Details

analyze1.7s (34.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
1.6%	98.1%	0.3%	13
2.3%	97.4%	0.3%	14

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample1.7s (34.3%)

Results

1.1s	8256×	body	128	valid
508.0ms	3812×	body	128	invalid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

89×	`fma-def_binary64`
24×	`associate-+l+_binary64`
22×	`associate-+r+_binary64`
19×	`+-commutative_binary64`
10×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	27	16
2	66	15
3	122	13
4	157	13
5	164	13
6	167	13
7	167	13

prune3.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	3.0b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
▶	3.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 105 to 60 computations (42.9% saved)

localize10.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	6.3b	(.f64 (.f64 a z) b)

series9.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

9.0ms

(*.f64 (*.f64 a z) b)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
3×	`associate-r_binary64`
3×	`cbrt-unprod_binary64`

Counts

1 → 20

Calls

1 calls:

4.0ms

(*.f64 (*.f64 a z) b)

simplify56.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

501×	`associate-*r/_binary64`
495×	`associate-*l/_binary64`
334×	`associate-/l/_binary64`
294×	`log-div_binary64`
292×	`cube-div_binary64`

Counts

56 → 28

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	473
1	100	428
2	378	428
3	527	428
4	688	428
5	934	428
6	1199	428
7	3794	428
8	4940	428

prune19.0ms (0.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	26	2	28
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	26	4	30

Error

0.0b

Counts

30 → 4

Alt Table

Status	Error	Program
	32.5b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b)))
	16.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 a z) b) (.f64 (.f64 a z) b)) (.f64 (.f64 a z) b))))
▶	3.0b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	3.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 727 to 208 computations (71.4% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.9b	(fma.f64 a (fma.f64 z b t) x)

series14.0ms (0.3%)

Counts

1 → 60

Calls

1 calls:

14.0ms

(fma.f64 a (fma.f64 z b t) x)

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 a (fma.f64 z b t) x)

simplify112.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

890×	`distribute-rgt-in_binary64`
886×	`distribute-lft-in_binary64`
636×	`unswap-sqr_binary64`
393×	`associate-l_binary64`
336×	`associate-r_binary64`

Counts

70 → 33

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	626
1	49	607
2	126	607
3	510	607
4	3225	607
5	3357	607
6	3579	607
7	3869	607
8	4363	607
9	4411	607
10	5048	607

prune25.0ms (0.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	33	4	37

Error

0.0b

Counts

37 → 4

Alt Table

Status	Error	Program
	32.5b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b)))
▶	16.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 a z) b) (.f64 (.f64 a z) b)) (.f64 (.f64 a z) b))))
✓	3.0b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	3.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 580 to 184 computations (68.3% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (.f64 (.f64 a z) b) (.f64 (.f64 a z) b)) (.f64 (.f64 a z) b))
✓	0.2b	(.f64 (.f64 (.f64 a z) b) (.f64 (*.f64 a z) b))
	6.3b	(.f64 (.f64 a z) b)
✓	28.8b	(cbrt.f64 (.f64 (.f64 (.f64 (.f64 a z) b) (.f64 (.f64 a z) b)) (.f64 (.f64 a z) b)))

series131.0ms (2.7%)

Counts

3 → 108

Calls

3 calls:

59.0ms

(*.f64 (*.f64 (*.f64 (*.f64 a z) b) (*.f64 (*.f64 a z) b)) (*.f64 (*.f64 a z) b))

36.0ms

(cbrt.f64 (*.f64 (*.f64 (*.f64 (*.f64 a z) b) (*.f64 (*.f64 a z) b)) (*.f64 (*.f64 a z) b)))

36.0ms

(*.f64 (*.f64 (*.f64 a z) b) (*.f64 (*.f64 a z) b))

rewrite105.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

732×	`pow1_binary64`
429×	`pow-prod-down_binary64`
228×	`add-cbrt-cube_binary64`
210×	`add-exp-log_binary64`
177×	`cbrt-unprod_binary64`

Counts

3 → 268

Calls

3 calls:

