Details

analyze1.6s (3.7%)

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)

sample1.5s (3.3%)

Results

1.3s	8031×	body	128	valid
74.0ms	535×	body	128	invalid
40.0ms	90×	body	1024	valid
24.0ms	77×	body	512	valid
14.0ms	57×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify42.0ms (0.1%)

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

2 alts after pruning (2 fresh and 0 done)

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

Error

4.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.0b	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

Compiler

Compiled 71 to 37 computations (47.9% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(tanh.f64 (/.f64 x y))
✓	0.0b	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
✓	0.0b	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
✓	4.0b	(.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))

series895.0ms (2%)

Counts

4 → 156

Calls

4 calls:

376.0ms	(.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))
244.0ms	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
210.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
64.0ms	(tanh.f64 (/.f64 x y))

rewrite40.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64`
46×	`add-sqr-sqrt_binary64`
45×	`prod-diff_binary64`
42×	`add-cube-cbrt_binary64`
26×	`associate-+r+_binary64`

Counts

4 → 152

Calls

4 calls:

11.0ms	(.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))
5.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
5.0ms	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
1.0ms	(tanh.f64 (/.f64 x y))

simplify289.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

311×	`fma-neg_binary64`
299×	`associate-l_binary64`
276×	`associate-r_binary64`
271×	`fma-def_binary64`
244×	`distribute-rgt-in_binary64`

Counts

308 → 303

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	462	18586
1	1347	13797
2	4946	13797
3	5180	13797

prune264.0ms (0.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	298	5	303
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	299	5	304

Error

Counts

304 → 5

Alt Table

Status	Error	Program
	22.5b	x
	5.1b	(+.f64 (fma.f64 y (.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x) (.f64 (fma.f64 (neg.f64 (tanh.f64 (/.f64 x y))) 1 (.f64 (tanh.f64 (/.f64 x y)) 1)) (.f64 y z)))
	40.9b	(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) 3)) (fma.f64 x x (.f64 y (.f64 (.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) (-.f64 (.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)))))
▶	4.0b	(+.f64 x (+.f64 (.f64 (tanh.f64 (/.f64 t y)) (.f64 y z)) (.f64 (neg.f64 (tanh.f64 (/.f64 x y))) (.f64 y z))))
	29.8b	(+.f64 x (*.f64 (-.f64 t x) z))

Compiler

Compiled 12989 to 3613 computations (72.2% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (+.f64 (.f64 (tanh.f64 (/.f64 t y)) (.f64 y z)) (.f64 (neg.f64 (tanh.f64 (/.f64 x y))) (.f64 y z))))
✓	0.3b	(+.f64 (.f64 (tanh.f64 (/.f64 t y)) (.f64 y z)) (.f64 (neg.f64 (tanh.f64 (/.f64 x y))) (.f64 y z)))
✓	4.9b	(.f64 (neg.f64 (tanh.f64 (/.f64 x y))) (.f64 y z))
✓	5.7b	(.f64 (tanh.f64 (/.f64 t y)) (.f64 y z))

series819.0ms (1.8%)

Counts

4 → 168

Calls

4 calls:

312.0ms	(+.f64 (.f64 (tanh.f64 (/.f64 t y)) (.f64 y z)) (.f64 (neg.f64 (tanh.f64 (/.f64 x y))) (.f64 y z)))
246.0ms	(+.f64 x (+.f64 (.f64 (tanh.f64 (/.f64 t y)) (.f64 y z)) (.f64 (neg.f64 (tanh.f64 (/.f64 x y))) (.f64 y z))))
134.0ms	(.f64 (neg.f64 (tanh.f64 (/.f64 x y))) (.f64 y z))
126.0ms	(.f64 (tanh.f64 (/.f64 t y)) (.f64 y z))

rewrite39.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`associate-*l/_binary64`
14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`pow1_binary64`
13×	`associate-l_binary64`

Counts

4 → 99

Calls

4 calls:

