Details

analyze332.0ms (3%)

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)

sample944.0ms (8.5%)

Infinites

20.5% of outputs are infinite.

Results

764.0ms

8256×

body

128

valid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify295.0ms (2.7%)

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

prune2.0ms (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)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series65.0ms (0.6%)

Counts

3 → 78

Calls

3 calls:

43.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
14.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
8.0ms	(/.f64 t (-.f64 1 z))

rewrite361.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

1447×	`times-frac_binary64`
1363×	`add-sqr-sqrt_binary64`
1359×	`*-un-lft-identity_binary64`
947×	`add-cube-cbrt_binary64`
936×	`prod-diff_binary64`

Counts

3 → 1117

Calls

3 calls:

37.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
25.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
4.0ms	(/.f64 t (-.f64 1 z))

simplify1.2s (10.4%)

Algorithm

1×	egg-herbie

Rules

854×	`times-frac_binary64`
575×	`associate-l_binary64`
560×	`associate-r_binary64`
316×	`*-commutative_binary64`
254×	`distribute-rgt-in_binary64`

Counts

1195 → 1129

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1019	86414
1	1779	44281
2	4035	42577
3	5036	42577

prune1.4s (12.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	1124	5	1129
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1125	5	1130

Error

0.0b

Counts

1130 → 5

Alt Table

Status	Error	Program
	42.1b	(/.f64 (.f64 x (-.f64 (pow.f64 (/.f64 y z) 3) (pow.f64 (/.f64 t (-.f64 1 z)) 3))) (+.f64 (.f64 (/.f64 y z) (/.f64 y z)) (+.f64 (.f64 (/.f64 t (-.f64 1 z)) (/.f64 t (-.f64 1 z))) (.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))))
	4.4b	(.f64 x (fma.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 y) (cbrt.f64 z)) (neg.f64 (/.f64 t (-.f64 1 z)))))
	17.1b	(/.f64 x (/.f64 z (+.f64 y t)))
▶	3.9b	(.f64 x (-.f64 (/.f64 y z) (.f64 t (/.f64 1 (-.f64 1 z)))))
	5.8b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))

Compiler

Compiled 58636 to 31722 computations (45.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 y z) (*.f64 t (/.f64 1 (-.f64 1 z))))
✓	0.0b	(/.f64 1 (-.f64 1 z))
✓	0.1b	(*.f64 t (/.f64 1 (-.f64 1 z)))
✓	3.9b	(.f64 x (-.f64 (/.f64 y z) (.f64 t (/.f64 1 (-.f64 1 z)))))

series55.0ms (0.5%)

Counts

4 → 120

Calls

4 calls:

30.0ms	(.f64 x (-.f64 (/.f64 y z) (.f64 t (/.f64 1 (-.f64 1 z)))))
13.0ms	(-.f64 (/.f64 y z) (*.f64 t (/.f64 1 (-.f64 1 z))))
8.0ms	(*.f64 t (/.f64 1 (-.f64 1 z)))
3.0ms	(/.f64 1 (-.f64 1 z))

rewrite39.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`add-sqr-sqrt_binary64`
78×	`*-un-lft-identity_binary64`
74×	`times-frac_binary64`
56×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`

Counts

4 → 192

Calls

4 calls:

8.0ms	(*.f64 t (/.f64 1 (-.f64 1 z)))
8.0ms	(.f64 x (-.f64 (/.f64 y z) (.f64 t (/.f64 1 (-.f64 1 z)))))
6.0ms	(-.f64 (/.f64 y z) (*.f64 t (/.f64 1 (-.f64 1 z))))
4.0ms	(/.f64 1 (-.f64 1 z))

simplify146.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

427×	`fma-neg_binary64`
277×	`distribute-rgt-in_binary64`
268×	`associate-/l*_binary64`
238×	`associate-*l/_binary64`
230×	`times-frac_binary64`

Counts

312 → 327

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	304	5450
1	679	4973
2	2116	4359
3	4364	4341
4	5016	4341

prune255.0ms (2.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	326	1	327
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	327	5	332

Error

0.0b

Counts

332 → 5

Alt Table

Status	Error	Program
	17.1b	(/.f64 x (/.f64 z (+.f64 y t)))
	18.2b	(*.f64 (/.f64 x z) (+.f64 y t))
	42.1b	(/.f64 (.f64 x (-.f64 (pow.f64 (/.f64 y z) 3) (pow.f64 (/.f64 t (-.f64 1 z)) 3))) (+.f64 (.f64 (/.f64 y z) (/.f64 y z)) (+.f64 (.f64 (/.f64 t (-.f64 1 z)) (/.f64 t (-.f64 1 z))) (.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))))
✓	3.9b	(.f64 x (-.f64 (/.f64 y z) (.f64 t (/.f64 1 (-.f64 1 z)))))
▶	5.8b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))

Compiler

Compiled 7271 to 4019 computations (44.7% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.4b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
✓	2.0b	(/.f64 (*.f64 t x) (-.f64 1 z))
✓	3.6b	(/.f64 (*.f64 y x) z)

series57.0ms (0.5%)

Counts

3 → 42

Calls

3 calls:

29.0ms	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
16.0ms	(/.f64 (*.f64 t x) (-.f64 1 z))
12.0ms	(/.f64 (*.f64 y x) z)

rewrite37.0ms (0.3%)

