Details

analyze1.1s (14.5%)

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
1.6%	98.2%	0.2%	8
19.1%	80.7%	0.2%	9
22%	77.8%	0.2%	10
34.5%	65.3%	0.2%	11
44.2%	55.7%	0.2%	12
53.3%	45.5%	1.2%	13
55.8%	42.7%	1.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.2s (15.4%)

Results

1.0s	8256×	body	128	valid
71.0ms	668×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify112.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1536×	`fma-neg_binary64`
909×	`div-sub_binary64`
615×	`times-frac_binary64`
547×	`fma-def_binary64`
362×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	18	13
2	29	13
3	67	13
4	136	13
5	250	13
6	551	13
7	1395	13
8	2791	13
9	2886	13
10	3210	13
11	3295	13
12	3304	13
13	3354	13
14	4929	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

2.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	2.2b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 z y))
✓	2.1b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

series75.0ms (1%)

Counts

2 → 84

Calls

2 calls:

38.0ms	(/.f64 (-.f64 x y) (-.f64 z y))
36.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
70×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-l_binary64`
26×	`add-cube-cbrt_binary64`

Counts

2 → 106

Calls

2 calls:

11.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
6.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

simplify136.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

951×	`fma-def_binary64`
905×	`times-frac_binary64`
465×	`fma-neg_binary64`
154×	`associate-/l*_binary64`
144×	`+-commutative_binary64`

Counts

190 → 193

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	283	4749
1	800	4617
2	2672	4102
3	4971	4102
4	5241	4102

prune123.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	188	5	193
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	188	6	194

Error

Counts

194 → 6

Alt Table

Status	Error	Program
	11.6b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
▶	2.8b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
✓	2.2b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	37.3b	(-.f64 (fma.f64 (/.f64 t y) z t) (/.f64 (*.f64 t x) y))
	14.2b	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))
	32.1b	(.f64 (/.f64 (sqrt.f64 (-.f64 x y)) 1) (.f64 (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z y)) t))

Compiler

Compiled 4600 to 1305 computations (71.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t)
✓	0.2b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
✓	0.3b	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))))
✓	4.1b	(cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))

series1.5s (19.2%)

Counts

4 → 168

Calls

4 calls:

658.0ms	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t)
535.0ms	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))))
223.0ms	(cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))
48.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))

rewrite122.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

304×	`*-un-lft-identity_binary64`
251×	`add-sqr-sqrt_binary64`
248×	`cbrt-prod_binary64`
205×	`times-frac_binary64`
96×	`distribute-lft-out--_binary64`

Counts

4 → 285

Calls

4 calls:

28.0ms	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))))
24.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
12.0ms	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t)
5.0ms	(cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))

simplify293.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

331×	`associate-r_binary64`
329×	`fma-def_binary64`
275×	`associate-+r+_binary64`
181×	`associate-/l*_binary64`
173×	`associate-*r/_binary64`

Counts

453 → 461

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1820	27927
1	5310	27927

prune790.0ms (10.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	661	0	661
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	661	6	667

Error

Counts

667 → 6

Alt Table

Status	Error	Program
▶	11.6b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
✓	2.8b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
✓	2.2b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	37.3b	(-.f64 (fma.f64 (/.f64 t y) z t) (/.f64 (*.f64 t x) y))
	14.2b	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))
	32.1b	(.f64 (/.f64 (sqrt.f64 (-.f64 x y)) 1) (.f64 (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z y)) t))

Compiler

Compiled 54183 to 23942 computations (55.8% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
✓	5.9b	(/.f64 (*.f64 t x) (-.f64 z y))
✓	9.1b	(/.f64 (*.f64 y t) (-.f64 z y))

series92.0ms (1.2%)

Counts

3 → 87

Calls

3 calls:

45.0ms	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
27.0ms	(/.f64 (*.f64 t x) (-.f64 z y))
19.0ms	(/.f64 (*.f64 y t) (-.f64 z y))

rewrite57.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`times-frac_binary64`
121×	`prod-diff_binary64`
113×	`*-un-lft-identity_binary64`
113×	`add-sqr-sqrt_binary64`
56×	`associate-/r/_binary64`

Counts

3 → 221

Calls

3 calls:

