Details

analyze1.7s (24.8%)

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)

sample1.4s (20.6%)

Results

1.2s	8045×	body	128	valid
77.0ms	589×	body	128	invalid
37.0ms	77×	body	1024	valid
27.0ms	80×	body	512	valid
12.0ms	54×	body	256	valid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify38.0ms (0.6%)

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%)

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

6.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.7b	(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 (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
✓	6.4b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

series400.0ms (5.9%)

Counts

2 → 84

Calls

2 calls:

214.0ms	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
186.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 49

Calls

2 calls:

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

simplify193.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

744×	`times-frac_binary64`
196×	`fma-def_binary64`
196×	`fma-neg_binary64`
174×	`distribute-rgt-in_binary64`
173×	`distribute-lft-in_binary64`

Counts

133 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	310	9777
1	961	7569
2	3326	7554
3	4980	7554
4	4968	7554

prune85.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	121	4	125

Error

0.0b

Counts

125 → 4

Alt Table

Status	Error	Program
▶	25.5b	x
	39.0b	(cbrt.f64 (pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 3))
✓	6.7b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
	26.4b	(-.f64 (fma.f64 z t x) (*.f64 x z))

Compiler

Compiled 5428 to 1770 computations (67.4% saved)

localize1.0ms (0%)

prune4.0ms (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
✓	25.5b	x
	39.0b	(cbrt.f64 (pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 3))
✓	6.7b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
▶	26.4b	(-.f64 (fma.f64 z t x) (*.f64 x z))

Compiler

Compiled 89 to 57 computations (36% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

7.0ms

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

rewrite3.0ms (0%)

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))

simplify75.0ms (1.1%)

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

prune25.0ms (0.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	41	5	46

Error

0.0b

Counts

46 → 5

Alt Table

Status	Error	Program
✓	25.5b	x
▶	39.0b	(cbrt.f64 (pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 3))
✓	6.7b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
✓	26.4b	(-.f64 (fma.f64 z t x) (*.f64 x z))
	47.9b	(fma.f64 (sqrt.f64 (fma.f64 z t x)) (sqrt.f64 (fma.f64 z t x)) (neg.f64 (*.f64 x z)))

Compiler

Compiled 668 to 193 computations (71.1% saved)

localize13.0ms (0.2%)

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)
	6.4b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
✓	36.0b	(cbrt.f64 (pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 3))

series1.4s (20.2%)

Counts

2 → 96

Calls

2 calls:

1.1s	(pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 3)
216.0ms	(cbrt.f64 (pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 3))

rewrite7.0ms (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	(pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 3)
1.0ms	(cbrt.f64 (pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 3))

simplify499.0ms (7.4%)

Algorithm

1×	egg-herbie

Rules

595×	`+-commutative_binary64`
548×	`associate-+r+_binary64`
479×	`fma-def_binary64`
383×	`*-commutative_binary64`
160×	`associate-r_binary64`

Counts

144 → 151

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1299	44113
1	4617	40962
2	4969	40962

prune591.0ms (8.7%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	274	1	275
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	274	6	280

Error

Counts

280 → 6

Alt Table

Status	Error	Program
	30.0b	(.f64 (cbrt.f64 (pow.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 2)) (cbrt.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))
✓	6.7b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
✓	25.5b	x
✓	39.0b	(cbrt.f64 (pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 3))
✓	26.4b	(-.f64 (fma.f64 z t x) (*.f64 x z))
	47.9b	(fma.f64 (sqrt.f64 (fma.f64 z t x)) (sqrt.f64 (fma.f64 z t x)) (neg.f64 (*.f64 x z)))

Compiler

Compiled 52453 to 20582 computations (60.8% saved)

regimes261.0ms (3.9%)

Accuracy

Total 1.2b remaining (98.4%)

Threshold costs 0b (0%)

Counts

33 → 3

Compiler

Compiled 3463 to 1811 computations (47.7% saved)

bsearch1.0ms (0%)

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

simplify7.0ms (0.1%)

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

end100.0ms (1.5%)

Compiler: Compiled 246 to 109 computations (55.7% 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

analyze1.7s (24.8%)

sample1.4s (20.6%)

simplify38.0ms (0.6%)

prune3.0ms (0%)

localize10.0ms (0.1%)

series400.0ms (5.9%)

rewrite9.0ms (0.1%)

simplify193.0ms (2.8%)

prune85.0ms (1.3%)

localize1.0ms (0%)

prune4.0ms (0.1%)

localize5.0ms (0.1%)

series7.0ms (0.1%)

rewrite3.0ms (0%)

simplify75.0ms (1.1%)

prune25.0ms (0.4%)

localize13.0ms (0.2%)

series1.4s (20.2%)

rewrite7.0ms (0.1%)

simplify499.0ms (7.4%)

prune591.0ms (8.7%)

regimes261.0ms (3.9%)

bsearch1.0ms (0%)

simplify7.0ms (0.1%)

end100.0ms (1.5%)

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