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:

12.0ms	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
5.0ms	(/.f64 (*.f64 t x) (-.f64 1 z))
3.0ms	(/.f64 (*.f64 y x) z)

simplify160.0ms (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

prune229.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	252	4	256
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	255	6	261

Error

0.0b

Counts

261 → 6

Alt Table

Status	Error	Program
	7.5b	(-.f64 (.f64 y (/.f64 x z)) (/.f64 (.f64 t x) (-.f64 1 z)))
	17.1b	(/.f64 x (/.f64 z (+.f64 y t)))
	7.1b	(-.f64 (/.f64 y (/.f64 z x)) (/.f64 (*.f64 t x) (-.f64 1 z)))
	6.3b	(-.f64 (/.f64 (*.f64 y x) z) (/.f64 t (/.f64 (-.f64 1 z) x)))
▶	5.8b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 1 (/.f64 (-.f64 1 z) (.f64 t x))))
✓	3.9b	(.f64 x (-.f64 (/.f64 y z) (.f64 t (/.f64 1 (-.f64 1 z)))))

Compiler

Compiled 8325 to 4059 computations (51.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 1 (/.f64 (-.f64 1 z) (*.f64 t x)))
✓	1.4b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 1 (/.f64 (-.f64 1 z) (.f64 t x))))
✓	2.2b	(/.f64 (-.f64 1 z) (*.f64 t x))
	3.6b	(/.f64 (*.f64 y x) z)

series58.0ms (0.5%)

Counts

3 → 96

Calls

3 calls:

27.0ms	(-.f64 (/.f64 (.f64 y x) z) (/.f64 1 (/.f64 (-.f64 1 z) (.f64 t x))))
16.0ms	(/.f64 1 (/.f64 (-.f64 1 z) (*.f64 t x)))
15.0ms	(/.f64 (-.f64 1 z) (*.f64 t x))

rewrite102.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

554×	`times-frac_binary64`
329×	`add-sqr-sqrt_binary64`
326×	`*-un-lft-identity_binary64`
245×	`prod-diff_binary64`
232×	`add-cube-cbrt_binary64`

Counts

3 → 408

Calls

3 calls:

24.0ms	(-.f64 (/.f64 (.f64 y x) z) (/.f64 1 (/.f64 (-.f64 1 z) (.f64 t x))))
6.0ms	(/.f64 1 (/.f64 (-.f64 1 z) (*.f64 t x)))
6.0ms	(/.f64 (-.f64 1 z) (*.f64 t x))

simplify435.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

446×	`fma-neg_binary64`
435×	`cancel-sign-sub-inv_binary64`
250×	`neg-mul-1_binary64`
242×	`div-sub_binary64`
228×	`exp-prod_binary64`

Counts

504 → 481

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	343	21651
1	801	14583
2	2764	11585
3	4076	11585
4	4951	11585
5	4849	11585

prune603.0ms (5.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	516	0	516
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	516	6	522

Error

0.0b

Counts

522 → 6

Alt Table

Status	Error	Program
	7.5b	(-.f64 (.f64 y (/.f64 x z)) (/.f64 (.f64 t x) (-.f64 1 z)))
	17.1b	(/.f64 x (/.f64 z (+.f64 y t)))
	7.1b	(-.f64 (/.f64 y (/.f64 z x)) (/.f64 (*.f64 t x) (-.f64 1 z)))
	6.3b	(-.f64 (/.f64 (*.f64 y x) z) (/.f64 t (/.f64 (-.f64 1 z) x)))
✓	5.8b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 1 (/.f64 (-.f64 1 z) (.f64 t x))))
✓	3.9b	(.f64 x (-.f64 (/.f64 y z) (.f64 t (/.f64 1 (-.f64 1 z)))))

Compiler

Compiled 23047 to 13672 computations (40.7% saved)

regimes4.2s (38%)

Accuracy

Total 1.3b remaining (99%)

Threshold costs 0b (0%)

Counts

340 → 3

Compiler

Compiled 60889 to 40768 computations (33% saved)

bsearch15.0ms (0.1%)

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

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
9×	`*-commutative_binary64`
9×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	79
1	44	79
2	61	79
3	73	79
4	81	79
5	84	79
6	85	79
7	82	79

end92.0ms (0.8%)

Compiler: Compiled 214 to 129 computations (39.7% saved)

Details

analyze332.0ms (3%)

sample944.0ms (8.5%)

simplify295.0ms (2.7%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series65.0ms (0.6%)

rewrite361.0ms (3.3%)

simplify1.2s (10.4%)

prune1.4s (12.5%)

localize9.0ms (0.1%)

series55.0ms (0.5%)

rewrite39.0ms (0.4%)

simplify146.0ms (1.3%)

prune255.0ms (2.3%)

localize8.0ms (0.1%)

series57.0ms (0.5%)

rewrite37.0ms (0.3%)

simplify160.0ms (1.4%)

prune229.0ms (2.1%)

localize9.0ms (0.1%)

series58.0ms (0.5%)

rewrite102.0ms (0.9%)

simplify435.0ms (3.9%)

prune603.0ms (5.5%)

regimes4.2s (38%)

bsearch15.0ms (0.1%)

simplify5.0ms (0%)

end92.0ms (0.8%)

Profiling