Details

analyze1.0s (28.2%)

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)

sample92.0ms (2.5%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
6.0ms	89×	body	128	invalid

Compiler

Compiled 43 to 31 computations (27.9% saved)

simplify82.0ms (2.2%)

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
	4.5b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
▶	4.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))

Compiler

Compiled 95 to 62 computations (34.7% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 z 3) y)
✓	0.2b	(/.f64 y (*.f64 z 3))
✓	8.0b	(/.f64 t (.f64 (.f64 z 3) y))

series31.0ms (0.8%)

Counts

3 → 84

Calls

3 calls:

20.0ms	(/.f64 t (.f64 (.f64 z 3) y))
6.0ms	(/.f64 y (*.f64 z 3))
5.0ms	(.f64 (.f64 z 3) y)

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-cbrt-cube_binary64`
22×	`add-exp-log_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`

Counts

3 → 68

Calls

3 calls:

4.0ms	(/.f64 t (.f64 (.f64 z 3) y))
4.0ms	(.f64 (.f64 z 3) y)
3.0ms	(/.f64 y (*.f64 z 3))

simplify109.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

744×	`associate-/r*_binary64`
690×	`associate-/l*_binary64`
535×	`associate-l_binary64`
369×	`associate-r_binary64`
286×	`associate-/l/_binary64`

Counts

152 → 98

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	1570
1	264	1395
2	1051	1395
3	3965	1394
4	4313	1394
5	4746	1394
6	4993	1394
7	4955	1394

prune97.0ms (2.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	93	7	100

Error

Counts

100 → 7

Alt Table

Status	Error	Program
	4.0b	(+.f64 (-.f64 x (/.f64 1 (/.f64 z (/.f64 y 3)))) (/.f64 t (.f64 (.f64 z 3) y)))
	4.0b	(+.f64 (-.f64 x (.f64 1/3 (/.f64 y z))) (/.f64 t (.f64 (*.f64 z 3) y)))
	4.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 1/3 (/.f64 t (*.f64 y z))))
▶	1.7b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))
	4.5b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
	4.0b	(+.f64 (-.f64 x (/.f64 (/.f64 y z) 3)) (/.f64 t (.f64 (.f64 z 3) y)))
	4.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 z (*.f64 3 y))))

Compiler

Compiled 2197 to 1317 computations (40.1% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.2b	(/.f64 y (*.f64 z 3))
✓	0.2b	(/.f64 t (*.f64 z 3))
✓	5.5b	(/.f64 (/.f64 t (*.f64 z 3)) y)

series26.0ms (0.7%)

Counts

2 → 60

Calls

2 calls:

20.0ms	(/.f64 (/.f64 t (*.f64 z 3)) y)
6.0ms	(/.f64 t (*.f64 z 3))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`

Counts

2 → 73

Calls

2 calls:

5.0ms	(/.f64 (/.f64 t (*.f64 z 3)) y)
3.0ms	(/.f64 t (*.f64 z 3))

simplify97.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

570×	`times-frac_binary64`
474×	`associate-/l*_binary64`
444×	`associate-/l/_binary64`
414×	`associate-/r*_binary64`
266×	`fma-def_binary64`

Counts

133 → 118

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	133	1704
1	295	1560
2	869	1559
3	3386	1559
4	3767	1559
5	4426	1559
6	5033	1559

prune139.0ms (3.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	148	7	155

Error

Counts

155 → 7

Alt Table

Status	Error	Program
	4.0b	(+.f64 (-.f64 x (/.f64 1 (/.f64 z (/.f64 y 3)))) (/.f64 t (.f64 (.f64 z 3) y)))
	4.0b	(+.f64 (-.f64 x (.f64 1/3 (/.f64 y z))) (/.f64 t (.f64 (*.f64 z 3) y)))
	4.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 1/3 (/.f64 t (*.f64 y z))))
✓	1.7b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))
	4.5b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
	4.0b	(+.f64 (-.f64 x (/.f64 (/.f64 y z) 3)) (/.f64 t (.f64 (.f64 z 3) y)))
▶	4.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 z (*.f64 3 y))))

Compiler

Compiled 3368 to 1951 computations (42.1% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 z (.f64 3 y))
	0.2b	(/.f64 y (*.f64 z 3))
✓	8.0b	(/.f64 t (.f64 z (.f64 3 y)))

series24.0ms (0.6%)

Counts

2 → 60

Calls

2 calls:

19.0ms	(/.f64 t (.f64 z (.f64 3 y)))
4.0ms	(.f64 z (.f64 3 y))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
7×	`pow1_binary64`
6×	`cbrt-unprod_binary64`
6×	`prod-exp_binary64`

Counts

2 → 45

Calls

2 calls:

