Details

analyze1.3s (11.6%)

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 (10.3%)

Results

1.0s	8253×	body	128	valid
99.0ms	804×	body	128	invalid
1.0ms	3×	body	1024	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify111.0ms (1%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	4.0b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	8.3b	(+.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 2 expressions with local error:

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

series50.0ms (0.4%)

Counts

2 → 84

Calls

2 calls:

34.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
16.0ms	(/.f64 t (-.f64 a z))

rewrite6.0ms (0.1%)

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)

simplify66.0ms (0.6%)

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

prune74.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	106	4	110

Error

0.0b

Counts

110 → 4

Alt Table

Status	Error	Program
✓	4.0b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
▶	1.1b	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
	42.3b	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x) 3))
	8.3b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

Compiler

Compiled 2369 to 741 computations (68.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series127.0ms (1.1%)

Counts

4 → 147

Calls

4 calls:

48.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
47.0ms	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
22.0ms	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
10.0ms	(/.f64 z (-.f64 a z))

rewrite1.1s (9.1%)

Algorithm

1×	rewrite-expression-head

Rules

3320×	`*-un-lft-identity_binary64`
3302×	`add-sqr-sqrt_binary64`
3291×	`times-frac_binary64`
2205×	`prod-diff_binary64`
1964×	`add-cube-cbrt_binary64`

Counts

4 → 2457

Calls

4 calls:

91.0ms	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
55.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
32.0ms	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
4.0ms	(/.f64 z (-.f64 a z))

simplify3.8s (33.1%)

Algorithm

1×	egg-herbie

Rules

933×	`times-frac_binary64`
426×	`*-commutative_binary64`
366×	`distribute-rgt-in_binary64`
308×	`fma-udef_binary64`
262×	`distribute-lft-in_binary64`

Counts

2604 → 2821

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1501	146886
1	2683	107534
2	4549	94985
3	4492	94985
4	5169	94985

prune2.0s (17.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	2819	2	2821
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	2819	6	2825

Error

Counts

2825 → 6

Alt Table

Status	Error	Program
	42.3b	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x) 3))
	30.7b	(+.f64 (-.f64 (+.f64 t (/.f64 (.f64 t a) z)) (+.f64 (.f64 (/.f64 y z) t) (.f64 (/.f64 y z) (/.f64 (.f64 t a) z)))) x)
✓	4.0b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
✓	1.1b	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
	8.3b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
▶	1.1b	(+.f64 (*.f64 t (fma.f64 y (/.f64 1 (-.f64 a z)) (neg.f64 (/.f64 z (-.f64 a z))))) x)

Compiler

Compiled 162171 to 28063 computations (82.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 a z))
✓	0.0b	(+.f64 (*.f64 t (fma.f64 y (/.f64 1 (-.f64 a z)) (neg.f64 (/.f64 z (-.f64 a z))))) x)
✓	0.1b	(fma.f64 y (/.f64 1 (-.f64 a z)) (neg.f64 (/.f64 z (-.f64 a z))))
✓	1.8b	(*.f64 t (fma.f64 y (/.f64 1 (-.f64 a z)) (neg.f64 (/.f64 z (-.f64 a z)))))

series140.0ms (1.2%)

Counts

4 → 168

Calls

4 calls:

56.0ms	(+.f64 (*.f64 t (fma.f64 y (/.f64 1 (-.f64 a z)) (neg.f64 (/.f64 z (-.f64 a z))))) x)
49.0ms	(*.f64 t (fma.f64 y (/.f64 1 (-.f64 a z)) (neg.f64 (/.f64 z (-.f64 a z)))))
27.0ms	(fma.f64 y (/.f64 1 (-.f64 a z)) (neg.f64 (/.f64 z (-.f64 a z))))
8.0ms	(/.f64 1 (-.f64 a z))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
15×	`times-frac_binary64`
10×	`add-exp-log_binary64`

Counts

4 → 91

Calls

4 calls:

