Details

analyze843.0ms (8.6%)

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
7.8%	92%	0.2%	8
16.4%	83.4%	0.2%	9
23.8%	76%	0.2%	10
25.1%	74.7%	0.2%	11
38.1%	59.4%	2.5%	12
41.8%	55.3%	2.9%	13
46.5%	50.3%	3.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample173.0ms (1.8%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
3.0ms	60×	body	128	invalid

Compiler

Compiled 35 to 25 computations (28.6% saved)

simplify291.0ms (3%)

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

3.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	3.7b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

Compiler

Compiled 45 to 30 computations (33.3% saved)

localize8.0ms (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)))
✓	3.5b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

series64.0ms (0.7%)

Counts

3 → 78

Calls

3 calls:

36.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
17.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
10.0ms	(/.f64 t (-.f64 1 z))

rewrite319.0ms (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:

36.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
23.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
4.0ms	(/.f64 t (-.f64 1 z))

simplify1.4s (14%)

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

prune1.3s (13.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	1122	7	1129
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1123	7	1130

Error

0.0b

Counts

1130 → 7

Alt Table

Status	Error	Program
	3.9b	(*.f64 x (+.f64 (/.f64 y z) (neg.f64 (/.f64 t (pow.f64 (cbrt.f64 (-.f64 1 z)) 3)))))
	4.2b	(.f64 x (fma.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 1) (/.f64 (cbrt.f64 y) z) (neg.f64 (/.f64 t (-.f64 1 z)))))
	9.7b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
▶	3.7b	(.f64 x (-.f64 (/.f64 y z) (.f64 t (/.f64 1 (-.f64 1 z)))))
	17.2b	(/.f64 x (/.f64 z (+.f64 y t)))
	25.3b	(/.f64 (.f64 x (-.f64 (.f64 (/.f64 y z) (/.f64 y z)) (*.f64 (/.f64 t (-.f64 1 z)) (/.f64 t (-.f64 1 z))))) (+.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
	26.5b	(/.f64 (.f64 x (-.f64 (.f64 y (-.f64 1 z)) (.f64 z t))) (.f64 z (-.f64 1 z)))

Compiler

Compiled 58678 to 31758 computations (45.9% saved)

localize127.0ms (1.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 1 z))
✓	0.0b	(-.f64 (/.f64 y z) (*.f64 t (/.f64 1 (-.f64 1 z))))
✓	0.1b	(*.f64 t (/.f64 1 (-.f64 1 z)))
✓	3.5b	(.f64 x (-.f64 (/.f64 y z) (.f64 t (/.f64 1 (-.f64 1 z)))))

series54.0ms (0.6%)

Counts

4 → 120

Calls

4 calls:

29.0ms	(.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))))
9.0ms	(*.f64 t (/.f64 1 (-.f64 1 z)))
2.0ms	(/.f64 1 (-.f64 1 z))

rewrite43.0ms (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:

10.0ms	(.f64 x (-.f64 (/.f64 y z) (.f64 t (/.f64 1 (-.f64 1 z)))))
8.0ms	(*.f64 t (/.f64 1 (-.f64 1 z)))
6.0ms	(/.f64 1 (-.f64 1 z))
5.0ms	(-.f64 (/.f64 y z) (*.f64 t (/.f64 1 (-.f64 1 z))))

simplify164.0ms (1.7%)

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

prune250.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	326	1	327
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	327	7	334

Error

0.0b

Counts

334 → 7

Alt Table

Status	Error	Program
	19.1b	(*.f64 (/.f64 x z) (+.f64 y t))
✓	3.7b	(.f64 x (-.f64 (/.f64 y z) (.f64 t (/.f64 1 (-.f64 1 z)))))
▶	3.9b	(*.f64 x (+.f64 (/.f64 y z) (neg.f64 (/.f64 t (pow.f64 (cbrt.f64 (-.f64 1 z)) 3)))))
	9.7b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
	17.2b	(/.f64 x (/.f64 z (+.f64 y t)))
	25.3b	(/.f64 (.f64 x (-.f64 (.f64 (/.f64 y z) (/.f64 y z)) (*.f64 (/.f64 t (-.f64 1 z)) (/.f64 t (-.f64 1 z))))) (+.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
	26.5b	(/.f64 (.f64 x (-.f64 (.f64 y (-.f64 1 z)) (.f64 z t))) (.f64 z (-.f64 1 z)))

Compiler

Compiled 7323 to 4057 computations (44.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 y z) (neg.f64 (/.f64 t (pow.f64 (cbrt.f64 (-.f64 1 z)) 3))))
✓	0.4b	(cbrt.f64 (-.f64 1 z))
✓	0.5b	(pow.f64 (cbrt.f64 (-.f64 1 z)) 3)
✓	3.5b	(*.f64 x (+.f64 (/.f64 y z) (neg.f64 (/.f64 t (pow.f64 (cbrt.f64 (-.f64 1 z)) 3)))))

series156.0ms (1.6%)

Counts

4 → 108

Calls

4 calls:

76.0ms	(pow.f64 (cbrt.f64 (-.f64 1 z)) 3)
40.0ms	(*.f64 x (+.f64 (/.f64 y z) (neg.f64 (/.f64 t (pow.f64 (cbrt.f64 (-.f64 1 z)) 3)))))
35.0ms	(+.f64 (/.f64 y z) (neg.f64 (/.f64 t (pow.f64 (cbrt.f64 (-.f64 1 z)) 3))))
4.0ms	(cbrt.f64 (-.f64 1 z))

rewrite157.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`
18×	`cbrt-prod_binary64`
13×	`fma-def_binary64`