11.0ms	(.f64 (tanh.f64 (/.f64 t y)) (.f64 y z))
8.0ms	(+.f64 (.f64 (tanh.f64 (/.f64 t y)) (.f64 y z)) (.f64 (neg.f64 (tanh.f64 (/.f64 x y))) (.f64 y z)))
6.0ms	(.f64 (neg.f64 (tanh.f64 (/.f64 x y))) (.f64 y z))
5.0ms	(+.f64 x (+.f64 (.f64 (tanh.f64 (/.f64 t y)) (.f64 y z)) (.f64 (neg.f64 (tanh.f64 (/.f64 x y))) (.f64 y z))))

simplify269.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

376×	`associate-r_binary64`
337×	`associate-l_binary64`
309×	`fma-neg_binary64`
287×	`fma-def_binary64`
273×	`*-commutative_binary64`

Counts

267 → 246

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	361	15536
1	1216	13312
2	4521	13306
3	5022	13306

prune209.0ms (0.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	245	1	246
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	246	5	251

Error

Counts

251 → 5

Alt Table

Status	Error	Program
	40.9b	(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) 3)) (fma.f64 x x (.f64 y (.f64 (.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) (-.f64 (.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)))))
✓	4.0b	(+.f64 x (+.f64 (.f64 (tanh.f64 (/.f64 t y)) (.f64 y z)) (.f64 (neg.f64 (tanh.f64 (/.f64 x y))) (.f64 y z))))
▶	1.6b	(+.f64 x (.f64 (.f64 (cbrt.f64 (.f64 z (.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))) (cbrt.f64 (.f64 z (.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))) (cbrt.f64 (.f64 z (.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))))
	5.1b	(+.f64 (fma.f64 y (.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x) (.f64 (fma.f64 (neg.f64 (tanh.f64 (/.f64 x y))) 1 (.f64 (tanh.f64 (/.f64 x y)) 1)) (.f64 y z)))
	29.8b	(+.f64 x (*.f64 (-.f64 t x) z))

Compiler

Compiled 9848 to 2720 computations (72.4% saved)

localize15.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 (.f64 z (.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))) (cbrt.f64 (.f64 z (.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))) (cbrt.f64 (.f64 z (.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))))
✓	0.4b	(.f64 (cbrt.f64 (.f64 z (.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))) (cbrt.f64 (.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))))
✓	1.7b	(*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))
✓	6.5b	(cbrt.f64 (.f64 z (.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))

series17.1s (38.6%)

Counts

4 → 180

Calls

4 calls:

9.9s	(.f64 (cbrt.f64 (.f64 z (.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))) (cbrt.f64 (.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))))
6.7s	(cbrt.f64 (.f64 z (.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))
336.0ms	(.f64 (.f64 (cbrt.f64 (.f64 z (.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))) (cbrt.f64 (.f64 z (.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))) (cbrt.f64 (.f64 z (.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))))
208.0ms	(*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))

rewrite3.7s (8.3%)

Algorithm

1×	rewrite-expression-head

Rules

10219×	`associate-*r/_binary64`
5027×	`cbrt-div_binary64`
4122×	`frac-sub_binary64`
3146×	`frac-times_binary64`
2748×	`tanh-def-a_binary64`

Counts

4 → 2019

Calls

4 calls:

59.0ms	(.f64 (.f64 (cbrt.f64 (.f64 z (.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))) (cbrt.f64 (.f64 z (.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))) (cbrt.f64 (.f64 z (.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))))
23.0ms	(.f64 (cbrt.f64 (.f64 z (.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))) (cbrt.f64 (.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))))
9.0ms	(*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))
8.0ms	(cbrt.f64 (.f64 z (.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))

simplify7.4s (16.7%)

Algorithm

1×	egg-herbie

Rules

250×	`fma-def_binary64`
12×	`fma-udef_binary64`
10×	`fma-neg_binary64`

Counts

2199 → 2514

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4885	512778
1	5164	512778

prune7.0s (15.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	2777	1	2778
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	2779	4	2783

