Details

analyze590.0ms (2.7%)

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
49.9%	49.9%	0.2%	8
49.9%	49.9%	0.2%	9
49.9%	49.9%	0.2%	10
49.9%	49.9%	0.2%	11
74.9%	25%	0.2%	12
74.9%	25%	0.2%	13
74.9%	25%	0.2%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.8s (8.1%)

Results

1.5s

8256×

body

128

valid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify521.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

2150×	`fma-neg_binary64`
1161×	`div-sub_binary64`
897×	`fma-def_binary64`
414×	`associate-/l*_binary64`
410×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	33	16
3	65	16
4	113	16
5	197	16
6	397	16
7	814	16
8	1449	16
9	1832	16
10	1941	16
11	2036	16
12	2110	16
13	2224	16
14	2174	16
15	2652	16
16	2330	16
17	2358	16
18	2376	16
19	2392	16
20	2384	16
21	2468	16
22	2468	16
23	2388	16
24	2450	16
25	2428	16
26	2426	16
27	2428	16
28	2430	16
29	2440	16
30	2440	16
31	2255	16

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

3.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	3.9b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

Compiler

Compiled 45 to 30 computations (33.3% saved)

localize14.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
✓	3.9b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

series98.0ms (0.5%)

Counts

2 → 66

Calls

2 calls:

65.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
33.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

rewrite705.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

1429×	`times-frac_binary64`
1339×	`add-sqr-sqrt_binary64`
1335×	`*-un-lft-identity_binary64`
936×	`prod-diff_binary64`
935×	`add-cube-cbrt_binary64`

Counts

2 → 1074

Calls

2 calls:

107.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
55.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

simplify2.5s (11.5%)

Algorithm

1×	egg-herbie

Rules

687×	`times-frac_binary64`
569×	`associate-l_binary64`
557×	`associate-r_binary64`
314×	`*-commutative_binary64`
243×	`distribute-rgt-in_binary64`

Counts

1140 → 1067

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	990	85623
1	1699	43502
2	3794	41798
3	4686	41798
4	5040	41798

prune2.8s (13%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	1061	6	1067
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1062	6	1068

Error

0.0b

Counts

1068 → 6

Alt Table

Status	Error	Program
	5.4b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
▶	3.9b	(*.f64 x (fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z)))))
	15.2b	(/.f64 x (/.f64 z (+.f64 y t)))
	4.3b	(.f64 x (fma.f64 (/.f64 1 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)) (neg.f64 (/.f64 t (-.f64 1 z)))))
	4.6b	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) (cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))) (cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
	5.3b	(+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z))) (cbrt.f64 (/.f64 y z)) (neg.f64 (.f64 (/.f64 1 (-.f64 1 z)) t))) x) (.f64 (fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (*.f64 (/.f64 1 (-.f64 1 z)) t)) x))

Compiler

Compiled 57553 to 31217 computations (45.8% saved)

localize16.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z))))
✓	3.9b	(*.f64 x (fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z)))))

series92.0ms (0.4%)

Counts

2 → 84

Calls

2 calls:

67.0ms	(*.f64 x (fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z)))))
25.0ms	(fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z))))

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

5.0ms	(*.f64 x (fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z)))))
1.0ms	(fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z))))

simplify177.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

797×	`fma-neg_binary64`
432×	`cancel-sign-sub-inv_binary64`
422×	`fma-def_binary64`
234×	`associate-/l/_binary64`
218×	`associate-l_binary64`

Counts

116 → 90

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	112	2138
1	274	1926
2	826	1862
3	2632	1827
4	4572	1827
5	4974	1827

prune141.0ms (0.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	91	5	96

Error

0.0b

Counts

96 → 5

Alt Table

Status	Error	Program
	5.4b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
✓	3.9b	(*.f64 x (fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z)))))
	15.2b	(/.f64 x (/.f64 z (+.f64 y t)))
	18.3b	(*.f64 (/.f64 x z) (+.f64 y t))
▶	5.3b	(+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z))) (cbrt.f64 (/.f64 y z)) (neg.f64 (.f64 (/.f64 1 (-.f64 1 z)) t))) x) (.f64 (fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (*.f64 (/.f64 1 (-.f64 1 z)) t)) x))

Compiler

Compiled 1797 to 961 computations (46.5% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z)))
✓	3.9b	(.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z))) (cbrt.f64 (/.f64 y z)) (neg.f64 (*.f64 (/.f64 1 (-.f64 1 z)) t))) x)
✓	16.2b	(cbrt.f64 (/.f64 y z))
✓	24.0b	(fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (*.f64 (/.f64 1 (-.f64 1 z)) t))

series5.1s (23.2%)

Counts

4 → 120

Calls

4 calls:

3.1s	(.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z))) (cbrt.f64 (/.f64 y z)) (neg.f64 (*.f64 (/.f64 1 (-.f64 1 z)) t))) x)
1.2s	(*.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z)))
746.0ms	(cbrt.f64 (/.f64 y z))
45.0ms	(fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (*.f64 (/.f64 1 (-.f64 1 z)) t))

rewrite59.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`cbrt-prod_binary64`
71×	`add-sqr-sqrt_binary64`
51×	`times-frac_binary64`
45×	`*-un-lft-identity_binary64`
45×	`add-cube-cbrt_binary64`

