Details

analyze1.9s (25.8%)

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
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
0%	99.8%	0.2%	13
0%	99.8%	0.2%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample2.8s (37.4%)

Results

1.5s	8044×	body	128	valid
810.0ms	310×	body	8192	exit
284.0ms	300×	body	128	invalid
37.0ms	75×	body	1024	valid
28.0ms	80×	body	512	valid
13.0ms	57×	body	256	valid

Compiler

Compiled 39 to 25 computations (35.9% saved)

simplify39.0ms (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

prune4.0ms (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

4.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.0b	(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)

localize11.0ms (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))
✓	0.3b	(-.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)

series539.0ms (7.3%)

Counts

4 → 132

Calls

4 calls:

240.0ms	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
177.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
61.0ms	(tanh.f64 (/.f64 x y))
60.0ms	(tanh.f64 (/.f64 t y))

rewrite14.0ms (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:

6.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
4.0ms	(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)

simplify190.0ms (2.6%)

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

prune137.0ms (1.9%)

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
▶	7.5b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (log.f64 (exp.f64 (tanh.f64 (/.f64 x y))))) x)
	31.5b	(.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)))
	22.0b	(expm1.f64 (log1p.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))
	26.5b	(-.f64 (fma.f64 z t x) (*.f64 x z))
	22.0b	x

Compiler

Compiled 6747 to 2173 computations (67.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(tanh.f64 (/.f64 t y))
✓	0.2b	(-.f64 (tanh.f64 (/.f64 t y)) (log.f64 (exp.f64 (tanh.f64 (/.f64 x y)))))
✓	2.5b	(log.f64 (exp.f64 (tanh.f64 (/.f64 x y))))
✓	3.9b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (log.f64 (exp.f64 (tanh.f64 (/.f64 x y))))) x)

series477.0ms (6.5%)

Counts

3 → 108

Calls

3 calls:

235.0ms

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

180.0ms

(-.f64 (tanh.f64 (/.f64 t y)) (log.f64 (exp.f64 (tanh.f64 (/.f64 x y)))))

61.0ms

(log.f64 (exp.f64 (tanh.f64 (/.f64 x y))))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64`
24×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
21×	`prod-diff_binary64`
21×	`log-pow_binary64`

Counts

3 → 77

Calls

3 calls:

6.0ms

(-.f64 (tanh.f64 (/.f64 t y)) (log.f64 (exp.f64 (tanh.f64 (/.f64 x y)))))

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)

simplify205.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

861×	`fma-def_binary64`
649×	`times-frac_binary64`
527×	`fma-neg_binary64`
153×	`+-commutative_binary64`
131×	`associate--l+_binary64`

Counts

185 → 176

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	308	12463
1	777	6980
2	2721	6732
3	4960	6732
4	5197	6732

prune137.0ms (1.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	198	0	198
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	198	5	203

Error

0.0b

Counts

203 → 5

Alt Table

Status	Error	Program
✓	7.5b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (log.f64 (exp.f64 (tanh.f64 (/.f64 x y))))) x)
	31.5b	(.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)))
	22.0b	(expm1.f64 (log1p.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))
	26.5b	(-.f64 (fma.f64 z t x) (*.f64 x z))
▶	22.0b	x

Compiler

Compiled 6970 to 1900 computations (72.7% 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
✓	7.5b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (log.f64 (exp.f64 (tanh.f64 (/.f64 x y))))) x)
	31.5b	(.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)))
▶	22.0b	(expm1.f64 (log1p.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))
	26.5b	(-.f64 (fma.f64 z t x) (*.f64 x z))
✓	22.0b	x

Compiler

Compiled 159 to 83 computations (47.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(tanh.f64 (/.f64 t y))
	0.3b	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
✓	2.1b	(expm1.f64 (log1p.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))
	3.9b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

series241.0ms (3.3%)

Counts

1 → 48

Calls

1 calls:

241.0ms

(expm1.f64 (log1p.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 11

Calls

1 calls:

0.0ms

(expm1.f64 (log1p.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))

simplify122.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

959×	`fma-neg_binary64`
407×	`associate--l+_binary64`
383×	`fma-def_binary64`
301×	`times-frac_binary64`
255×	`associate-/l*_binary64`

Counts

59 → 50

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	137	5014
1	422	4621
2	1406	3823
3	4737	3769
4	5586	3769

prune141.0ms (1.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	199	1	200
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	199	6	205

Error

0.0b

Counts

205 → 6

Alt Table

Status	Error	Program
✓	7.5b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (log.f64 (exp.f64 (tanh.f64 (/.f64 x y))))) x)
	31.5b	(.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)))
	26.5b	(-.f64 (fma.f64 z t x) (*.f64 x z))
	38.4b	(+.f64 x (*.f64 z (-.f64 (fma.f64 (/.f64 y (+.f64 (exp.f64 (/.f64 t y)) (exp.f64 (neg.f64 (/.f64 t y))))) (exp.f64 (/.f64 t y)) (/.f64 y (+.f64 1 (pow.f64 (exp.f64 (/.f64 x y)) 2)))) (fma.f64 (/.f64 y (+.f64 (exp.f64 (/.f64 x y)) (exp.f64 (neg.f64 (/.f64 x y))))) (exp.f64 (/.f64 x y)) (/.f64 y (+.f64 1 (pow.f64 (exp.f64 (/.f64 t y)) 2)))))))
✓	22.0b	(expm1.f64 (log1p.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))
✓	22.0b	x

Compiler

Compiled 8487 to 2833 computations (66.6% saved)

regimes278.0ms (3.8%)

Accuracy

Total 0.8b remaining (96%)

Threshold costs 0.8b (96%)

Counts

44 → 3

Compiler

Compiled 4318 to 2641 computations (38.8% saved)

bsearch1.0ms (0%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	89
1	40	89
2	47	89
3	51	89
4	53	89
5	52	89

end110.0ms (1.5%)

Compiler: Compiled 279 to 127 computations (54.5% saved)

Details

analyze1.9s (25.8%)

sample2.8s (37.4%)

simplify39.0ms (0.5%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

series539.0ms (7.3%)

rewrite14.0ms (0.2%)

simplify190.0ms (2.6%)

prune137.0ms (1.9%)

localize13.0ms (0.2%)

series477.0ms (6.5%)

rewrite15.0ms (0.2%)

simplify205.0ms (2.8%)

prune137.0ms (1.9%)

localize1.0ms (0%)

prune4.0ms (0.1%)

localize13.0ms (0.2%)

series241.0ms (3.3%)

rewrite1.0ms (0%)

simplify122.0ms (1.7%)

prune141.0ms (1.9%)

regimes278.0ms (3.8%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end110.0ms (1.5%)

Profiling