
5	5190	3568

prune206.0ms (1.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	228	1	229
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	229	2	231

Error

0.0b

Counts

231 → 2

Alt Table

Status	Error	Program
▶	0.2b	(+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x))))
	1.5b	(+.f64 x (-.f64 (/.f64 y z) (/.f64 x z)))

Compiler

Compiled 4110 to 1522 computations (63% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series66.0ms (0.6%)

Counts

3 → 96

Calls

3 calls:

28.0ms	(/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x)))
20.0ms	(+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x))))
17.0ms	(/.f64 1 (-.f64 y x))

rewrite256.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

696×	`times-frac_binary64`
388×	`*-un-lft-identity_binary64`
386×	`add-sqr-sqrt_binary64`
294×	`add-cube-cbrt_binary64`
47×	`add-exp-log_binary64`

Counts

3 → 401

Calls

3 calls:

91.0ms	(+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x))))
46.0ms	(/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x)))
6.0ms	(/.f64 1 (-.f64 y x))

simplify568.0ms (5%)

Algorithm

1×	egg-herbie

Rules

650×	`times-frac_binary64`
393×	`distribute-rgt-in_binary64`
362×	`distribute-lft-in_binary64`
335×	`associate-/l*_binary64`
312×	`associate-/l/_binary64`

Counts

497 → 426

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	251	9950
1	626	8913
2	1815	8653
3	4662	8653
4	5311	8653

prune534.0ms (4.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	425	1	426
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	425	3	428

Error

0.0b

Counts

428 → 3

Alt Table

Status	Error	Program
✓	0.2b	(+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x))))
▶	1.1b	(.f64 (.f64 (cbrt.f64 (+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x))))) (cbrt.f64 (+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x)))))) (cbrt.f64 (+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x))))))
	1.5b	(+.f64 x (-.f64 (/.f64 y z) (/.f64 x z)))

Compiler

Compiled 10131 to 5471 computations (46% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x)))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x))))) (cbrt.f64 (+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x)))))) (cbrt.f64 (+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x))))))
✓	0.5b	(*.f64 (cbrt.f64 (+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x))))) (cbrt.f64 (+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x))))))
✓	10.7b	(cbrt.f64 (+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x)))))

series1.0s (9%)

Counts

3 → 108

Calls

3 calls:

633.0ms

(*.f64 (cbrt.f64 (+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x))))) (cbrt.f64 (+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x))))))

211.0ms

(*.f64 (*.f64 (cbrt.f64 (+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x))))) (cbrt.f64 (+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x)))))) (cbrt.f64 (+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x))))))

159.0ms

(cbrt.f64 (+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x)))))

rewrite873.0ms (7.7%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`cbrt-div_binary64`
34×	`flip-+_binary64`
34×	`flip3-+_binary64`
33×	`cbrt-prod_binary64`
32×	`frac-times_binary64`

Counts

3 → 136

Calls

3 calls:

485.0ms

(*.f64 (*.f64 (cbrt.f64 (+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x))))) (cbrt.f64 (+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x)))))) (cbrt.f64 (+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x))))))

235.0ms

(*.f64 (cbrt.f64 (+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x))))) (cbrt.f64 (+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x))))))

98.0ms

(cbrt.f64 (+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x)))))

simplify621.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

851×	`times-frac_binary64`
807×	`fma-def_binary64`
371×	`*-commutative_binary64`
179×	`+-commutative_binary64`
133×	`associate-r_binary64`

Counts

244 → 324

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	960	17819
1	3152	16755
2	5231	16755

prune4.0s (35.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	1512	1	1513
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	1513	3	1516

Error

Counts

1516 → 3

Alt Table

Status	Error	Program
✓	0.2b	(+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x))))
	1.2b	(.f64 (.f64 (cbrt.f64 (+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x))))) (cbrt.f64 (+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x)))))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x))))) (cbrt.f64 (+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x))))))) (cbrt.f64 (cbrt.f64 (+.f64 x (/.f64 (/.f64 1 z) (/.f64 1 (-.f64 y x))))))))
	1.5b	(+.f64 x (-.f64 (/.f64 y z) (/.f64 x z)))

Compiler

Compiled 93593 to 57256 computations (38.8% saved)

regimes521.0ms (4.6%)

Accuracy

Total 0.0b remaining (38.8%)

Threshold costs 0.0b (38.8%)

Counts

62 → 1

Compiler

Compiled 5323 to 3413 computations (35.9% saved)

simplify4.0ms (0%)

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	7	10
1	10	10
2	15	10
3	17	10
4	18	10
5	18	10

end130.0ms (1.2%)

Compiler: Compiled 115 to 74 computations (35.7% saved)

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	42	10
4	80	10
5	138	10
6	302	10
7	420	10
8	581	10
9	647	10
10	718	10
11	740	10
12	744	10
13	699	10

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	42	10
4	80	10
5	138	10
6	302	10
7	420	10
8	581	10
9	647	10
10	718	10
11	740	10
12	744	10
13	699	10

Details

analyze166.0ms (1.5%)

sample1.4s (12.3%)

simplify58.0ms (0.5%)

prune2.0ms (0%)

localize19.0ms (0.2%)

series72.0ms (0.6%)

rewrite32.0ms (0.3%)

simplify145.0ms (1.3%)

prune55.0ms (0.5%)

localize13.0ms (0.1%)

series77.0ms (0.7%)

rewrite78.0ms (0.7%)

simplify337.0ms (3%)

prune206.0ms (1.8%)

localize12.0ms (0.1%)

series66.0ms (0.6%)

rewrite256.0ms (2.3%)

simplify568.0ms (5%)

prune534.0ms (4.7%)

localize26.0ms (0.2%)

series1.0s (9%)

rewrite873.0ms (7.7%)

simplify621.0ms (5.5%)

prune4.0s (35.5%)

regimes521.0ms (4.6%)

simplify4.0ms (0%)

end130.0ms (1.2%)

Profiling

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	42	10
4	80	10
5	138	10
6	302	10
7	420	10
8	581	10
9	647	10
10	718	10
11	740	10
12	744	10
13	699	10