Details

analyze1.3s (6.8%)

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
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
16.5%	83.2%	0.2%	13
25.9%	73.9%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (6.4%)

Results

1.1s	8253×	body	128	valid
95.0ms	768×	body	128	invalid
0.0ms	1×	body	2048	valid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify116.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1893×	`fma-neg_binary64`
867×	`div-sub_binary64`
749×	`fma-def_binary64`
696×	`distribute-rgt-in_binary64`
535×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	40	14
3	81	14
4	160	14
5	302	14
6	620	14
7	1528	14
8	2624	14
9	2858	14
10	3205	14
11	3392	14
12	3498	14
13	3533	14
14	5398	14

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	13.1b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
▶	1.8b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 a z))
✓	1.8b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

series52.0ms (0.3%)

Counts

2 → 84

Calls

2 calls:

35.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
17.0ms	(/.f64 t (-.f64 a z))

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`associate-/r*_binary64`

Counts

2 → 49

Calls

2 calls:

3.0ms	(/.f64 t (-.f64 a z))
0.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

simplify79.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

690×	`times-frac_binary64`
633×	`fma-def_binary64`
620×	`associate-/l*_binary64`
272×	`cancel-sign-sub-inv_binary64`
175×	`associate-/l/_binary64`

Counts

133 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	198	3215
1	492	3156
2	1711	2520
3	5110	2520

prune83.0ms (0.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	105	5	110

Error

0.0b

Counts

110 → 5

Alt Table

Status	Error	Program
	15.4b	(fma.f64 (-.f64 y z) (cbrt.f64 (.f64 (.f64 (/.f64 t (-.f64 a z)) (/.f64 t (-.f64 a z))) (/.f64 t (-.f64 a z)))) x)
▶	0.6b	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
	2.1b	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) t)) x)
✓	1.8b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	13.1b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))

Compiler

Compiled 2435 to 767 computations (68.5% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 a z))
✓	0.0b	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
✓	0.0b	(/.f64 z (-.f64 a z))
✓	0.8b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))

series89.0ms (0.5%)

Counts

4 → 111

Calls

4 calls:

41.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
24.0ms	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
15.0ms	(/.f64 y (-.f64 a z))
8.0ms	(/.f64 z (-.f64 a z))

rewrite529.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

2048×	`*-un-lft-identity_binary64`
2030×	`add-sqr-sqrt_binary64`
2016×	`times-frac_binary64`
1323×	`prod-diff_binary64`
1200×	`add-cube-cbrt_binary64`

Counts

4 → 1556

Calls

4 calls:

53.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
30.0ms	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
6.0ms	(/.f64 z (-.f64 a z))
3.0ms	(/.f64 y (-.f64 a z))

simplify1.9s (9.9%)

Algorithm

1×	egg-herbie

Rules

422×	`*-commutative_binary64`
357×	`distribute-rgt-in_binary64`
306×	`fma-udef_binary64`
263×	`unsub-neg_binary64`
251×	`distribute-lft-in_binary64`

Counts

1667 → 1696

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1400	120634
1	2423	87989
2	4585	87650
3	5024	87650

prune1.5s (7.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	1693	3	1696
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	1695	6	1701

Error

Counts

1701 → 6

Alt Table

Status	Error	Program
	2.1b	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) t)) x)
▶	0.6b	(+.f64 (+.f64 (.f64 (fma.f64 1 (/.f64 y (-.f64 a z)) (neg.f64 (.f64 (/.f64 1 (-.f64 a z)) z))) t) (.f64 (fma.f64 (neg.f64 (/.f64 1 (-.f64 a z))) z (.f64 (/.f64 1 (-.f64 a z)) z)) t)) x)
	1.1b	(+.f64 (.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (*.f64 (cbrt.f64 t) (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))) x)
	15.4b	(fma.f64 (-.f64 y z) (cbrt.f64 (.f64 (.f64 (/.f64 t (-.f64 a z)) (/.f64 t (-.f64 a z))) (/.f64 t (-.f64 a z)))) x)
	6.1b	(+.f64 (+.f64 (/.f64 (.f64 t y) (-.f64 a z)) (.f64 t (neg.f64 (/.f64 z (-.f64 a z))))) x)
✓	1.8b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

Compiler

Compiled 96423 to 16753 computations (82.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 a z))
✓	0.2b	(*.f64 (/.f64 1 (-.f64 a z)) z)
✓	0.8b	(.f64 (fma.f64 1 (/.f64 y (-.f64 a z)) (neg.f64 (.f64 (/.f64 1 (-.f64 a z)) z))) t)
✓	51.6b	(fma.f64 (neg.f64 (/.f64 1 (-.f64 a z))) z (*.f64 (/.f64 1 (-.f64 a z)) z))

series354.0ms (1.8%)

Counts

4 → 120

Calls

4 calls:

292.0ms	(fma.f64 (neg.f64 (/.f64 1 (-.f64 a z))) z (*.f64 (/.f64 1 (-.f64 a z)) z))
45.0ms	(.f64 (fma.f64 1 (/.f64 y (-.f64 a z)) (neg.f64 (.f64 (/.f64 1 (-.f64 a z)) z))) t)
9.0ms	(/.f64 1 (-.f64 a z))
8.0ms	(*.f64 (/.f64 1 (-.f64 a z)) z)

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
26×	`add-cube-cbrt_binary64`
24×	`associate-l_binary64`

Counts

4 → 118

Calls

4 calls:

