Details

analyze1.5s (32.4%)

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 (26.3%)

Results

1.1s	8256×	body	128	valid
102.0ms	784×	body	128	invalid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify111.0ms (2.3%)

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

prune4.0ms (0.1%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.5b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	12.7b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.4b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

series33.0ms (0.7%)

Counts

1 → 60

Calls

1 calls:

33.0ms

(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) 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 → 10

Calls

1 calls:

0.0ms

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

simplify46.0ms (1%)

Algorithm

1×	egg-herbie

Rules

548×	`associate--l+_binary64`
522×	`times-frac_binary64`
457×	`fma-def_binary64`
425×	`associate-/l*_binary64`
241×	`cancel-sign-sub-inv_binary64`

Counts

70 → 54

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	2043
1	312	2014
2	1168	1481
3	5033	1481

prune38.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	52	2	54
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	52	4	56

Error

0.0b

Counts

56 → 4

Alt Table

Status	Error	Program
✓	2.5b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
▶	12.7b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
	37.6b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	33.7b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)) (sqrt.f64 (fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)))

Compiler

Compiled 1390 to 444 computations (68.1% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y z) t)
✓	12.9b	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

series37.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

29.0ms	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))
7.0ms	(*.f64 (-.f64 y z) t)

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 55

Calls

2 calls:

7.0ms	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))
4.0ms	(*.f64 (-.f64 y z) t)

simplify86.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

592×	`fma-def_binary64`
310×	`associate-/l/_binary64`
309×	`cancel-sign-sub-inv_binary64`
267×	`distribute-rgt-in_binary64`
239×	`distribute-lft-in_binary64`

Counts

139 → 125

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	184	2883
1	524	2478
2	1984	2217
3	4866	2212
4	4984	2212

prune83.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	123	6	129

Error

Counts

129 → 6

Alt Table

Status	Error	Program
✓	2.5b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	31.6b	(+.f64 x (*.f64 (/.f64 (-.f64 y z) (sqrt.f64 (-.f64 a z))) (/.f64 t (sqrt.f64 (-.f64 a z)))))
	49.0b	(+.f64 x (/.f64 (*.f64 (/.f64 (-.f64 y z) (+.f64 (sqrt.f64 a) (sqrt.f64 z))) t) (-.f64 (sqrt.f64 a) (sqrt.f64 z))))
▶	2.5b	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) t)))
	37.6b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	33.7b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)) (sqrt.f64 (fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)))

Compiler

Compiled 2881 to 930 computations (67.7% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	13.7b	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) t))

series31.0ms (0.7%)

Counts

1 → 48

Calls

1 calls:

31.0ms

(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) t))

rewrite27.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

185×	`times-frac_binary64`
151×	`*-un-lft-identity_binary64`
151×	`add-sqr-sqrt_binary64`
75×	`add-cube-cbrt_binary64`
38×	`distribute-lft-out--_binary64`

Counts

1 → 139

Calls

1 calls:

10.0ms

(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) t))

simplify119.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

944×	`times-frac_binary64`
546×	`fma-def_binary64`
307×	`associate-/r/_binary64`
216×	`div-sub_binary64`
163×	`fma-neg_binary64`

Counts

187 → 204

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	308	5747
1	902	5339
2	2898	5207
3	5076	5207

prune109.0ms (2.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	202	2	204
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	204	6	210

Error

Counts

210 → 6

Alt Table

Status	Error	Program
	49.0b	(+.f64 x (/.f64 (*.f64 (/.f64 (-.f64 y z) (+.f64 (sqrt.f64 a) (sqrt.f64 z))) t) (-.f64 (sqrt.f64 a) (sqrt.f64 z))))
✓	2.5b	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) t)))
✓	2.5b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	37.6b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	32.0b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (sqrt.f64 t)) (/.f64 (-.f64 a z) (sqrt.f64 t))))
▶	29.5b	(+.f64 x (*.f64 (sqrt.f64 t) (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (sqrt.f64 t)))))

Compiler

Compiled 5335 to 1266 computations (76.3% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 a z) (sqrt.f64 t))
✓	0.4b	(*.f64 (sqrt.f64 t) (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (sqrt.f64 t))))
✓	5.1b	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (sqrt.f64 t)))

series92.0ms (1.9%)

Counts

3 → 104

Calls

3 calls:

40.0ms	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (sqrt.f64 t)))
33.0ms	(*.f64 (sqrt.f64 t) (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (sqrt.f64 t))))
19.0ms	(/.f64 (-.f64 a z) (sqrt.f64 t))

rewrite144.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

710×	`times-frac_binary64`
591×	`add-sqr-sqrt_binary64`
565×	`*-un-lft-identity_binary64`
281×	`add-cube-cbrt_binary64`
192×	`sqrt-prod_binary64`

Counts

3 → 494

Calls

3 calls:

39.0ms	(*.f64 (sqrt.f64 t) (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (sqrt.f64 t))))
12.0ms	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (sqrt.f64 t)))
6.0ms	(/.f64 (-.f64 a z) (sqrt.f64 t))

simplify338.0ms (7.1%)

Algorithm

1×	egg-herbie

Rules

707×	`fma-def_binary64`
518×	`associate-/r/_binary64`
358×	`associate-/l*_binary64`
275×	`associate-/l/_binary64`
271×	`associate-*l/_binary64`

Counts

598 → 566

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	580	16782
1	1715	16115
2	4721	15939
3	5379	15939

prune264.0ms (5.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	566	0	566
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	566	6	572

Error

Counts

572 → 6

Alt Table

Status	Error	Program
	49.0b	(+.f64 x (/.f64 (*.f64 (/.f64 (-.f64 y z) (+.f64 (sqrt.f64 a) (sqrt.f64 z))) t) (-.f64 (sqrt.f64 a) (sqrt.f64 z))))
✓	2.5b	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) t)))
✓	2.5b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	37.6b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	32.0b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (sqrt.f64 t)) (/.f64 (-.f64 a z) (sqrt.f64 t))))
✓	29.5b	(+.f64 x (*.f64 (sqrt.f64 t) (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (sqrt.f64 t)))))

Compiler

Compiled 16971 to 3471 computations (79.5% saved)

regimes272.0ms (5.7%)

Accuracy

Total 1.3b remaining (89.5%)

Threshold costs 0b (0%)

Counts

44 → 1

Compiler

Compiled 4979 to 3082 computations (38.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	16	16
2	22	16
3	24	16
4	25	16
5	25	16

end75.0ms (1.6%)

Compiler: Compiled 145 to 87 computations (40% saved)

Details

analyze1.5s (32.4%)

sample1.2s (26.3%)

simplify111.0ms (2.3%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series33.0ms (0.7%)

rewrite1.0ms (0%)

simplify46.0ms (1%)

prune38.0ms (0.8%)

localize7.0ms (0.2%)

series37.0ms (0.8%)

rewrite14.0ms (0.3%)

simplify86.0ms (1.8%)

prune83.0ms (1.7%)

localize8.0ms (0.2%)

series31.0ms (0.7%)

rewrite27.0ms (0.6%)

simplify119.0ms (2.5%)

prune109.0ms (2.3%)

localize10.0ms (0.2%)

series92.0ms (1.9%)

rewrite144.0ms (3%)

simplify338.0ms (7.1%)

prune264.0ms (5.6%)

regimes272.0ms (5.7%)

simplify2.0ms (0%)

end75.0ms (1.6%)

Profiling