Details

analyze949.0ms (13.6%)

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
13.3%	86.5%	0.2%	9
19.9%	79.9%	0.2%	10
24%	75.2%	0.8%	11
25.4%	72.7%	1.9%	12
35.8%	59.6%	4.6%	13
42%	52.3%	5.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.9s (26.8%)

Results

1.4s	8256×	body	128	valid
313.0ms	2196×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify66.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

799×	`fma-def_binary64`
661×	`fma-neg_binary64`
203×	`cancel-sign-sub-inv_binary64`
145×	`distribute-rgt-in_binary64`
99×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	30	11
3	61	11
4	129	11
5	232	11
6	397	11
7	667	11
8	1062	11
9	1355	11
10	1480	11
11	1529	11
12	1535	11
13	1540	11
14	1540	11
15	1455	11

prune5.0ms (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
	6.4b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
▶	6.1b	(fma.f64 y (/.f64 (-.f64 z x) t) x)

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z x) t)
✓	5.8b	(fma.f64 y (/.f64 (-.f64 z x) t) x)

series30.0ms (0.4%)

Counts

2 → 76

Calls

2 calls:

21.0ms	(fma.f64 y (/.f64 (-.f64 z x) t) x)
9.0ms	(/.f64 (-.f64 z x) t)

rewrite113.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

756×	`prod-diff_binary64`
211×	`fma-def_binary64`
197×	`egg-rr`
174×	`expm1-udef_binary64`
174×	`log1p-udef_binary64`

Counts

2 → 197

Calls

2 calls:

106.0ms	(/.f64 (-.f64 z x) t)
106.0ms	(fma.f64 y (/.f64 (-.f64 z x) t) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	178	18
2	2501	18
3	4858	18
4	5184	18
0	0	0
1	0	0

simplify94.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

884×	`fma-def_binary64`
693×	`fma-neg_binary64`
194×	`cancel-sign-sub-inv_binary64`
147×	`distribute-rgt-in_binary64`
130×	`unsub-neg_binary64`

Counts

273 → 213

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	1027
1	83	811
2	181	780
3	320	664
4	652	664
5	1146	664
6	1449	664
7	1541	664
8	1548	664
9	1553	664
10	1553	664
11	1468	664

prune251.0ms (3.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	206	7	213
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	208	7	215

Error

0.0b

Counts

215 → 7

Alt Table

Status	Error	Program
	6.4b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y x) t))
	17.5b	(fma.f64 y (fma.f64 (/.f64 1 (cbrt.f64 (*.f64 t t))) (/.f64 z (cbrt.f64 t)) (neg.f64 (/.f64 x t))) x)
	6.4b	(fma.f64 y (fma.f64 (*.f64 (cbrt.f64 (/.f64 z t)) (cbrt.f64 (/.f64 z t))) (cbrt.f64 (/.f64 z t)) (neg.f64 (/.f64 x t))) x)
	38.0b	(pow.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z x) t) x)) 2)
	6.1b	(fma.f64 y (pow.f64 (/.f64 t (-.f64 z x)) -1) x)
	7.2b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z x) t) x)) (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z x) t) x)) 2))
▶	1.7b	(fma.f64 (/.f64 y t) (-.f64 z x) x)

Compiler

Compiled 7231 to 1685 computations (76.7% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.6b	(fma.f64 (/.f64 y t) (-.f64 z x) x)

series18.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

18.0ms

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

rewrite48.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

455×	`log-prod_binary64`
446×	`prod-diff_binary64`
199×	`fma-def_binary64`
170×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`

Counts

1 → 30

Calls

1 calls:

47.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	175	11
2	2373	11
3	5034	11
0	0	0
1	0	0

simplify88.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

752×	`fma-def_binary64`
736×	`fma-neg_binary64`
246×	`cancel-sign-sub-inv_binary64`
155×	`distribute-rgt-in_binary64`
107×	`distribute-lft-in_binary64`

Counts

78 → 41

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	777
1	71	561
2	157	552
3	276	480
4	537	480
5	954	480
6	1341	480
7	1459	480
8	1491	480
9	1535	480
10	1545	480
11	1545	480
12	1460	480

prune26.0ms (0.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	40	1	41
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	41	7	48

Error

0.0b

Counts

48 → 7

Alt Table

Status	Error	Program
▶	2.8b	(*.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (pow.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) 2))
	6.4b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y x) t))
	17.5b	(fma.f64 y (fma.f64 (/.f64 1 (cbrt.f64 (*.f64 t t))) (/.f64 z (cbrt.f64 t)) (neg.f64 (/.f64 x t))) x)
	6.4b	(fma.f64 y (fma.f64 (*.f64 (cbrt.f64 (/.f64 z t)) (cbrt.f64 (/.f64 z t))) (cbrt.f64 (/.f64 z t)) (neg.f64 (/.f64 x t))) x)
	38.0b	(pow.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z x) t) x)) 2)
	6.1b	(fma.f64 y (pow.f64 (/.f64 t (-.f64 z x)) -1) x)
✓	1.7b	(fma.f64 (/.f64 y t) (-.f64 z x) x)

