Details

analyze715.0ms (12.2%)

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
7%	92.8%	0.2%	8
19.1%	80.7%	0.2%	9
29.8%	70%	0.2%	10
31.3%	68.5%	0.2%	11
42.3%	57.2%	0.6%	12
53.3%	45.5%	1.2%	13
59.2%	39.3%	1.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.1s (18%)

Results

881.0ms	8256×	body	128	valid
67.0ms	619×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify113.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1630×	`fma-neg_binary64`
896×	`div-sub_binary64`
582×	`times-frac_binary64`
579×	`fma-def_binary64`
367×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	34	13
3	74	13
4	145	13
5	245	13
6	572	13
7	1407	13
8	2937	13
9	2993	13
10	3292	13
11	3338	13
12	3355	13
13	3404	13
14	4948	13

prune1.0ms (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

11.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	11.0b	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

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 x (-.f64 y z))
✓	10.3b	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

series40.0ms (0.7%)

Counts

2 → 84

Calls

2 calls:

34.0ms	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))
6.0ms	(*.f64 x (-.f64 y z))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 81

Calls

2 calls:

8.0ms	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))
5.0ms	(*.f64 x (-.f64 y z))

simplify99.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

526×	`cancel-sign-sub-inv_binary64`
513×	`fma-neg_binary64`
365×	`div-sub_binary64`
202×	`associate-/l*_binary64`
196×	`sub-neg_binary64`

Counts

165 → 145

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	244	2954
1	576	2753
2	2576	2555
3	4147	2552
4	5042	2552

prune112.0ms (1.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	137	8	145
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	137	9	146

Error

0.0b

Counts

146 → 9

Alt Table

Status	Error	Program
	36.3b	(/.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 y z))) (-.f64 t z))
	49.3b	(*.f64 (/.f64 x (+.f64 (sqrt.f64 t) (sqrt.f64 z))) (/.f64 (-.f64 y z) (-.f64 (sqrt.f64 t) (sqrt.f64 z))))
✓	11.0b	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))
	31.9b	(*.f64 (/.f64 x (sqrt.f64 (-.f64 t z))) (/.f64 (-.f64 y z) (sqrt.f64 (-.f64 t z))))
	34.8b	(/.f64 (*.f64 (/.f64 x (sqrt.f64 (-.f64 t z))) (-.f64 y z)) (sqrt.f64 (-.f64 t z)))
▶	1.4b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
	11.0b	(.f64 (.f64 x (-.f64 y z)) (/.f64 1 (-.f64 t z)))
	35.3b	(/.f64 (.f64 (.f64 x (sqrt.f64 (-.f64 y z))) (sqrt.f64 (-.f64 y z))) (-.f64 t z))
	1.4b	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))

Compiler

Compiled 3332 to 1014 computations (69.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) (-.f64 y z))
✓	1.4b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))

series63.0ms (1.1%)

Counts

2 → 84

Calls

2 calls:

42.0ms	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
20.0ms	(/.f64 (-.f64 t z) (-.f64 y z))

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
194×	`*-un-lft-identity_binary64`
194×	`add-sqr-sqrt_binary64`
90×	`add-cube-cbrt_binary64`
52×	`distribute-lft-out--_binary64`

Counts

2 → 198

Calls

2 calls:

10.0ms	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
6.0ms	(/.f64 (-.f64 t z) (-.f64 y z))

simplify157.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

562×	`cancel-sign-sub-inv_binary64`
374×	`sub-neg_binary64`
271×	`associate-/r/_binary64`
224×	`fma-neg_binary64`
198×	`associate-/l/_binary64`

Counts

282 → 300

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	408	7629
1	1057	7410
2	3983	7368
3	5298	7368

prune155.0ms (2.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	296	4	300
Fresh	5	2	7
Picked	0	1	1
Done	0	1	1
Total	301	8	309

Error

Counts

309 → 8

Alt Table

Status	Error	Program
✓	1.4b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
	11.0b	(*.f64 (/.f64 1 (-.f64 t z)) (/.f64 x (/.f64 1 (-.f64 y z))))
	2.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (/.f64 (-.f64 t z) (-.f64 y z))))
✓	11.0b	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))
	31.9b	(*.f64 (/.f64 x (sqrt.f64 (-.f64 t z))) (/.f64 (-.f64 y z) (sqrt.f64 (-.f64 t z))))
	31.0b	(/.f64 (sqrt.f64 x) (/.f64 (/.f64 (-.f64 t z) (-.f64 y z)) (sqrt.f64 x)))
▶	1.8b	(/.f64 1 (/.f64 (/.f64 (-.f64 t z) (-.f64 y z)) x))
	34.8b	(/.f64 (*.f64 (/.f64 x (sqrt.f64 (-.f64 t z))) (-.f64 y z)) (sqrt.f64 (-.f64 t z)))

Compiler

Compiled 7294 to 1735 computations (76.2% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 t z) (-.f64 y z))
✓	0.5b	(/.f64 1 (/.f64 (/.f64 (-.f64 t z) (-.f64 y z)) x))
✓	1.3b	(/.f64 (/.f64 (-.f64 t z) (-.f64 y z)) x)

series69.0ms (1.2%)

Counts

2 → 96

Calls

2 calls:

36.0ms	(/.f64 (/.f64 (-.f64 t z) (-.f64 y z)) x)
33.0ms	(/.f64 1 (/.f64 (/.f64 (-.f64 t z) (-.f64 y z)) x))

rewrite140.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

1156×	`times-frac_binary64`
756×	`*-un-lft-identity_binary64`
756×	`add-sqr-sqrt_binary64`
436×	`add-cube-cbrt_binary64`
160×	`distribute-lft-out--_binary64`

