Details

analyze1.9s (17.3%)

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
7.8%	92%	0.2%	8
7.8%	92%	0.2%	9
10.9%	88.9%	0.2%	10
34.7%	65.1%	0.2%	11
43.1%	56.7%	0.2%	12
44.2%	55.7%	0.2%	13
49.5%	50.3%	0.2%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample55.0ms (0.5%)

Algorithm

1×

intervals

Results

31.0ms	252×	body	128	valid
2.0ms	13×	body	128	invalid
1.0ms	2×	body	1024	valid
0.0ms	2×	body	256	valid

Compiler

Compiled 43 to 29 computations (32.6% saved)

simplify60.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

509×	`fma-neg_binary64`
396×	`distribute-rgt-in_binary64`
366×	`distribute-lft-in_binary64`
289×	`fma-def_binary64`
260×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	55	21
2	153	21
3	362	21
4	1315	21
5	4639	21
6	5067	21

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

6.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.5b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

Compiler

Compiled 69 to 35 computations (49.3% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(tanh.f64 (/.f64 x y))
✓	0.0b	(tanh.f64 (/.f64 t y))
✓	0.0b	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
✓	6.1b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`frac-sub_binary64`
9×	`prod-diff_binary64`

Counts

4 → 73

Calls

4 calls:

11.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
2.0ms	(tanh.f64 (/.f64 t y))
2.0ms	(tanh.f64 (/.f64 x y))
1.0ms	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

series1.3s (12%)

Counts

4 → 132

Calls

4 calls:

620.0ms	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
462.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
164.0ms	(tanh.f64 (/.f64 x y))
97.0ms	(tanh.f64 (/.f64 t y))

simplify363.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

709×	`times-frac_binary64`
219×	`fma-neg_binary64`
187×	`fma-def_binary64`
174×	`distribute-lft-in_binary64`
174×	`distribute-rgt-in_binary64`

Counts

205 → 357

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	316	9607
1	981	8091
2	3437	8091
3	5018	8091

prune227.0ms (2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	354	3	357
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	354	4	358

Error

0.0b

Counts

358 → 4

Alt Table

Status	Error	Program
✓	6.5b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
	40.1b	(cbrt.f64 (pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 3))
	25.1b	(-.f64 (fma.f64 z t x) (*.f64 x z))
▶	21.4b	x

Compiler

Compiled 6081 to 2517 computations (58.6% saved)

localize1.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify26.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune6.0ms (0.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	1	1
Total	4	4

Error

0.0b

Counts

4 → 4

Alt Table

Status	Error	Program
✓	6.5b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
	40.1b	(cbrt.f64 (pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 3))
▶	25.1b	(-.f64 (fma.f64 z t x) (*.f64 x z))
✓	21.4b	x

Compiler

Compiled 89 to 57 computations (36% saved)

localize11.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.9b	(-.f64 (fma.f64 z t x) (*.f64 x z))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64`
3×	`fma-neg_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`prod-diff_binary64`

Counts

1 → 21

Calls

1 calls:

5.0ms

(-.f64 (fma.f64 z t x) (*.f64 x z))

series54.0ms (0.5%)

Counts

1 → 36

Calls

1 calls:

54.0ms

(-.f64 (fma.f64 z t x) (*.f64 x z))

simplify129.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

625×	`fma-neg_binary64`
539×	`associate-+l+_binary64`
512×	`associate-+r+_binary64`
301×	`*-commutative_binary64`
241×	`neg-sub0_binary64`

Counts

57 → 103

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	60	695
1	142	615
2	415	596
3	1618	595
4	3553	508
5	4678	508
6	4933	508

prune47.0ms (0.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	102	5	107

Error

Counts

107 → 5

Alt Table

Status	Error	Program
✓	6.5b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
▶	40.1b	(cbrt.f64 (pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 3))
	47.0b	(fma.f64 (sqrt.f64 (fma.f64 z t x)) (sqrt.f64 (fma.f64 z t x)) (neg.f64 (*.f64 x z)))
✓	25.1b	(-.f64 (fma.f64 z t x) (*.f64 x z))
✓	21.4b	x