Compiler

Compiled 775 to 263 computations (66.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (pow.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) 2)
✓	0.5b	(cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x))
	1.6b	(fma.f64 (/.f64 y t) (-.f64 z x) x)

series303.0ms (4.3%)

Counts

3 → 144

Calls

3 calls:

144.0ms

(pow.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) 2)

137.0ms

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

21.0ms

(*.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (pow.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) 2))

rewrite117.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

503×	`prod-diff_binary64`
383×	`fma-udef_binary64`
217×	`fma-def_binary64`
208×	`expm1-udef_binary64`
208×	`log1p-udef_binary64`

Counts

3 → 81

Calls

3 calls:

114.0ms

(*.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (pow.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) 2))

114.0ms

(pow.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) 2)

114.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	40
1	238	40
2	2881	40
3	4794	40
4	4941	40
5	4912	40
0	0	0
1	0	0

simplify164.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

625×	`fma-def_binary64`
622×	`associate-/l*_binary64`
281×	`*-commutative_binary64`
177×	`cancel-sign-sub-inv_binary64`
161×	`sqr-pow_binary64`

Counts

225 → 253

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	719	11387
1	2642	11054
2	5318	11054

prune398.0ms (5.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	434	3	437
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	437	7	444

Error

Counts

444 → 7

Alt Table

Status	Error	Program
	6.4b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y x) t))
	32.8b	(/.f64 y (/.f64 t (-.f64 z x)))
✓	2.8b	(*.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (pow.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) 2))
	17.5b	(fma.f64 y (fma.f64 (/.f64 1 (cbrt.f64 (*.f64 t t))) (/.f64 z (cbrt.f64 t)) (neg.f64 (/.f64 x t))) x)
▶	3.3b	(.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x))) 2)) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)))))
✓	1.7b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	16.1b	(.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (pow.f64 (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) 4))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x))) 2))) 2))

Compiler

Compiled 25154 to 11024 computations (56.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x))) 2)
	0.5b	(cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x))
✓	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)))
	1.6b	(fma.f64 (/.f64 y t) (-.f64 z x) x)

series234.0ms (3.3%)

Counts

2 → 96

Calls

2 calls:

143.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x))) 2)
90.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)))

rewrite110.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

446×	`prod-diff_binary64`
329×	`fma-udef_binary64`
249×	`fma-def_binary64`
220×	`expm1-udef_binary64`
220×	`log1p-udef_binary64`

Counts

2 → 44

Calls

2 calls:

109.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x))) 2)
109.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	33
1	251	33
2	3024	33
3	4799	33
4	4882	33
5	4944	33
0	0	0
1	0	0

simplify194.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

666×	`associate-/l*_binary64`
597×	`fma-def_binary64`
288×	`*-commutative_binary64`
186×	`sqr-pow_binary64`
169×	`cancel-sign-sub-inv_binary64`

Counts

140 → 200

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	747	13262
1	2624	12732
2	5403	12732

prune1.3s (18.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	875	0	875
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	875	7	882

Error

Counts

882 → 7

Alt Table

Status	Error	Program
	6.4b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y x) t))
	32.8b	(/.f64 y (/.f64 t (-.f64 z x)))
✓	2.8b	(*.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (pow.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) 2))
	17.5b	(fma.f64 y (fma.f64 (/.f64 1 (cbrt.f64 (*.f64 t t))) (/.f64 z (cbrt.f64 t)) (neg.f64 (/.f64 x t))) x)
✓	3.3b	(.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x))) 2)) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)))))
✓	1.7b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	16.1b	(.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (pow.f64 (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) 4))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x))) 2))) 2))

Compiler

Compiled 76526 to 28076 computations (63.3% saved)

regimes488.0ms (7%)

Accuracy

Total 2.0b remaining (99.1%)

Threshold costs 0b (0%)

Counts

80 → 1

Compiler

Compiled 8366 to 4623 computations (44.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11
2	15	11
3	17	11
4	18	11
5	18	11

end105.0ms (1.5%)

Compiler: Compiled 201 to 97 computations (51.7% saved)

Details

analyze949.0ms (13.6%)

sample1.9s (26.8%)

simplify66.0ms (0.9%)

prune5.0ms (0.1%)

localize6.0ms (0.1%)

series30.0ms (0.4%)

rewrite113.0ms (1.6%)

simplify94.0ms (1.4%)

prune251.0ms (3.6%)

localize7.0ms (0.1%)

series18.0ms (0.3%)

rewrite48.0ms (0.7%)

simplify88.0ms (1.3%)

prune26.0ms (0.4%)

localize12.0ms (0.2%)

series303.0ms (4.3%)

rewrite117.0ms (1.7%)

simplify164.0ms (2.4%)

prune398.0ms (5.7%)

localize12.0ms (0.2%)

series234.0ms (3.3%)

rewrite110.0ms (1.6%)

simplify194.0ms (2.8%)

prune1.3s (18.1%)

regimes488.0ms (7%)

simplify2.0ms (0%)

end105.0ms (1.5%)

Profiling