Details

analyze175.0ms (6.9%)

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
49.9%	49.9%	0.2%	5
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
49.9%	49.9%	0.2%	8
74.9%	25%	0.2%	9
74.9%	25%	0.2%	10
74.9%	25%	0.2%	11
74.9%	25%	0.2%	12
87.3%	12.5%	0.2%	13
87.3%	12.5%	0.2%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample805.0ms (31.6%)

Infinites

24.9% of outputs are infinite.

Results

675.0ms

8256×

body

128

valid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify69.0ms (2.7%)

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)
	4.1b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series17.0ms (0.7%)

Counts

1 → 48

Calls

1 calls:

17.0ms

(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)

simplify64.0ms (2.5%)

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

prune20.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	28	3	31
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	28	5	33

Error

0.0b

Counts

33 → 5

Alt Table

Status	Error	Program
	27.7b	(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)))
	25.3b	(*.f64 z (/.f64 (-.f64 y x) t))
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
▶	4.1b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))
	34.0b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))

Compiler

Compiled 522 to 154 computations (70.5% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))
✓	0.0b	(*.f64 (-.f64 y x) z)
✓	4.4b	(/.f64 (*.f64 (-.f64 y x) z) t)

series53.0ms (2.1%)

Counts

3 → 132

Calls

3 calls:

27.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))
19.0ms	(/.f64 (*.f64 (-.f64 y x) z) t)
7.0ms	(*.f64 (-.f64 y x) z)

rewrite18.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 66

Calls

3 calls:

7.0ms	(/.f64 (*.f64 (-.f64 y x) z) t)
4.0ms	(*.f64 (-.f64 y x) z)
4.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

simplify88.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

546×	`times-frac_binary64`
512×	`associate-/l*_binary64`
379×	`div-sub_binary64`
319×	`distribute-rgt-in_binary64`
318×	`associate-*l/_binary64`

Counts

198 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	138	2596
1	365	2080
2	1123	1980
3	4594	1980
4	5596	1980

prune79.0ms (3.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	125	6	131

Error

Counts

131 → 6

Alt Table

Status	Error	Program
	25.3b	(*.f64 z (/.f64 (-.f64 y x) t))
▶	1.5b	(+.f64 x (/.f64 (-.f64 y x) (/.f64 t z)))
	4.1b	(+.f64 x (.f64 (.f64 (-.f64 y x) z) (/.f64 1 t)))
	17.3b	(+.f64 x (cbrt.f64 (.f64 (.f64 (/.f64 (.f64 (-.f64 y x) z) t) (/.f64 (.f64 (-.f64 y x) z) t)) (/.f64 (*.f64 (-.f64 y x) z) t))))
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	4.1b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

Compiler

Compiled 1966 to 561 computations (71.5% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (-.f64 y x) (/.f64 t z)))
✓	7.0b	(/.f64 (-.f64 y x) (/.f64 t z))

series40.0ms (1.6%)

Counts

2 → 96

Calls

2 calls:

20.0ms	(+.f64 x (/.f64 (-.f64 y x) (/.f64 t z)))
19.0ms	(/.f64 (-.f64 y x) (/.f64 t z))

rewrite34.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

119×	`times-frac_binary64`
89×	`*-un-lft-identity_binary64`
87×	`add-sqr-sqrt_binary64`
59×	`add-cube-cbrt_binary64`
14×	`distribute-lft-out--_binary64`

Counts

2 → 121

Calls

2 calls:

14.0ms	(+.f64 x (/.f64 (-.f64 y x) (/.f64 t z)))
8.0ms	(/.f64 (-.f64 y x) (/.f64 t z))

simplify120.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

507×	`associate-/r/_binary64`
407×	`div-sub_binary64`
361×	`associate-/l*_binary64`
352×	`associate-/l/_binary64`
304×	`times-frac_binary64`

Counts

217 → 185

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	4031
1	657	3505
2	1847	3496
3	4543	3496
4	5374	3496

prune111.0ms (4.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	183	2	185
Fresh	3	0	3
Picked	0	1	1
Done	0	2	2
Total	186	5	191