Error

Counts

2783 → 4

Alt Table

Status	Error	Program
✓	4.0b	(+.f64 x (+.f64 (.f64 (tanh.f64 (/.f64 t y)) (.f64 y z)) (.f64 (neg.f64 (tanh.f64 (/.f64 x y))) (.f64 y z))))
▶	5.1b	(+.f64 (fma.f64 y (.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x) (.f64 (fma.f64 (neg.f64 (tanh.f64 (/.f64 x y))) 1 (.f64 (tanh.f64 (/.f64 x y)) 1)) (.f64 y z)))
	16.4b	(+.f64 x (cbrt.f64 (.f64 (.f64 (.f64 z (.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) (.f64 z (.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))) (.f64 z (.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))))
	29.8b	(+.f64 x (*.f64 (-.f64 t x) z))

Compiler

Compiled 437144 to 170712 computations (60.9% saved)

localize15.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
✓	0.9b	(*.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))
✓	1.4b	(fma.f64 y (*.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)
✓	3.4b	(.f64 (fma.f64 (neg.f64 (tanh.f64 (/.f64 x y))) 1 (.f64 (tanh.f64 (/.f64 x y)) 1)) (*.f64 y z))

series2.0s (4.5%)

Counts

3 → 132

Calls

3 calls:

1.4s

(*.f64 (fma.f64 (neg.f64 (tanh.f64 (/.f64 x y))) 1 (*.f64 (tanh.f64 (/.f64 x y)) 1)) (*.f64 y z))

293.0ms

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

280.0ms

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

rewrite25.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 89

Calls

3 calls:

9.0ms

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

4.0ms

(*.f64 (fma.f64 (neg.f64 (tanh.f64 (/.f64 x y))) 1 (*.f64 (tanh.f64 (/.f64 x y)) 1)) (*.f64 y z))

0.0ms

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

simplify239.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

333×	`sub-neg_binary64`
288×	`fma-neg_binary64`
254×	`associate-r_binary64`
240×	`associate-l_binary64`
192×	`*-commutative_binary64`

Counts

221 → 175

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	401	12565
1	1077	9256
2	4116	9231
3	4955	9231
4	4977	9231

prune254.0ms (0.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	256	4	260

Error

Counts

260 → 4

Alt Table

Status	Error	Program
✓	4.0b	(+.f64 x (+.f64 (.f64 (tanh.f64 (/.f64 t y)) (.f64 y z)) (.f64 (neg.f64 (tanh.f64 (/.f64 x y))) (.f64 y z))))
✓	5.1b	(+.f64 (fma.f64 y (.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x) (.f64 (fma.f64 (neg.f64 (tanh.f64 (/.f64 x y))) 1 (.f64 (tanh.f64 (/.f64 x y)) 1)) (.f64 y z)))
	16.4b	(+.f64 x (cbrt.f64 (.f64 (.f64 (.f64 z (.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) (.f64 z (.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))) (.f64 z (.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))))
	29.8b	(+.f64 x (*.f64 (-.f64 t x) z))

Compiler

Compiled 15087 to 4758 computations (68.5% saved)

regimes631.0ms (1.4%)

Accuracy

Total 1.6b remaining (98.2%)

Threshold costs 0b (0%)

Counts

115 → 1

Compiler

Compiled 17341 to 9376 computations (45.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	23
1	27	23
2	31	23
3	33	23
4	34	23
5	31	23

end68.0ms (0.2%)

Compiler: Compiled 157 to 79 computations (49.7% saved)

Details

analyze1.6s (3.7%)

sample1.5s (3.3%)

simplify42.0ms (0.1%)

prune3.0ms (0%)

localize11.0ms (0%)

series895.0ms (2%)

rewrite40.0ms (0.1%)

simplify289.0ms (0.7%)

prune264.0ms (0.6%)

localize14.0ms (0%)

series819.0ms (1.8%)

rewrite39.0ms (0.1%)

simplify269.0ms (0.6%)

prune209.0ms (0.5%)

localize15.0ms (0%)

series17.1s (38.6%)

rewrite3.7s (8.3%)

simplify7.4s (16.7%)

prune7.0s (15.7%)

localize15.0ms (0%)

series2.0s (4.5%)

rewrite25.0ms (0.1%)

simplify239.0ms (0.5%)

prune254.0ms (0.6%)

regimes631.0ms (1.4%)

simplify2.0ms (0%)

end68.0ms (0.2%)

Profiling