Counts

4 → 119

Calls

4 calls:

77.0ms	(*.f64 x (+.f64 (/.f64 y z) (neg.f64 (/.f64 t (pow.f64 (cbrt.f64 (-.f64 1 z)) 3)))))
68.0ms	(+.f64 (/.f64 y z) (neg.f64 (/.f64 t (pow.f64 (cbrt.f64 (-.f64 1 z)) 3))))
4.0ms	(pow.f64 (cbrt.f64 (-.f64 1 z)) 3)
2.0ms	(cbrt.f64 (-.f64 1 z))

simplify158.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

479×	`distribute-rgt-in_binary64`
465×	`fma-neg_binary64`
249×	`cancel-sign-sub-inv_binary64`
214×	`unswap-sqr_binary64`
147×	`associate-r_binary64`

Counts

227 → 215

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	257	3395
1	701	3175
2	2396	3069
3	4636	3069
4	4982	3069

prune191.0ms (1.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	215	7	222

Error

0.0b

Counts

222 → 7

Alt Table

Status	Error	Program
	19.1b	(*.f64 (/.f64 x z) (+.f64 y t))
✓	3.7b	(.f64 x (-.f64 (/.f64 y z) (.f64 t (/.f64 1 (-.f64 1 z)))))
✓	3.9b	(*.f64 x (+.f64 (/.f64 y z) (neg.f64 (/.f64 t (pow.f64 (cbrt.f64 (-.f64 1 z)) 3)))))
▶	9.7b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
	17.2b	(/.f64 x (/.f64 z (+.f64 y t)))
	25.3b	(/.f64 (.f64 x (-.f64 (.f64 (/.f64 y z) (/.f64 y z)) (*.f64 (/.f64 t (-.f64 1 z)) (/.f64 t (-.f64 1 z))))) (+.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
	26.5b	(/.f64 (.f64 x (-.f64 (.f64 y (-.f64 1 z)) (.f64 z t))) (.f64 z (-.f64 1 z)))

Compiler

Compiled 4916 to 2948 computations (40% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
✓	3.4b	(/.f64 (*.f64 t x) (-.f64 1 z))
✓	8.0b	(/.f64 (*.f64 y x) z)

series109.0ms (1.1%)

Counts

3 → 42

Calls

3 calls:

66.0ms	(/.f64 (*.f64 t x) (-.f64 1 z))
30.0ms	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
12.0ms	(/.f64 (*.f64 y x) z)

rewrite39.0ms (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:

13.0ms	(-.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)

simplify165.0ms (1.7%)

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

prune233.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	254	2	256
Fresh	2	2	4
Picked	1	0	1
Done	1	1	2
Total	258	5	263

Error

Counts

263 → 5

Alt Table

Status	Error	Program
	8.8b	(-.f64 (.f64 y (/.f64 x z)) (/.f64 (.f64 t x) (-.f64 1 z)))
✓	3.7b	(.f64 x (-.f64 (/.f64 y z) (.f64 t (/.f64 1 (-.f64 1 z)))))
	17.2b	(/.f64 x (/.f64 z (+.f64 y t)))
	8.1b	(-.f64 (/.f64 (.f64 y x) z) (.f64 t (/.f64 x (-.f64 1 z))))
	25.3b	(/.f64 (.f64 x (-.f64 (.f64 (/.f64 y z) (/.f64 y z)) (*.f64 (/.f64 t (-.f64 1 z)) (/.f64 t (-.f64 1 z))))) (+.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

Compiler

Compiled 8243 to 4002 computations (51.4% saved)

regimes2.6s (26.3%)

Accuracy

Total 2.0b remaining (98.9%)

Threshold costs 0b (0%)

Counts

206 → 4

Compiler

Compiled 34397 to 23204 computations (32.5% saved)

bsearch9.0ms (0.1%)

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

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	116
1	46	116
2	63	116
3	74	116
4	81	116
5	83	116
6	82	116

end1.0ms (0%)

Compiler: Compiled 82 to 48 computations (41.5% saved)

sample944.0ms (9.7%)

Algorithm

1×

intervals

Results

392.0ms	8000×	body	128	valid
85.0ms	1882×	body	128	invalid

Compiler

Compiled 199 to 124 computations (37.7% saved)

Details

analyze843.0ms (8.6%)

sample173.0ms (1.8%)

simplify291.0ms (3%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series64.0ms (0.7%)

rewrite319.0ms (3.3%)

simplify1.4s (14%)

prune1.3s (13.4%)

localize127.0ms (1.3%)

series54.0ms (0.6%)

rewrite43.0ms (0.4%)

simplify164.0ms (1.7%)

prune250.0ms (2.6%)

localize11.0ms (0.1%)

series156.0ms (1.6%)

rewrite157.0ms (1.6%)

simplify158.0ms (1.6%)

prune191.0ms (1.9%)

localize8.0ms (0.1%)

series109.0ms (1.1%)

rewrite39.0ms (0.4%)

simplify165.0ms (1.7%)

prune233.0ms (2.4%)

regimes2.6s (26.3%)

bsearch9.0ms (0.1%)

simplify8.0ms (0.1%)

end1.0ms (0%)

sample944.0ms (9.7%)

Profiling