4.0ms	(/.f64 1 (-.f64 a z))
3.0ms	(+.f64 (*.f64 t (fma.f64 y (/.f64 1 (-.f64 a z)) (neg.f64 (/.f64 z (-.f64 a z))))) x)
3.0ms	(*.f64 t (fma.f64 y (/.f64 1 (-.f64 a z)) (neg.f64 (/.f64 z (-.f64 a z)))))
0.0ms	(fma.f64 y (/.f64 1 (-.f64 a z)) (neg.f64 (/.f64 z (-.f64 a z))))

simplify158.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

851×	`cancel-sign-sub-inv_binary64`
465×	`sub-neg_binary64`
280×	`fma-neg_binary64`
227×	`+-commutative_binary64`
215×	`associate--l+_binary64`

Counts

259 → 248

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	335	6890
1	874	6471
2	3121	6309
3	4971	6308
4	4995	6308

prune195.0ms (1.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	248	0	248
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	248	6	254

Error

Counts

254 → 6

Alt Table

Status	Error	Program
	42.3b	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x) 3))
	30.7b	(+.f64 (-.f64 (+.f64 t (/.f64 (.f64 t a) z)) (+.f64 (.f64 (/.f64 y z) t) (.f64 (/.f64 y z) (/.f64 (.f64 t a) z)))) x)
✓	4.0b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
✓	1.1b	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
▶	8.3b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
✓	1.1b	(+.f64 (*.f64 t (fma.f64 y (/.f64 1 (-.f64 a z)) (neg.f64 (/.f64 z (-.f64 a z))))) x)

Compiler

Compiled 7130 to 2465 computations (65.4% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
✓	0.0b	(*.f64 (-.f64 y z) t)
✓	8.6b	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

series86.0ms (0.7%)

Counts

3 → 144

Calls

3 calls:

46.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
33.0ms	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))
6.0ms	(*.f64 (-.f64 y z) t)

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 72

Calls

3 calls:

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

simplify144.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

898×	`fma-def_binary64`
587×	`cancel-sign-sub-inv_binary64`
313×	`sub-neg_binary64`
179×	`fma-neg_binary64`
159×	`associate-/l*_binary64`

Counts

216 → 188

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	248	5006
1	725	4379
2	2654	3966
3	4886	3964
4	5000	3964
5	4974	3964

prune148.0ms (1.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	2	0	2
Picked	1	0	1
Done	1	2	3
Total	190	4	194

Error

Counts

194 → 4

Alt Table

Status	Error	Program
✓	4.0b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	4.0b	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) t)))
	8.4b	(+.f64 x (/.f64 1 (/.f64 (-.f64 a z) (*.f64 (-.f64 y z) t))))
✓	1.1b	(+.f64 (*.f64 t (fma.f64 y (/.f64 1 (-.f64 a z)) (neg.f64 (/.f64 z (-.f64 a z))))) x)

Compiler

Compiled 4340 to 1227 computations (71.7% saved)

regimes731.0ms (6.3%)

Accuracy

Total 1.3b remaining (99%)

Threshold costs 0b (0%)

Counts

116 → 1

Compiler

Compiled 15247 to 9232 computations (39.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	15	20
2	24	20
3	28	20
4	30	20
5	30	20

end60.0ms (0.5%)

Compiler: Compiled 109 to 64 computations (41.3% saved)

Details

analyze1.3s (11.6%)

sample1.2s (10.3%)

simplify111.0ms (1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series50.0ms (0.4%)

rewrite6.0ms (0.1%)

simplify66.0ms (0.6%)

prune74.0ms (0.6%)

localize12.0ms (0.1%)

series127.0ms (1.1%)

rewrite1.1s (9.1%)

simplify3.8s (33.1%)

prune2.0s (17.1%)

localize10.0ms (0.1%)

series140.0ms (1.2%)

rewrite15.0ms (0.1%)

simplify158.0ms (1.4%)

prune195.0ms (1.7%)

localize7.0ms (0.1%)

series86.0ms (0.7%)

rewrite22.0ms (0.2%)

simplify144.0ms (1.2%)

prune148.0ms (1.3%)

regimes731.0ms (6.3%)

simplify2.0ms (0%)

end60.0ms (0.5%)

Profiling