Details

analyze1.3s (28.1%)

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
15.6%	84.2%	0.2%	8
15.6%	84.2%	0.2%	9
20.3%	79.5%	0.2%	10
25.3%	74.5%	0.2%	11
34.2%	65.6%	0.2%	12
37.4%	62%	0.6%	13
41.7%	57.7%	0.6%	14

Compiler

Compiled 20 to 14 computations (30% saved)

sample100.0ms (2.2%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
7.0ms	93×	body	128	invalid

Compiler

Compiled 43 to 31 computations (27.9% saved)

simplify93.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

871×	`distribute-rgt-in_binary64`
685×	`div-sub_binary64`
652×	`distribute-lft-in_binary64`
409×	`distribute-neg-frac_binary64`
395×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	25	22
2	58	22
3	109	22
4	223	20
5	437	16
6	876	14
7	2098	14
8	2320	14
9	2451	14
10	3042	14
11	3226	14
12	3327	14
13	4913	14

prune4.0ms (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
	3.7b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
▶	2.7b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))

Compiler

Compiled 95 to 62 computations (34.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
✓	0.2b	(/.f64 y (*.f64 z 3))
✓	0.4b	(.f64 (.f64 z 3) y)
✓	5.7b	(/.f64 t (.f64 (.f64 z 3) y))

series57.0ms (1.3%)

Counts

4 → 132

Calls

4 calls:

27.0ms	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
19.0ms	(/.f64 t (.f64 (.f64 z 3) y))
6.0ms	(/.f64 y (*.f64 z 3))
4.0ms	(.f64 (.f64 z 3) y)

rewrite35.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
29×	`associate-+l+_binary64`
27×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
23×	`add-cbrt-cube_binary64`

Counts

4 → 121

Calls

4 calls:

10.0ms	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
8.0ms	(/.f64 t (.f64 (.f64 z 3) y))
4.0ms	(.f64 (.f64 z 3) y)
3.0ms	(/.f64 y (*.f64 z 3))

simplify120.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

588×	`fma-def_binary64`
317×	`associate-/l/_binary64`
254×	`distribute-rgt-in_binary64`
243×	`fma-neg_binary64`
235×	`distribute-lft-in_binary64`

Counts

253 → 200

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	214	4171
1	601	3297
2	2065	2964
3	4498	2964
4	4876	2964

prune189.0ms (4.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	195	5	200
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	196	6	202

Error

Counts

202 → 6

Alt Table

Status	Error	Program
	2.7b	(+.f64 (-.f64 x (/.f64 (/.f64 y z) 3)) (/.f64 t (.f64 (.f64 z 3) y)))
	2.5b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 z (*.f64 3 y))))
▶	1.1b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))
	3.7b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
	2.7b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 1 (/.f64 (.f64 (*.f64 z 3) y) t)))
	32.5b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 (/.f64 (sqrt.f64 t) (*.f64 z 3)) (/.f64 (sqrt.f64 t) y)))

Compiler

Compiled 5104 to 2950 computations (42.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))
	0.2b	(/.f64 y (*.f64 z 3))
✓	0.4b	(/.f64 t (*.f64 z 3))
✓	4.2b	(/.f64 (/.f64 t (*.f64 z 3)) y)

series55.0ms (1.2%)

Counts

3 → 108

Calls

3 calls:

28.0ms	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))
19.0ms	(/.f64 (/.f64 t (*.f64 z 3)) y)
8.0ms	(/.f64 t (*.f64 z 3))

rewrite34.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`times-frac_binary64`
44×	`*-un-lft-identity_binary64`
39×	`add-sqr-sqrt_binary64`
37×	`add-cube-cbrt_binary64`
29×	`associate-+l+_binary64`

Counts

3 → 126

Calls

3 calls:

14.0ms	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))
5.0ms	(/.f64 (/.f64 t (*.f64 z 3)) y)
3.0ms	(/.f64 t (*.f64 z 3))

simplify89.0ms (2%)

Algorithm

1×	egg-herbie

Rules

755×	`associate-/l*_binary64`
531×	`associate-/l/_binary64`
508×	`fma-def_binary64`
216×	`distribute-rgt-in_binary64`
210×	`associate-/r/_binary64`

Counts

234 → 214

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	250	3420
1	652	3138
2	1896	3026
3	5074	3026

prune204.0ms (4.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	248	1	249
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	250	5	255

Error

Counts

255 → 5

Alt Table

Status	Error	Program
	2.7b	(+.f64 (-.f64 x (/.f64 (/.f64 y z) 3)) (/.f64 t (.f64 (.f64 z 3) y)))
	2.5b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 z (*.f64 3 y))))
✓	1.1b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))
	3.7b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
▶	0.9b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (.f64 1/3 (/.f64 t z)) y))

Compiler

Compiled 6160 to 3471 computations (43.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (.f64 1/3 (/.f64 t z)) y))
	0.2b	(/.f64 y (*.f64 z 3))
✓	0.3b	(*.f64 1/3 (/.f64 t z))
✓	4.2b	(/.f64 (*.f64 1/3 (/.f64 t z)) y)

series59.0ms (1.3%)