Compiler

Compiled 668 to 193 computations (71.1% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
✓	0.1b	(pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 3)
	6.1b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
✓	37.0b	(cbrt.f64 (pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 3))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`

Counts

2 → 48

Calls

2 calls:

3.0ms	(cbrt.f64 (pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 3))
3.0ms	(pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 3)

series2.5s (22.7%)

Counts

2 → 96

Calls

2 calls:

1.9s	(pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 3)
592.0ms	(cbrt.f64 (pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 3))

simplify899.0ms (8.1%)

Algorithm

1×	egg-herbie

Rules

739×	`times-frac_binary64`
336×	`+-commutative_binary64`
302×	`associate-+r+_binary64`
275×	`fma-def_binary64`
243×	`*-commutative_binary64`

Counts

144 → 264

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	846	33808
1	3184	33565
2	4983	33565

prune1.0s (9.2%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	508	0	508
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	508	5	513

Error

Counts

513 → 5

Alt Table

Status	Error	Program
✓	6.5b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
✓	40.1b	(cbrt.f64 (pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 3))
	47.0b	(fma.f64 (sqrt.f64 (fma.f64 z t x)) (sqrt.f64 (fma.f64 z t x)) (neg.f64 (*.f64 x z)))
✓	25.1b	(-.f64 (fma.f64 z t x) (*.f64 x z))
✓	21.4b	x

Compiler

Compiled 29336 to 17374 computations (40.8% saved)

regimes613.0ms (5.5%)

Accuracy

Total 1.0b remaining (98.5%)

Threshold costs 0b (0%)

Compiler

Compiled 3063 to 1956 computations (36.1% saved)

bsearch2.0ms (0%)

Compiler: Compiled 19 to 12 computations (36.8% saved)

simplify18.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
12×	`*-commutative_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-neg-in_binary64`
10×	`neg-sub0_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	28	97
1	44	97
2	65	97
3	81	95
4	101	95
5	110	95
6	113	95
7	118	95
8	123	95
9	125	95
10	121	95

end2.0ms (0%)

Compiler: Compiled 67 to 24 computations (64.2% saved)

sample1.7s (15.4%)

Algorithm

1×

intervals

Results

902.0ms	7781×	body	128	valid
62.0ms	522×	body	128	invalid
35.0ms	76×	body	1024	valid
28.0ms	86×	body	512	valid
12.0ms	54×	body	256	valid
3.0ms	3×	body	2048	valid

Compiler

Compiled 166 to 86 computations (48.2% saved)

Iter	Nodes	Cost
0	28	97
1	44	97
2	65	97
3	81	95
4	101	95
5	110	95
6	113	95
7	118	95
8	123	95
9	125	95
10	121	95

Iter	Nodes	Cost
0	28	97
1	44	97
2	65	97
3	81	95
4	101	95
5	110	95
6	113	95
7	118	95
8	123	95
9	125	95
10	121	95

Details

analyze1.9s (17.3%)

sample55.0ms (0.5%)

simplify60.0ms (0.5%)

prune6.0ms (0.1%)

localize21.0ms (0.2%)

rewrite27.0ms (0.2%)

series1.3s (12%)

simplify363.0ms (3.3%)

prune227.0ms (2%)

localize1.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify26.0ms (0.2%)

prune6.0ms (0.1%)

localize11.0ms (0.1%)

rewrite7.0ms (0.1%)

series54.0ms (0.5%)

simplify129.0ms (1.2%)

prune47.0ms (0.4%)

localize29.0ms (0.3%)

rewrite13.0ms (0.1%)

series2.5s (22.7%)

simplify899.0ms (8.1%)

prune1.0s (9.2%)

regimes613.0ms (5.5%)

bsearch2.0ms (0%)

simplify18.0ms (0.2%)

end2.0ms (0%)

sample1.7s (15.4%)

Profiling

Iter	Nodes	Cost
0	28	97
1	44	97
2	65	97
3	81	95
4	101	95
5	110	95
6	113	95
7	118	95
8	123	95
9	125	95
10	121	95