Counts

4 → 134

Calls

4 calls:

30.0ms	(*.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z)))
5.0ms	(.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z))) (cbrt.f64 (/.f64 y z)) (neg.f64 (*.f64 (/.f64 1 (-.f64 1 z)) t))) x)
3.0ms	(cbrt.f64 (/.f64 y z))
1.0ms	(fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (*.f64 (/.f64 1 (-.f64 1 z)) t))

simplify329.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

677×	`fma-neg_binary64`
587×	`fma-def_binary64`
330×	`*-commutative_binary64`
216×	`exp-prod_binary64`
179×	`distribute-rgt-in_binary64`

Counts

254 → 246

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	295	5460
1	625	4906
2	1597	4252
3	4235	4050
4	4951	4050

prune893.0ms (4.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	322	0	322
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	322	5	327

Error

0.0b

Counts

327 → 5

Alt Table

Status	Error	Program
▶	5.4b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
✓	3.9b	(*.f64 x (fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z)))))
	15.2b	(/.f64 x (/.f64 z (+.f64 y t)))
	18.3b	(*.f64 (/.f64 x z) (+.f64 y t))
✓	5.3b	(+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z))) (cbrt.f64 (/.f64 y z)) (neg.f64 (.f64 (/.f64 1 (-.f64 1 z)) t))) x) (.f64 (fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (*.f64 (/.f64 1 (-.f64 1 z)) t)) x))

Compiler

Compiled 15840 to 8322 computations (47.5% saved)

localize18.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.2b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
✓	2.4b	(/.f64 (*.f64 t x) (-.f64 1 z))
✓	3.1b	(/.f64 (*.f64 y x) z)

series159.0ms (0.7%)

Counts

3 → 42

Calls

3 calls:

79.0ms	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
42.0ms	(/.f64 (*.f64 y x) z)
37.0ms	(/.f64 (*.f64 t x) (-.f64 1 z))

rewrite95.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`times-frac_binary64`
84×	`prod-diff_binary64`
81×	`*-un-lft-identity_binary64`
81×	`add-sqr-sqrt_binary64`
49×	`add-cube-cbrt_binary64`

Counts

3 → 173

Calls

3 calls:

24.0ms	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
10.0ms	(/.f64 (*.f64 t x) (-.f64 1 z))
7.0ms	(/.f64 (*.f64 y x) z)

simplify313.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

543×	`fma-neg_binary64`
265×	`cancel-sign-sub-inv_binary64`
213×	`distribute-rgt-neg-in_binary64`
205×	`div-sub_binary64`
190×	`distribute-rgt-out_binary64`

Counts

215 → 256

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	316	7070
1	799	5494
2	2811	4354
3	4318	4354
4	4944	4354

prune535.0ms (2.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	255	1	256
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	255	6	261

Error

Counts

261 → 6

Alt Table

Status	Error	Program
✓	5.4b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
✓	3.9b	(*.f64 x (fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z)))))
✓	5.3b	(+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z))) (cbrt.f64 (/.f64 y z)) (neg.f64 (.f64 (/.f64 1 (-.f64 1 z)) t))) x) (.f64 (fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (*.f64 (/.f64 1 (-.f64 1 z)) t)) x))
	5.5b	(-.f64 (/.f64 1 (/.f64 z (.f64 y x))) (/.f64 (.f64 t x) (-.f64 1 z)))
	15.2b	(/.f64 x (/.f64 z (+.f64 y t)))
	18.3b	(*.f64 (/.f64 x z) (+.f64 y t))

Compiler

Compiled 8267 to 4019 computations (51.4% saved)

regimes4.6s (21.1%)

Accuracy

Total 1.1b remaining (97.9%)

Threshold costs 0b (0%)

Counts

192 → 3

Compiler

Compiled 35786 to 23900 computations (33.2% saved)

bsearch18.0ms (0.1%)

Compiler: Compiled 13 to 9 computations (30.8% saved)

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	96
1	46	96
2	60	96
3	68	96
4	73	96
5	74	96
6	73	96

end249.0ms (1.1%)

Compiler: Compiled 259 to 162 computations (37.5% saved)

Details

analyze590.0ms (2.7%)

sample1.8s (8.1%)

simplify521.0ms (2.4%)

prune3.0ms (0%)

localize14.0ms (0.1%)

series98.0ms (0.5%)

rewrite705.0ms (3.2%)

simplify2.5s (11.5%)

prune2.8s (13%)

localize16.0ms (0.1%)

series92.0ms (0.4%)

rewrite8.0ms (0%)

simplify177.0ms (0.8%)

prune141.0ms (0.6%)

localize30.0ms (0.1%)

series5.1s (23.2%)

rewrite59.0ms (0.3%)

simplify329.0ms (1.5%)

prune893.0ms (4.1%)

localize18.0ms (0.1%)

series159.0ms (0.7%)

rewrite95.0ms (0.4%)

simplify313.0ms (1.4%)

prune535.0ms (2.4%)

regimes4.6s (21.1%)

bsearch18.0ms (0.1%)

simplify10.0ms (0%)

end249.0ms (1.1%)

Profiling