Details

analyze1.1s (18.8%)

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
6.2%	93.6%	0.2%	8
6.2%	93.6%	0.2%	9
10.1%	89.7%	0.2%	10
32%	67.8%	0.2%	11
39.4%	60.4%	0.2%	12
40.2%	59.6%	0.2%	13
47.5%	52.3%	0.2%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample1.9s (32.6%)

Results

1.7s	8027×	body	128	valid
85.0ms	599×	body	128	invalid
36.0ms	80×	body	1024	valid
31.0ms	90×	body	512	valid
13.0ms	59×	body	256	valid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify42.0ms (0.7%)

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

prune3.0ms (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

4.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.4b	(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)

localize10.0ms (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))
✓	0.2b	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
✓	4.1b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

series591.0ms (10.1%)

Counts

4 → 132

Calls

4 calls:

310.0ms	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
160.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
64.0ms	(tanh.f64 (/.f64 t y))
57.0ms	(tanh.f64 (/.f64 x y))

rewrite12.0ms (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:

5.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
1.0ms	(tanh.f64 (/.f64 t y))
1.0ms	(tanh.f64 (/.f64 x y))
0.0ms	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

simplify176.0ms (3%)

Algorithm

1×	egg-herbie

Rules

750×	`times-frac_binary64`
231×	`fma-neg_binary64`
202×	`fma-def_binary64`
174×	`distribute-rgt-in_binary64`
173×	`distribute-lft-in_binary64`

Counts

205 → 173

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	330	12435
1	1006	7805
2	3497	7805
3	5159	7805

prune119.0ms (2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	170	3	173
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	170	4	174

Error

0.0b

Counts

174 → 4

Alt Table

Status	Error	Program
✓	4.4b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
	39.0b	(cbrt.f64 (.f64 (.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))
	28.3b	(-.f64 (fma.f64 z t x) (*.f64 x z))
▶	22.4b	x

Compiler

Compiled 6713 to 2134 computations (68.2% saved)

localize1.0ms (0%)

prune3.0ms (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
✓	4.4b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
	39.0b	(cbrt.f64 (.f64 (.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))
▶	28.3b	(-.f64 (fma.f64 z t x) (*.f64 x z))
✓	22.4b	x

Compiler

Compiled 145 to 57 computations (60.7% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.2b	(-.f64 (fma.f64 z t x) (*.f64 x z))

series8.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

8.0ms

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

rewrite3.0ms (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:

2.0ms

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

simplify78.0ms (1.3%)

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 → 42

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

prune23.0ms (0.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	42	4	46

Error

0.0b

Counts

46 → 4

Alt Table

Status	Error	Program
✓	4.4b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
▶	39.0b	(cbrt.f64 (.f64 (.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))
✓	28.3b	(-.f64 (fma.f64 z t x) (*.f64 x z))
✓	22.4b	x

Compiler

Compiled 686 to 175 computations (74.5% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x))
	0.2b	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
	4.1b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
✓	36.0b	(cbrt.f64 (.f64 (.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))

series652.0ms (11.1%)

Counts

2 → 96

Calls

2 calls:

420.0ms

(*.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x))

231.0ms

(cbrt.f64 (*.f64 (*.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 41

Calls

2 calls:

3.0ms

(cbrt.f64 (*.f64 (*.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))

3.0ms

(*.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x))

simplify323.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

624×	`fma-def_binary64`
387×	`associate-/l*_binary64`
377×	`times-frac_binary64`
257×	`associate-/r*_binary64`
218×	`+-commutative_binary64`

Counts

137 → 136

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	599	22974
1	1923	20134
2	5045	20134

prune416.0ms (7.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	520	0	520
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	520	4	524

Error

0.0b

Counts

524 → 4

Alt Table

Status	Error	Program
✓	4.4b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
✓	39.0b	(cbrt.f64 (.f64 (.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))
✓	28.3b	(-.f64 (fma.f64 z t x) (*.f64 x z))
✓	22.4b	x

Compiler

Compiled 46062 to 10960 computations (76.2% saved)

regimes283.0ms (4.8%)

Accuracy

Total 3.1b remaining (98.9%)

Threshold costs 0b (0%)

Counts

31 → 2

Compiler

Compiled 4258 to 1931 computations (54.7% saved)

bsearch2.0ms (0%)

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	57
1	27	57
2	35	57
3	39	57
4	41	57
5	41	57

end69.0ms (1.2%)

Compiler: Compiled 168 to 72 computations (57.1% saved)

Details

analyze1.1s (18.8%)

sample1.9s (32.6%)

simplify42.0ms (0.7%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

series591.0ms (10.1%)

rewrite12.0ms (0.2%)

simplify176.0ms (3%)

prune119.0ms (2%)

localize1.0ms (0%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series8.0ms (0.1%)

rewrite3.0ms (0.1%)

simplify78.0ms (1.3%)

prune23.0ms (0.4%)

localize15.0ms (0.3%)

series652.0ms (11.1%)

rewrite9.0ms (0.2%)

simplify323.0ms (5.5%)

prune416.0ms (7.1%)

regimes283.0ms (4.8%)

bsearch2.0ms (0%)

simplify5.0ms (0.1%)

end69.0ms (1.2%)

Profiling