Details

analyze922.0ms (7.1%)

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
15.6%	84.2%	0.2%	9
23.4%	76.4%	0.2%	10
25%	74.9%	0.2%	11
37.9%	59.6%	2.5%	12
41.4%	55.7%	2.9%	13
46.3%	50.6%	3.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.3s (10.4%)

Results

948.0ms	8256×	body	128	valid
237.0ms	1803×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify285.0ms (2.2%)

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

7.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	7.0b	(*.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 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
✓	6.7b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

series44.0ms (0.3%)

Counts

2 → 66

Calls

2 calls:

30.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
15.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

rewrite335.0ms (2.6%)

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:

38.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
24.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

simplify1.2s (9.5%)

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

prune1.3s (10.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	1063	4	1067
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1064	4	1068

Error

0.0b

Counts

1068 → 4

Alt Table

Status	Error	Program
	22.7b	(/.f64 x (/.f64 z (+.f64 y t)))
	23.5b	(*.f64 x (+.f64 (/.f64 y z) (/.f64 (neg.f64 (/.f64 t (sqrt.f64 (-.f64 1 z)))) (sqrt.f64 (-.f64 1 z)))))
	7.3b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
▶	7.1b	(.f64 x (+.f64 (fma.f64 y (/.f64 1 z) (neg.f64 (.f64 (/.f64 1 (-.f64 1 z)) t))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (*.f64 (/.f64 1 (-.f64 1 z)) t))))

Compiler

Compiled 57417 to 31145 computations (45.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (/.f64 1 (-.f64 1 z)) t)
✓	0.1b	(fma.f64 y (/.f64 1 z) (neg.f64 (*.f64 (/.f64 1 (-.f64 1 z)) t)))
✓	6.7b	(.f64 x (+.f64 (fma.f64 y (/.f64 1 z) (neg.f64 (.f64 (/.f64 1 (-.f64 1 z)) t))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (*.f64 (/.f64 1 (-.f64 1 z)) t))))
✓	27.0b	(fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (*.f64 (/.f64 1 (-.f64 1 z)) t))

series110.0ms (0.8%)

Counts

4 → 132

Calls

4 calls:

56.0ms	(.f64 x (+.f64 (fma.f64 y (/.f64 1 z) (neg.f64 (.f64 (/.f64 1 (-.f64 1 z)) t))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (*.f64 (/.f64 1 (-.f64 1 z)) t))))
30.0ms	(fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (*.f64 (/.f64 1 (-.f64 1 z)) t))
15.0ms	(fma.f64 y (/.f64 1 z) (neg.f64 (*.f64 (/.f64 1 (-.f64 1 z)) t)))
8.0ms	(*.f64 (/.f64 1 (-.f64 1 z)) t)

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
27×	`associate-l_binary64`
20×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`

Counts

4 → 93

Calls

4 calls:

7.0ms	(*.f64 (/.f64 1 (-.f64 1 z)) t)
5.0ms	(.f64 x (+.f64 (fma.f64 y (/.f64 1 z) (neg.f64 (.f64 (/.f64 1 (-.f64 1 z)) t))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (*.f64 (/.f64 1 (-.f64 1 z)) t))))
0.0ms	(fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (*.f64 (/.f64 1 (-.f64 1 z)) t))
0.0ms	(fma.f64 y (/.f64 1 z) (neg.f64 (*.f64 (/.f64 1 (-.f64 1 z)) t)))

simplify127.0ms (1%)

Algorithm

1×	egg-herbie

Rules

870×	`fma-def_binary64`
557×	`distribute-rgt-in_binary64`
451×	`distribute-lft-in_binary64`
407×	`fma-neg_binary64`
361×	`times-frac_binary64`

Counts

225 → 203

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	210	3715
1	511	3140
2	1693	2694
3	4433	2694
4	4976	2694
5	4904	2694

prune355.0ms (2.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	292	1	293
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	292	5	297

Error

0.0b

Counts

297 → 5

Alt Table

Status	Error	Program
	22.7b	(/.f64 x (/.f64 z (+.f64 y t)))
	23.5b	(*.f64 x (+.f64 (/.f64 y z) (/.f64 (neg.f64 (/.f64 t (sqrt.f64 (-.f64 1 z)))) (sqrt.f64 (-.f64 1 z)))))
▶	7.3b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
	33.0b	(/.f64 (.f64 x (-.f64 (.f64 (fma.f64 y (/.f64 1 z) (neg.f64 (.f64 (/.f64 1 (-.f64 1 z)) t))) (fma.f64 y (/.f64 1 z) (neg.f64 (.f64 (/.f64 1 (-.f64 1 z)) t)))) (.f64 (fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (.f64 (/.f64 1 (-.f64 1 z)) t)) (fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (.f64 (/.f64 1 (-.f64 1 z)) t))))) (-.f64 (fma.f64 y (/.f64 1 z) (neg.f64 (.f64 (/.f64 1 (-.f64 1 z)) t))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (*.f64 (/.f64 1 (-.f64 1 z)) t))))
✓	7.1b	(.f64 x (+.f64 (fma.f64 y (/.f64 1 z) (neg.f64 (.f64 (/.f64 1 (-.f64 1 z)) t))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (*.f64 (/.f64 1 (-.f64 1 z)) t))))

Compiler

Compiled 10909 to 7493 computations (31.3% 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))
✓	6.4b	(/.f64 (*.f64 y x) z)

series59.0ms (0.5%)