Counts

2 → 563

Calls

2 calls:

20.0ms	(/.f64 1 (/.f64 (/.f64 (-.f64 t z) (-.f64 y z)) x))
11.0ms	(/.f64 (/.f64 (-.f64 t z) (-.f64 y z)) x)

simplify796.0ms (13.6%)

Algorithm

1×	egg-herbie

Rules

479×	`associate-/r/_binary64`
337×	`associate-/l/_binary64`
313×	`associate-/r*_binary64`
253×	`fma-neg_binary64`
220×	`times-frac_binary64`

Counts

659 → 683

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	552	21221
1	1391	19126
2	4727	19126
3	4996	19126
4	5000	19126
5	4982	19126

prune380.0ms (6.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	764	3	767
Fresh	3	2	5
Picked	1	0	1
Done	0	2	2
Total	768	7	775

Error

Counts

775 → 7

Alt Table

Status	Error	Program
	2.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (/.f64 (-.f64 t z) (-.f64 y z))))
✓	11.0b	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))
	1.8b	(/.f64 1 (/.f64 (/.f64 (/.f64 (-.f64 t z) 1) (-.f64 y z)) x))
▶	1.5b	(/.f64 (/.f64 (-.f64 y z) (-.f64 t z)) (/.f64 1 x))
	10.7b	(/.f64 (/.f64 1 (-.f64 t z)) (/.f64 (/.f64 1 (-.f64 y z)) x))
	34.8b	(/.f64 (*.f64 (/.f64 x (sqrt.f64 (-.f64 t z))) (-.f64 y z)) (sqrt.f64 (-.f64 t z)))
✓	1.4b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))

Compiler

Compiled 21163 to 5521 computations (73.9% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 y z) (-.f64 t z))
✓	1.4b	(/.f64 (/.f64 (-.f64 y z) (-.f64 t z)) (/.f64 1 x))

series58.0ms (1%)

Counts

2 → 84

Calls

2 calls:

36.0ms	(/.f64 (/.f64 (-.f64 y z) (-.f64 t z)) (/.f64 1 x))
22.0ms	(/.f64 (-.f64 y z) (-.f64 t z))

rewrite404.0ms (6.9%)

Algorithm

1×	rewrite-expression-head

Rules

1066×	`times-frac_binary64`
696×	`*-un-lft-identity_binary64`
696×	`add-sqr-sqrt_binary64`
392×	`add-cube-cbrt_binary64`
152×	`distribute-lft-out--_binary64`

Counts

2 → 528

Calls

2 calls:

104.0ms	(/.f64 (/.f64 (-.f64 y z) (-.f64 t z)) (/.f64 1 x))
6.0ms	(/.f64 (-.f64 y z) (-.f64 t z))

simplify413.0ms (7%)

Algorithm

1×	egg-herbie

Rules

573×	`fma-def_binary64`
450×	`associate-/l/_binary64`
293×	`associate-/r*_binary64`
290×	`associate-/r/_binary64`
233×	`associate-*l/_binary64`

Counts

612 → 572

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	520	20218
1	1474	18565
2	4705	18405
3	5450	18405

prune316.0ms (5.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	571	1	572
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	572	7	579

Error

Counts

579 → 7

Alt Table

Status	Error	Program
	2.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (/.f64 (-.f64 t z) (-.f64 y z))))
✓	11.0b	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))
✓	1.5b	(/.f64 (/.f64 (-.f64 y z) (-.f64 t z)) (/.f64 1 x))
	10.7b	(/.f64 (/.f64 1 (-.f64 t z)) (/.f64 (/.f64 1 (-.f64 y z)) x))
	1.4b	(.f64 1 (.f64 (/.f64 (-.f64 y z) (-.f64 t z)) x))
	34.8b	(/.f64 (*.f64 (/.f64 x (sqrt.f64 (-.f64 t z))) (-.f64 y z)) (sqrt.f64 (-.f64 t z)))
✓	1.4b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))

Compiler

Compiled 15840 to 5056 computations (68.1% saved)

regimes606.0ms (10.3%)

Accuracy

Total 2.1b remaining (99.5%)

Threshold costs 0b (0%)

Counts

114 → 1

Compiler

Compiled 9680 to 5874 computations (39.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`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	9	13
1	12	13
2	18	13
3	20	13
4	21	13
5	21	13

end80.0ms (1.4%)

Compiler: Compiled 138 to 85 computations (38.4% saved)

Details

analyze715.0ms (12.2%)

sample1.1s (18%)

simplify113.0ms (1.9%)

prune1.0ms (0%)

localize6.0ms (0.1%)

series40.0ms (0.7%)

rewrite19.0ms (0.3%)

simplify99.0ms (1.7%)

prune112.0ms (1.9%)

localize6.0ms (0.1%)

series63.0ms (1.1%)

rewrite41.0ms (0.7%)

simplify157.0ms (2.7%)

prune155.0ms (2.6%)

localize7.0ms (0.1%)

series69.0ms (1.2%)

rewrite140.0ms (2.4%)

simplify796.0ms (13.6%)

prune380.0ms (6.5%)

localize7.0ms (0.1%)

series58.0ms (1%)

rewrite404.0ms (6.9%)

simplify413.0ms (7%)

prune316.0ms (5.4%)

regimes606.0ms (10.3%)

simplify3.0ms (0.1%)

end80.0ms (1.4%)

Profiling