7.0ms	(*.f64 (/.f64 1 (-.f64 a z)) z)
4.0ms	(/.f64 1 (-.f64 a z))
2.0ms	(.f64 (fma.f64 1 (/.f64 y (-.f64 a z)) (neg.f64 (.f64 (/.f64 1 (-.f64 a z)) z))) t)
0.0ms	(fma.f64 (neg.f64 (/.f64 1 (-.f64 a z))) z (*.f64 (/.f64 1 (-.f64 a z)) z))

simplify139.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

877×	`fma-def_binary64`
375×	`cancel-sign-sub-inv_binary64`
341×	`fma-neg_binary64`
260×	`distribute-rgt-in_binary64`
205×	`distribute-lft-in_binary64`

Counts

238 → 232

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	264	4559
1	642	4170
2	2183	3608
3	4726	3603
4	4988	3603
5	4913	3603

prune546.0ms (2.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	431	0	431
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	431	6	437

Error

Counts

437 → 6

Alt Table

Status	Error	Program
	2.1b	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) t)) x)
✓	0.6b	(+.f64 (+.f64 (.f64 (fma.f64 1 (/.f64 y (-.f64 a z)) (neg.f64 (.f64 (/.f64 1 (-.f64 a z)) z))) t) (.f64 (fma.f64 (neg.f64 (/.f64 1 (-.f64 a z))) z (.f64 (/.f64 1 (-.f64 a z)) z)) t)) x)
▶	1.1b	(+.f64 (.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (*.f64 (cbrt.f64 t) (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))) x)
	15.4b	(fma.f64 (-.f64 y z) (cbrt.f64 (.f64 (.f64 (/.f64 t (-.f64 a z)) (/.f64 t (-.f64 a z))) (/.f64 t (-.f64 a z)))) x)
	6.1b	(+.f64 (+.f64 (/.f64 (.f64 t y) (-.f64 a z)) (.f64 t (neg.f64 (/.f64 z (-.f64 a z))))) x)
✓	1.8b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

Compiler

Compiled 19444 to 8966 computations (53.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (*.f64 (cbrt.f64 t) (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))
✓	0.5b	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
✓	0.6b	(cbrt.f64 t)
✓	0.6b	(*.f64 (cbrt.f64 t) (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))

series268.0ms (1.4%)

Counts

4 → 120

Calls

4 calls:

139.0ms	(*.f64 (cbrt.f64 t) (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
57.0ms	(.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (*.f64 (cbrt.f64 t) (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))
36.0ms	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
35.0ms	(cbrt.f64 t)

rewrite1.5s (7.6%)

Algorithm

1×	rewrite-expression-head

Rules

3916×	`add-sqr-sqrt_binary64`
3914×	`*-un-lft-identity_binary64`
3888×	`times-frac_binary64`
2646×	`prod-diff_binary64`
2340×	`add-cube-cbrt_binary64`

Counts

4 → 2904

Calls

4 calls:

88.0ms	(.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (*.f64 (cbrt.f64 t) (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))
51.0ms	(*.f64 (cbrt.f64 t) (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
4.0ms	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
1.0ms	(cbrt.f64 t)

simplify4.5s (23%)

Algorithm

1×	egg-herbie

Rules

1335×	`associate-l_binary64`
306×	`fma-udef_binary64`
48×	`neg-mul-1_binary64`
46×	`neg-sub0_binary64`
39×	`sub-neg_binary64`

Counts

3024 → 3458

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2724	287144
1	5408	287144

prune3.1s (15.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	3486	0	3486
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	3486	6	3492

Error

Counts

3492 → 6

Alt Table

Status	Error	Program
	2.1b	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) t)) x)
✓	0.6b	(+.f64 (+.f64 (.f64 (fma.f64 1 (/.f64 y (-.f64 a z)) (neg.f64 (.f64 (/.f64 1 (-.f64 a z)) z))) t) (.f64 (fma.f64 (neg.f64 (/.f64 1 (-.f64 a z))) z (.f64 (/.f64 1 (-.f64 a z)) z)) t)) x)
✓	1.1b	(+.f64 (.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (*.f64 (cbrt.f64 t) (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))) x)
	15.4b	(fma.f64 (-.f64 y z) (cbrt.f64 (.f64 (.f64 (/.f64 t (-.f64 a z)) (/.f64 t (-.f64 a z))) (/.f64 t (-.f64 a z)))) x)
	6.1b	(+.f64 (+.f64 (/.f64 (.f64 t y) (-.f64 a z)) (.f64 t (neg.f64 (/.f64 z (-.f64 a z))))) x)
✓	1.8b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

Compiler

Compiled 257569 to 39905 computations (84.5% saved)

regimes2.0s (10.3%)

Accuracy

Total 1.2b remaining (98.9%)

Threshold costs 0b (0%)

Counts

264 → 1

Compiler

Compiled 51921 to 28331 computations (45.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	27
1	27	25
2	38	25
3	46	25
4	50	25
5	51	25
6	51	25

end93.0ms (0.5%)

Compiler: Compiled 196 to 107 computations (45.4% saved)

Details

analyze1.3s (6.8%)

sample1.2s (6.4%)

simplify116.0ms (0.6%)

prune3.0ms (0%)

localize7.0ms (0%)

series52.0ms (0.3%)

rewrite6.0ms (0%)

simplify79.0ms (0.4%)

prune83.0ms (0.4%)

localize9.0ms (0%)

series89.0ms (0.5%)

rewrite529.0ms (2.7%)

simplify1.9s (9.9%)

prune1.5s (7.6%)

localize15.0ms (0.1%)

series354.0ms (1.8%)

rewrite21.0ms (0.1%)

simplify139.0ms (0.7%)

prune546.0ms (2.8%)

localize13.0ms (0.1%)

series268.0ms (1.4%)

rewrite1.5s (7.6%)

simplify4.5s (23%)

prune3.1s (15.9%)

regimes2.0s (10.3%)

simplify3.0ms (0%)

end93.0ms (0.5%)

Profiling