Error

Counts

191 → 5

Alt Table

Status	Error	Program
▶	4.1b	(+.f64 x (*.f64 (/.f64 1 t) (/.f64 (-.f64 y x) (/.f64 1 z))))
✓	1.5b	(+.f64 x (/.f64 (-.f64 y x) (/.f64 t z)))
	4.3b	(fma.f64 z (/.f64 (-.f64 y x) t) x)
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	4.1b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

Compiler

Compiled 3403 to 809 computations (76.2% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 (/.f64 1 t) (/.f64 (-.f64 y x) (/.f64 1 z))))
✓	0.2b	(/.f64 (-.f64 y x) (/.f64 1 z))
✓	4.5b	(*.f64 (/.f64 1 t) (/.f64 (-.f64 y x) (/.f64 1 z)))

series48.0ms (1.9%)

Counts

3 → 132

Calls

3 calls:

22.0ms	(+.f64 x (*.f64 (/.f64 1 t) (/.f64 (-.f64 y x) (/.f64 1 z))))
19.0ms	(*.f64 (/.f64 1 t) (/.f64 (-.f64 y x) (/.f64 1 z)))
6.0ms	(/.f64 (-.f64 y x) (/.f64 1 z))

rewrite64.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

261×	`times-frac_binary64`
210×	`add-sqr-sqrt_binary64`
177×	`*-un-lft-identity_binary64`
116×	`add-cube-cbrt_binary64`
77×	`add-exp-log_binary64`

Counts

3 → 256

Calls

3 calls:

24.0ms	(*.f64 (/.f64 1 t) (/.f64 (-.f64 y x) (/.f64 1 z)))
8.0ms	(/.f64 (-.f64 y x) (/.f64 1 z))
3.0ms	(+.f64 x (*.f64 (/.f64 1 t) (/.f64 (-.f64 y x) (/.f64 1 z))))

simplify162.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

501×	`distribute-rgt-in_binary64`
491×	`distribute-lft-in_binary64`
317×	`fma-def_binary64`
175×	`associate-*l/_binary64`
170×	`associate-r_binary64`

Counts

388 → 362

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	246	5938
1	675	5266
2	2107	5164
3	4780	5164
4	4993	5164

prune237.0ms (9.3%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	362	0	362
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	362	5	367

Error

Counts

367 → 5

Alt Table

Status	Error	Program
✓	4.1b	(+.f64 x (*.f64 (/.f64 1 t) (/.f64 (-.f64 y x) (/.f64 1 z))))
✓	1.5b	(+.f64 x (/.f64 (-.f64 y x) (/.f64 t z)))
	4.3b	(fma.f64 z (/.f64 (-.f64 y x) t) x)
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	4.1b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

Compiler

Compiled 7984 to 3713 computations (53.5% saved)

regimes246.0ms (9.6%)

Accuracy

Total 0.8b remaining (99.3%)

Threshold costs 0.8b (99.3%)

Counts

32 → 3

Compiler

Compiled 2521 to 1503 computations (40.4% saved)

bsearch1.0ms (0%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	73
1	26	73
2	31	73
3	33	73
4	34	73
5	34	73

end64.0ms (2.5%)

Compiler: Compiled 175 to 80 computations (54.3% saved)

Details

analyze175.0ms (6.9%)

sample805.0ms (31.6%)

simplify69.0ms (2.7%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series17.0ms (0.7%)

rewrite1.0ms (0%)

simplify64.0ms (2.5%)

prune20.0ms (0.8%)

localize6.0ms (0.2%)

series53.0ms (2.1%)

rewrite18.0ms (0.7%)

simplify88.0ms (3.4%)

prune79.0ms (3.1%)

localize8.0ms (0.3%)

series40.0ms (1.6%)

rewrite34.0ms (1.3%)

simplify120.0ms (4.7%)

prune111.0ms (4.3%)

localize8.0ms (0.3%)

series48.0ms (1.9%)

rewrite64.0ms (2.5%)

simplify162.0ms (6.3%)

prune237.0ms (9.3%)

regimes246.0ms (9.6%)

bsearch1.0ms (0%)

simplify4.0ms (0.2%)

end64.0ms (2.5%)

Profiling