19.0ms

(*.f64 (*.f64 (*.f64 (*.f64 a z) b) (*.f64 (*.f64 a z) b)) (*.f64 (*.f64 a z) b))

16.0ms

(cbrt.f64 (*.f64 (*.f64 (*.f64 (*.f64 a z) b) (*.f64 (*.f64 a z) b)) (*.f64 (*.f64 a z) b)))

7.0ms

(*.f64 (*.f64 (*.f64 a z) b) (*.f64 (*.f64 a z) b))

simplify211.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

681×	`*-commutative_binary64`
613×	`associate-l_binary64`
503×	`log-prod_binary64`
468×	`exp-prod_binary64`
429×	`cube-prod_binary64`

Counts

376 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	165	6706
1	317	3353
2	1139	3213
3	2972	3213
4	4926	3213
5	5009	3213

prune240.0ms (4.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	246	0	246
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	246	4	250

Error

0.0b

Counts

250 → 4

Alt Table

Status	Error	Program
▶	32.5b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b)))
✓	16.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 a z) b) (.f64 (.f64 a z) b)) (.f64 (.f64 a z) b))))
✓	3.0b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	3.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 9047 to 1192 computations (86.8% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.5b	(.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b))
✓	2.1b	(.f64 (.f64 a z) (sqrt.f64 b))

series28.0ms (0.6%)

Counts

2 → 32

Calls

2 calls:

16.0ms	(.f64 (.f64 a z) (sqrt.f64 b))
12.0ms	(.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`
12×	`associate-r_binary64`
9×	`cbrt-unprod_binary64`

Counts

2 → 49

Calls

2 calls:

6.0ms	(.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b))
4.0ms	(.f64 (.f64 a z) (sqrt.f64 b))

simplify97.0ms (2%)

Algorithm

1×	egg-herbie

Rules

395×	`unswap-sqr_binary64`
364×	`*-commutative_binary64`
348×	`log-div_binary64`
322×	`sqr-pow_binary64`
223×	`associate-l_binary64`

Counts

81 → 60

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	71	823
1	172	727
2	661	727
3	979	727
4	1277	727
5	1827	727
6	3254	727
7	4264	719
8	4987	719
9	4938	719

prune49.0ms (1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	60	4	64

Error

0.0b

Counts

64 → 4

Alt Table

Status	Error	Program
✓	32.5b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b)))
✓	16.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 a z) b) (.f64 (.f64 a z) b)) (.f64 (.f64 a z) b))))
✓	3.0b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	3.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 1546 to 298 computations (80.7% saved)

regimes210.0ms (4.3%)

Accuracy

Total 0.6b remaining (96.8%)

Threshold costs 0.6b (96.8%)

Counts

16 → 3

Compiler

Compiled 2436 to 1414 computations (42% saved)

bsearch71.0ms (1.5%)

Steps

Iters	Range		Point
9	1.127228249193571e-142	2.5659736219772833e-137	1.6657956137560575e-137
4	-1.4457770748400676e-54	-1.0433824011809959e-54	-1.1990245494804759e-54

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	60
1	31	60
2	31	60

end81.0ms (1.7%)

Compiler: Compiled 194 to 97 computations (50% saved)

Details

analyze1.7s (34.4%)

sample1.7s (34.3%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

series9.0ms (0.2%)

rewrite5.0ms (0.1%)

simplify56.0ms (1.2%)

prune19.0ms (0.4%)

localize7.0ms (0.2%)

series14.0ms (0.3%)

rewrite2.0ms (0%)

simplify112.0ms (2.3%)

prune25.0ms (0.5%)

localize13.0ms (0.3%)

series131.0ms (2.7%)

rewrite105.0ms (2.1%)

simplify211.0ms (4.3%)

prune240.0ms (4.9%)

localize11.0ms (0.2%)

series28.0ms (0.6%)

rewrite13.0ms (0.3%)

simplify97.0ms (2%)

prune49.0ms (1%)

regimes210.0ms (4.3%)

bsearch71.0ms (1.5%)

simplify3.0ms (0.1%)

end81.0ms (1.7%)

Profiling