Counts

3 → 84

Calls

3 calls:

31.0ms	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (.f64 1/3 (/.f64 t z)) y))
21.0ms	(/.f64 (*.f64 1/3 (/.f64 t z)) y)
7.0ms	(*.f64 1/3 (/.f64 t z))

rewrite30.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary64`
36×	`add-sqr-sqrt_binary64`
29×	`associate-+l+_binary64`
29×	`add-cube-cbrt_binary64`
25×	`times-frac_binary64`

Counts

3 → 113

Calls

3 calls:

12.0ms	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (.f64 1/3 (/.f64 t z)) y))
5.0ms	(*.f64 1/3 (/.f64 t z))
5.0ms	(/.f64 (*.f64 1/3 (/.f64 t z)) y)

simplify108.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

799×	`times-frac_binary64`
536×	`fma-def_binary64`
395×	`fma-neg_binary64`
234×	`distribute-rgt-in_binary64`
226×	`distribute-lft-in_binary64`

Counts

197 → 175

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	233	2853
1	621	2520
2	1835	2466
3	4787	2466
4	4894	2466

prune186.0ms (4.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	210	5	215

Error

Counts

215 → 5

Alt Table

Status	Error	Program
	2.7b	(+.f64 (-.f64 x (/.f64 (/.f64 y z) 3)) (/.f64 t (.f64 (.f64 z 3) y)))
▶	2.5b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 z (*.f64 3 y))))
✓	1.1b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))
	3.7b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
✓	0.9b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (.f64 1/3 (/.f64 t z)) y))

Compiler

Compiled 5224 to 2802 computations (46.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 z (*.f64 3 y))))
	0.2b	(/.f64 y (*.f64 z 3))
✓	0.2b	(.f64 z (.f64 3 y))
✓	5.7b	(/.f64 t (.f64 z (.f64 3 y)))

series58.0ms (1.3%)

Counts

3 → 108

Calls

3 calls:

28.0ms	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 z (*.f64 3 y))))
23.0ms	(/.f64 t (.f64 z (.f64 3 y)))
7.0ms	(.f64 z (.f64 3 y))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`associate-+l+_binary64`
29×	`*-un-lft-identity_binary64`
24×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
21×	`prod-diff_binary64`

Counts

3 → 98

Calls

3 calls:

12.0ms	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 z (*.f64 3 y))))
4.0ms	(/.f64 t (.f64 z (.f64 3 y)))
4.0ms	(.f64 z (.f64 3 y))

simplify85.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

665×	`associate-/l*_binary64`
584×	`fma-def_binary64`
297×	`associate-/l/_binary64`
275×	`distribute-rgt-in_binary64`
261×	`distribute-lft-in_binary64`

Counts

206 → 166

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	204	2864
1	557	2601
2	1886	2490
3	5091	2490

prune203.0ms (4.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	201	5	206

Error

Counts

206 → 5

Alt Table

Status	Error	Program
	2.7b	(+.f64 (-.f64 x (/.f64 (/.f64 y z) 3)) (/.f64 t (.f64 (.f64 z 3) y)))
✓	2.5b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 z (*.f64 3 y))))
✓	1.1b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))
	3.7b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
✓	0.9b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (.f64 1/3 (/.f64 t z)) y))

Compiler

Compiled 4969 to 2814 computations (43.4% saved)

regimes232.0ms (5.2%)

Accuracy

Total 1.7b remaining (98.3%)

Threshold costs 0b (0%)

Counts

35 → 1

Compiler

Compiled 4598 to 3168 computations (31.1% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	19	22
2	26	22
3	30	22
4	33	22
5	34	22
6	34	22

end1.0ms (0%)

Compiler: Compiled 19 to 13 computations (31.6% saved)

sample1.2s (26.7%)

Algorithm

1×

intervals

Results

521.0ms	8000×	body	128	valid
183.0ms	2999×	body	128	invalid

Compiler

Compiled 133 to 92 computations (30.8% saved)

Details

analyze1.3s (28.1%)

sample100.0ms (2.2%)

simplify93.0ms (2.1%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series57.0ms (1.3%)

rewrite35.0ms (0.8%)

simplify120.0ms (2.7%)

prune189.0ms (4.2%)

localize9.0ms (0.2%)

series55.0ms (1.2%)

rewrite34.0ms (0.8%)

simplify89.0ms (2%)

prune204.0ms (4.6%)

localize10.0ms (0.2%)

series59.0ms (1.3%)

rewrite30.0ms (0.7%)

simplify108.0ms (2.4%)

prune186.0ms (4.2%)

localize10.0ms (0.2%)

series58.0ms (1.3%)

rewrite28.0ms (0.6%)

simplify85.0ms (1.9%)

prune203.0ms (4.6%)

regimes232.0ms (5.2%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample1.2s (26.7%)

Profiling