15.0ms	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
5.0ms	(/.f64 (*.f64 y t) (-.f64 z y))
5.0ms	(/.f64 (*.f64 t x) (-.f64 z y))

simplify284.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

435×	`fma-neg_binary64`
321×	`sub-neg_binary64`
215×	`associate-/l*_binary64`
197×	`unsub-neg_binary64`
172×	`associate-l_binary64`

Counts

308 → 343

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	386	12003
1	994	10068
2	3722	8341
3	4484	8341
4	4970	8341
5	4868	8341

prune193.0ms (2.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	343	0	343
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	343	6	349

Error

Counts

349 → 6

Alt Table

Status	Error	Program
✓	11.6b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
✓	2.8b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
✓	2.2b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	37.3b	(-.f64 (fma.f64 (/.f64 t y) z t) (/.f64 (*.f64 t x) y))
▶	14.2b	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))
	32.1b	(.f64 (/.f64 (sqrt.f64 (-.f64 x y)) 1) (.f64 (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z y)) t))

Compiler

Compiled 12905 to 2269 computations (82.4% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 z y))
✓	0.2b	(*.f64 (/.f64 1 (-.f64 z y)) t)
✓	14.1b	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))

series61.0ms (0.8%)

Counts

3 → 108

Calls

3 calls:

34.0ms	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))
18.0ms	(*.f64 (/.f64 1 (-.f64 z y)) t)
8.0ms	(/.f64 1 (-.f64 z y))

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
31×	`add-exp-log_binary64`
26×	`associate-l_binary64`

Counts

3 → 119

Calls

3 calls:

9.0ms	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))
9.0ms	(*.f64 (/.f64 1 (-.f64 z y)) t)
4.0ms	(/.f64 1 (-.f64 z y))

simplify172.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

827×	`fma-def_binary64`
337×	`distribute-rgt-in_binary64`
289×	`cancel-sign-sub-inv_binary64`
283×	`fma-neg_binary64`
207×	`sub-neg_binary64`

Counts

227 → 221

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	260	4516
1	675	4300
2	2529	3660
3	4920	3660
4	5052	3660

prune131.0ms (1.7%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	221	0	221
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	221	6	227

Error

Counts

227 → 6

Alt Table

Status	Error	Program
✓	11.6b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
✓	2.8b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
✓	2.2b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	37.3b	(-.f64 (fma.f64 (/.f64 t y) z t) (/.f64 (*.f64 t x) y))
✓	14.2b	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))
	32.1b	(.f64 (/.f64 (sqrt.f64 (-.f64 x y)) 1) (.f64 (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z y)) t))

Compiler

Compiled 4599 to 1802 computations (60.8% saved)

regimes1.0s (13.3%)

Accuracy

Total 2.2b remaining (98.7%)

Threshold costs 0b (0%)

Counts

125 → 3

Compiler

Compiled 15351 to 8724 computations (43.2% saved)

bsearch42.0ms (0.5%)

Steps

Iters	Range		Point
8	1.0159782160905358e-69	5.988865689934763e-67	2.9971915677477026e-68
9	-7.550484780560298e+27	-1.3696513843288772e+22	-1.1171825476782533e+25

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
9×	`+-commutative_binary64`
9×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	84
1	44	84
2	58	84
3	71	84
4	78	84
5	81	84
6	82	84
7	81	84

end92.0ms (1.2%)

Compiler: Compiled 236 to 112 computations (52.5% saved)

Details

analyze1.1s (14.5%)

sample1.2s (15.4%)

simplify112.0ms (1.5%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series75.0ms (1%)

rewrite28.0ms (0.4%)

simplify136.0ms (1.8%)

prune123.0ms (1.6%)

localize11.0ms (0.1%)

series1.5s (19.2%)

rewrite122.0ms (1.6%)

simplify293.0ms (3.8%)

prune790.0ms (10.4%)

localize8.0ms (0.1%)

series92.0ms (1.2%)

rewrite57.0ms (0.7%)

simplify284.0ms (3.7%)

prune193.0ms (2.5%)

localize7.0ms (0.1%)

series61.0ms (0.8%)

rewrite29.0ms (0.4%)

simplify172.0ms (2.2%)

prune131.0ms (1.7%)

regimes1.0s (13.3%)

bsearch42.0ms (0.5%)

simplify5.0ms (0.1%)

end92.0ms (1.2%)

Profiling