Counts

3 → 42

Calls

3 calls:

28.0ms	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
17.0ms	(/.f64 (*.f64 t x) (-.f64 1 z))
14.0ms	(/.f64 (*.f64 y x) z)

rewrite53.0ms (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:

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)

simplify159.0ms (1.2%)

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

prune221.0ms (1.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	252	4	256
Fresh	2	1	3
Picked	1	0	1
Done	1	0	1
Total	256	5	261

Error

Counts

261 → 5

Alt Table

Status	Error	Program
▶	6.4b	(-.f64 (/.f64 (*.f64 y x) z) (/.f64 t (/.f64 (-.f64 1 z) x)))
	7.0b	(-.f64 (/.f64 y (/.f64 z x)) (/.f64 (*.f64 t x) (-.f64 1 z)))
	22.7b	(/.f64 x (/.f64 z (+.f64 y t)))
	7.0b	(neg.f64 (*.f64 x (-.f64 (/.f64 t (-.f64 1 z)) (/.f64 y z))))
	7.6b	(fma.f64 (/.f64 y (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 x (cbrt.f64 z)) (neg.f64 (/.f64 (.f64 t x) (-.f64 1 z))))

Compiler

Compiled 8316 to 4049 computations (51.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (*.f64 y x) z) (/.f64 t (/.f64 (-.f64 1 z) x)))
✓	0.0b	(/.f64 (-.f64 1 z) x)
✓	1.6b	(/.f64 t (/.f64 (-.f64 1 z) x))
	6.4b	(/.f64 (*.f64 y x) z)

series51.0ms (0.4%)

Counts

3 → 100

Calls

3 calls:

29.0ms	(-.f64 (/.f64 (*.f64 y x) z) (/.f64 t (/.f64 (-.f64 1 z) x)))
16.0ms	(/.f64 t (/.f64 (-.f64 1 z) x))
6.0ms	(/.f64 (-.f64 1 z) x)

rewrite222.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

1335×	`times-frac_binary64`
918×	`add-sqr-sqrt_binary64`
911×	`*-un-lft-identity_binary64`
645×	`add-cube-cbrt_binary64`
497×	`prod-diff_binary64`

Counts

3 → 745

Calls

3 calls:

39.0ms	(-.f64 (/.f64 (*.f64 y x) z) (/.f64 t (/.f64 (-.f64 1 z) x)))
13.0ms	(/.f64 (-.f64 1 z) x)
6.0ms	(/.f64 t (/.f64 (-.f64 1 z) x))

simplify960.0ms (7.4%)

Algorithm

1×	egg-herbie

Rules

392×	`fma-udef_binary64`
363×	`associate-/r/_binary64`
325×	`unsub-neg_binary64`
215×	`fma-neg_binary64`
213×	`fma-def_binary64`

Counts

845 → 979

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	936	61665
1	2477	41503
2	4802	41503
3	4985	41503

prune911.0ms (7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	1014	0	1014
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	1014	5	1019

Error

Counts

1019 → 5

Alt Table

Status	Error	Program
✓	6.4b	(-.f64 (/.f64 (*.f64 y x) z) (/.f64 t (/.f64 (-.f64 1 z) x)))
	7.0b	(-.f64 (/.f64 y (/.f64 z x)) (/.f64 (*.f64 t x) (-.f64 1 z)))
	22.7b	(/.f64 x (/.f64 z (+.f64 y t)))
	7.0b	(neg.f64 (*.f64 x (-.f64 (/.f64 t (-.f64 1 z)) (/.f64 y z))))
	7.6b	(fma.f64 (/.f64 y (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 x (cbrt.f64 z)) (neg.f64 (/.f64 (.f64 t x) (-.f64 1 z))))

Compiler

Compiled 51313 to 24810 computations (51.6% saved)

regimes4.1s (31.5%)

Accuracy

Total 0.5b remaining (95.6%)

Threshold costs 0.5b (95.6%)

Counts

255 → 5

Compiler

Compiled 39654 to 26837 computations (32.3% saved)

bsearch11.0ms (0.1%)

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

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

17×	`*-commutative_binary64`
15×	`+-commutative_binary64`
14×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
9×	`neg-mul-1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	44	172
1	70	172
2	100	170
3	119	170
4	132	170
5	136	170
6	133	170

end97.0ms (0.7%)

Compiler: Compiled 323 to 182 computations (43.7% saved)

Details

analyze922.0ms (7.1%)

sample1.3s (10.4%)

simplify285.0ms (2.2%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series44.0ms (0.3%)

rewrite335.0ms (2.6%)

simplify1.2s (9.5%)

prune1.3s (10.3%)

localize13.0ms (0.1%)

series110.0ms (0.8%)

rewrite19.0ms (0.1%)

simplify127.0ms (1%)

prune355.0ms (2.7%)

localize8.0ms (0.1%)

series59.0ms (0.5%)

rewrite53.0ms (0.4%)

simplify159.0ms (1.2%)

prune221.0ms (1.7%)

localize9.0ms (0.1%)

series51.0ms (0.4%)

rewrite222.0ms (1.7%)

simplify960.0ms (7.4%)

prune911.0ms (7%)

regimes4.1s (31.5%)

bsearch11.0ms (0.1%)

simplify9.0ms (0.1%)

end97.0ms (0.7%)

Profiling