Details

analyze1.8s (30.2%)

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
7.8%	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)

sample32.0ms (0.5%)

Algorithm

1×

intervals

Results

17.0ms	245×	body	128	valid
1.0ms	22×	body	128	invalid
1.0ms	6×	body	512	valid
1.0ms	4×	body	1024	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 43 to 29 computations (32.6% 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

4.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.1b	(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)

localize35.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(tanh.f64 (/.f64 t y))
✓	0.0b	(tanh.f64 (/.f64 x y))
✓	0.0b	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
✓	3.9b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

series675.0ms (11.4%)

Counts

4 → 132

Calls

4 calls:

250.0ms	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
178.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
124.0ms	(tanh.f64 (/.f64 t y))
122.0ms	(tanh.f64 (/.f64 x y))

rewrite17.0ms (0.3%)

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:

9.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
2.0ms	(tanh.f64 (/.f64 x y))
1.0ms	(tanh.f64 (/.f64 t y))
1.0ms	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

simplify187.0ms (3.2%)

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

prune138.0ms (2.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	168	5	173
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	169	5	174

Error

0.0b

Counts

174 → 5

Alt Table

Status	Error	Program
	25.2b	x
	33.6b	(.f64 (sqrt.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (sqrt.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))
	44.7b	(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)))
▶	7.8b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (log.f64 (exp.f64 (tanh.f64 (/.f64 x y))))) x)
	29.5b	(-.f64 (fma.f64 z t x) (*.f64 x z))

Compiler

Compiled 6805 to 2176 computations (68% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(tanh.f64 (/.f64 t y))
	0.0b	(tanh.f64 (/.f64 x y))
✓	2.8b	(log.f64 (exp.f64 (tanh.f64 (/.f64 x y))))
✓	4.5b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (log.f64 (exp.f64 (tanh.f64 (/.f64 x y))))) x)

series339.0ms (5.7%)

Counts

2 → 72

Calls

2 calls:

277.0ms	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (log.f64 (exp.f64 (tanh.f64 (/.f64 x y))))) x)
62.0ms	(log.f64 (exp.f64 (tanh.f64 (/.f64 x y))))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`log-pow_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`log-prod_binary64`

Counts

2 → 27

Calls

2 calls:

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

simplify134.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

560×	`times-frac_binary64`
459×	`fma-neg_binary64`
420×	`fma-def_binary64`
376×	`associate-/l*_binary64`
280×	`associate-/r*_binary64`

Counts

99 → 86

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	179	5589
1	504	5162
2	1679	4357
3	4859	4357
4	5196	4357

prune86.0ms (1.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	131	5	136

Error

0.0b

Counts

136 → 5

Alt Table

Status	Error	Program
▶	25.2b	x
	33.6b	(.f64 (sqrt.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (sqrt.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))
	44.7b	(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)))
✓	7.8b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (log.f64 (exp.f64 (tanh.f64 (/.f64 x y))))) x)
	29.5b	(+.f64 x (*.f64 z (-.f64 t x)))

Compiler

Compiled 4267 to 1373 computations (67.8% saved)

localize1.0ms (0%)

prune4.0ms (0.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	1	1
Total	5	5

Error

0.0b

Counts

5 → 5

Alt Table

Status	Error	Program
✓	25.2b	x
	33.6b	(.f64 (sqrt.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (sqrt.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))
	44.7b	(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)))
✓	7.8b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (log.f64 (exp.f64 (tanh.f64 (/.f64 x y))))) x)
▶	29.5b	(+.f64 x (*.f64 z (-.f64 t x)))

Compiler

Compiled 215 to 85 computations (60.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series14.0ms (0.2%)

Counts

2 → 72

Calls

2 calls:

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

rewrite45.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
36×	`prod-diff_binary64`
35×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
26×	`associate-+r+_binary64`

Counts

2 → 92

Calls

2 calls:

6.0ms	(*.f64 z (-.f64 t x))
4.0ms	(+.f64 x (*.f64 z (-.f64 t x)))

simplify95.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

721×	`fma-neg_binary64`
644×	`fma-def_binary64`
344×	`distribute-rgt-in_binary64`
306×	`distribute-lft-in_binary64`
290×	`cancel-sign-sub-inv_binary64`

Counts

164 → 139

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	167	1649
1	290	1433
2	966	1375
3	2924	1321
4	4424	1321
5	4858	1321

prune67.0ms (1.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	139	5	144

Error

0.0b

Counts

144 → 5

Alt Table

Status	Error	Program
✓	25.2b	x
	33.6b	(.f64 (sqrt.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (sqrt.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))
	44.7b	(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)))
✓	7.8b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (log.f64 (exp.f64 (tanh.f64 (/.f64 x y))))) x)
✓	29.5b	(+.f64 x (*.f64 z (-.f64 t x)))

Compiler

Compiled 2526 to 625 computations (75.3% saved)

regimes342.0ms (5.8%)

Accuracy

Total 0.8b remaining (94.2%)

Threshold costs 0.8b (94.2%)

Counts

41 → 3

Compiler

Compiled 5443 to 2721 computations (50% saved)

bsearch3.0ms (0.1%)

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

simplify10.0ms (0.2%)

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	23	87
1	33	87
2	41	87
3	45	87
4	47	87
5	47	87

end1.0ms (0%)

Compiler: Compiled 61 to 22 computations (63.9% saved)

sample1.8s (31%)

Algorithm

1×

intervals

Results

972.0ms	7775×	body	128	valid
68.0ms	566×	body	128	invalid
43.0ms	85×	body	1024	valid
33.0ms	89×	body	512	valid
12.0ms	51×	body	256	valid
0.0ms	1×	body	512	invalid

Compiler

Compiled 205 to 90 computations (56.1% saved)

Details

analyze1.8s (30.2%)

sample32.0ms (0.5%)

simplify42.0ms (0.7%)

prune3.0ms (0.1%)

localize35.0ms (0.6%)

series675.0ms (11.4%)

rewrite17.0ms (0.3%)

simplify187.0ms (3.2%)

prune138.0ms (2.3%)

localize13.0ms (0.2%)

series339.0ms (5.7%)

rewrite3.0ms (0%)

simplify134.0ms (2.3%)

prune86.0ms (1.5%)

localize1.0ms (0%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series14.0ms (0.2%)

rewrite45.0ms (0.8%)

simplify95.0ms (1.6%)

prune67.0ms (1.1%)

regimes342.0ms (5.8%)

bsearch3.0ms (0.1%)

simplify10.0ms (0.2%)

end1.0ms (0%)

sample1.8s (31%)

Profiling