6.0ms	(/.f64 t (.f64 z (.f64 3 y)))
4.0ms	(.f64 z (.f64 3 y))

simplify88.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

896×	`times-frac_binary64`
581×	`associate-/r*_binary64`
497×	`associate-l_binary64`
455×	`associate-/l*_binary64`
340×	`associate-r_binary64`

Counts

105 → 70

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	82	1136
1	187	1011
2	728	1010
3	3684	1010
4	4035	1010
5	4588	1010
6	4971	1010
7	4994	1010

prune93.0ms (2.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	100	7	107

Error

Counts

107 → 7

Alt Table

Status	Error	Program
	4.0b	(+.f64 (-.f64 x (/.f64 1 (/.f64 z (/.f64 y 3)))) (/.f64 t (.f64 (.f64 z 3) y)))
	4.0b	(+.f64 (-.f64 x (.f64 1/3 (/.f64 y z))) (/.f64 t (.f64 (*.f64 z 3) y)))
	4.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 1/3 (/.f64 t (*.f64 y z))))
✓	1.7b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))
	4.5b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
▶	4.0b	(+.f64 (-.f64 x (/.f64 (/.f64 y z) 3)) (/.f64 t (.f64 (.f64 z 3) y)))
✓	4.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 z (*.f64 3 y))))

Compiler

Compiled 2213 to 1328 computations (40% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.2b	(.f64 (.f64 z 3) y)
✓	0.3b	(/.f64 (/.f64 y z) 3)
	8.0b	(/.f64 t (.f64 (.f64 z 3) y))

series8.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

8.0ms

(/.f64 (/.f64 y z) 3)

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
43×	`add-cube-cbrt_binary64`
13×	`associate-/l*_binary64`

Counts

1 → 72

Calls

1 calls:

4.0ms

(/.f64 (/.f64 y z) 3)

simplify154.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

467×	`fma-neg_binary64`
395×	`associate-*l/_binary64`
383×	`associate-/r/_binary64`
358×	`distribute-rgt-in_binary64`
354×	`sqr-pow_binary64`

Counts

96 → 100

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	154	1418
1	322	1370
2	717	1370
3	1544	1370
4	2662	1370
5	2725	1370
6	3192	1370
7	4330	1370
8	4173	1370
9	4494	1370
10	4999	1370
11	4775	1370

prune148.0ms (4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	168	7	175

Error

Counts

175 → 7

Alt Table

Status	Error	Program
	4.0b	(+.f64 (-.f64 x (/.f64 1 (/.f64 z (/.f64 y 3)))) (/.f64 t (.f64 (.f64 z 3) y)))
	4.0b	(+.f64 (-.f64 x (.f64 1/3 (/.f64 y z))) (/.f64 t (.f64 (*.f64 z 3) y)))
	4.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 1/3 (/.f64 t (*.f64 y z))))
✓	1.7b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))
	4.5b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
✓	4.0b	(+.f64 (-.f64 x (/.f64 (/.f64 y z) 3)) (/.f64 t (.f64 (.f64 z 3) y)))
✓	4.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 z (*.f64 3 y))))

Compiler

Compiled 3824 to 2058 computations (46.2% saved)

regimes248.0ms (6.7%)

Accuracy

Total 0.7b remaining (97.3%)

Threshold costs 0.7b (97.3%)

Counts

22 → 3

Compiler

Compiled 3187 to 2182 computations (31.5% saved)

bsearch1.0ms (0%)

Compiler: Compiled 7 to 6 computations (14.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	87
1	45	87
2	56	87
3	65	87
4	71	87
5	73	87
6	72	87

end1.0ms (0%)

Compiler: Compiled 63 to 43 computations (31.7% saved)

sample1.1s (30.7%)

Algorithm

1×

intervals

Results

473.0ms	8000×	body	128	valid
176.0ms	3027×	body	128	invalid

Compiler

Compiled 217 to 150 computations (30.9% saved)

Details

analyze1.0s (28.2%)

sample92.0ms (2.5%)

simplify82.0ms (2.2%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series31.0ms (0.8%)

rewrite14.0ms (0.4%)

simplify109.0ms (2.9%)

prune97.0ms (2.6%)

localize9.0ms (0.2%)

series26.0ms (0.7%)

rewrite12.0ms (0.3%)

simplify97.0ms (2.6%)

prune139.0ms (3.7%)

localize10.0ms (0.3%)

series24.0ms (0.6%)

rewrite11.0ms (0.3%)

simplify88.0ms (2.4%)

prune93.0ms (2.5%)

localize9.0ms (0.2%)

series8.0ms (0.2%)

rewrite9.0ms (0.2%)

simplify154.0ms (4.1%)

prune148.0ms (4%)

regimes248.0ms (6.7%)

bsearch1.0ms (0%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.1s (30.7%)

Profiling