Details

analyze1.2s (27.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	87.5%	12.5%	4
0%	87.5%	12.5%	5
0%	84.3%	15.7%	6
0%	84.3%	15.7%	7
0%	83.6%	16.4%	8
0%	83.6%	16.4%	9
0%	83.4%	16.6%	10
0%	83.4%	16.6%	11
0%	83.3%	16.7%	12
0%	83.3%	16.7%	13
0%	83.3%	16.7%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.1s (46.7%)

Results

1.1s	2088×	body	8192	exit
862.0ms	8256×	body	128	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify149.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

1355×	`fma-neg_binary64`
877×	`fma-def_binary64`
720×	`distribute-rgt-neg-in_binary64`
564×	`cancel-sign-sub-inv_binary64`
530×	`sqr-pow_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	21	11
2	49	11
3	107	11
4	170	11
5	291	11
6	516	11
7	1002	11
8	1492	11
9	2128	11
10	2734	11
11	3154	11
12	3358	11
13	3535	11
14	4106	11
15	3099	11
16	3528	11
17	4668	11
18	4732	11

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(.f64 x (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))
▶	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))

Status

Error

Program

0.2b

(*.f64 x (fma.f64 (*.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))

▶

0.2b

(-.f64 (*.f64 238732414637843/250000000000000 x) (*.f64 6450306886639899/50000000000000000 (*.f64 (*.f64 x x) x)))

Compiler

Compiled 62 to 40 computations (35.5% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
✓	0.1b	(.f64 (.f64 x x) x)
✓	0.1b	(*.f64 238732414637843/250000000000000 x)
✓	0.1b	(.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x))

series15.0ms (0.3%)

Counts

4 → 36

Calls

4 calls:

4.0ms	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
3.0ms	(.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x))
3.0ms	(.f64 (.f64 x x) x)
2.0ms	(*.f64 238732414637843/250000000000000 x)

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`pow1_binary64`
23×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`cbrt-unprod_binary64`

Counts

4 → 90

Calls

4 calls:

7.0ms	(.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x))
5.0ms	(.f64 (.f64 x x) x)
4.0ms	(*.f64 238732414637843/250000000000000 x)
3.0ms	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))

simplify78.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

926×	`fma-def_binary64`
402×	`fma-neg_binary64`
340×	`distribute-rgt-neg-in_binary64`
321×	`distribute-lft-neg-in_binary64`
303×	`cancel-sign-sub-inv_binary64`

Counts

126 → 123

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	118	1075
1	244	966
2	796	954
3	1898	929
4	4654	929
5	4817	929

prune124.0ms (2.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	113	10	123
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	114	11	125

Error

0.0b

Counts

125 → 11

Alt Table

Status	Error	Program
	0.3b	(-.f64 (.f64 (sqrt.f64 238732414637843/250000000000000) (.f64 (sqrt.f64 238732414637843/250000000000000) x)) (.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x)))
	33.6b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 (*.f64 x x) (sqrt.f64 x)) (sqrt.f64 x))))
	0.2b	(.f64 x (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))
	0.2b	(.f64 x (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))
	1.2b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 238732414637843/250000000000000 x)) (cbrt.f64 (.f64 238732414637843/250000000000000 x))) (cbrt.f64 (.f64 238732414637843/250000000000000 x))) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
	31.3b	(/.f64 (fma.f64 (pow.f64 x 6) -41606458931834106848498498730201/2500000000000000000000000000000000 (.f64 x (.f64 x 56993165798814994692847692649/62500000000000000000000000000))) (fma.f64 6450306886639899/50000000000000000 (pow.f64 x 3) (*.f64 x 238732414637843/250000000000000)))
	1.1b	(-.f64 (.f64 (.f64 238732414637843/250000000000000 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
	31.2b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 238732414637843/250000000000000 x) (.f64 238732414637843/250000000000000 x)) (.f64 238732414637843/250000000000000 x))) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
	0.4b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 (.f64 (cbrt.f64 (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x))) (cbrt.f64 (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))) (cbrt.f64 (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))))
	33.8b	(-.f64 (.f64 (.f64 (sqrt.f64 238732414637843/250000000000000) (sqrt.f64 x)) (.f64 (sqrt.f64 238732414637843/250000000000000) (sqrt.f64 x))) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
▶	0.2b	(fma.f64 238732414637843/250000000000000 x (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))

Compiler

Compiled 2270 to 1354 computations (40.4% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 238732414637843/250000000000000 x (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))
✓	0.1b	(*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000)

series7.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(fma.f64 238732414637843/250000000000000 x (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))
3.0ms	(*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000)

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
12×	`associate-l_binary64`
7×	`add-exp-log_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 43

Calls

2 calls:

4.0ms	(*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000)
0.0ms	(fma.f64 238732414637843/250000000000000 x (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))

simplify71.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

996×	`fma-def_binary64`
421×	`exp-prod_binary64`
402×	`log-prod_binary64`
287×	`cube-prod_binary64`
285×	`*-commutative_binary64`

Counts

67 → 67

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	72	698
1	130	663
2	484	663
3	1057	639
4	2821	633
5	4771	633
6	4929	633

prune70.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	69	9	78

Error

0.0b

Counts

78 → 9

Alt Table

Status	Error	Program
	1.2b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 238732414637843/250000000000000 x)) (cbrt.f64 (.f64 238732414637843/250000000000000 x))) (cbrt.f64 (.f64 238732414637843/250000000000000 x))) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
	31.3b	(/.f64 (fma.f64 (pow.f64 x 6) -41606458931834106848498498730201/2500000000000000000000000000000000 (.f64 x (.f64 x 56993165798814994692847692649/62500000000000000000000000000))) (fma.f64 6450306886639899/50000000000000000 (pow.f64 x 3) (*.f64 x 238732414637843/250000000000000)))
	1.1b	(-.f64 (.f64 (.f64 238732414637843/250000000000000 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
	31.2b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 238732414637843/250000000000000 x) (.f64 238732414637843/250000000000000 x)) (.f64 238732414637843/250000000000000 x))) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
	0.3b	(-.f64 (.f64 (sqrt.f64 238732414637843/250000000000000) (.f64 (sqrt.f64 238732414637843/250000000000000) x)) (.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x)))
▶	0.2b	(fma.f64 238732414637843/250000000000000 x (.f64 (.f64 x x) (*.f64 x -6450306886639899/50000000000000000)))
	33.8b	(-.f64 (.f64 (.f64 (sqrt.f64 238732414637843/250000000000000) (sqrt.f64 x)) (.f64 (sqrt.f64 238732414637843/250000000000000) (sqrt.f64 x))) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
	0.2b	(.f64 x (fma.f64 x (.f64 x -6450306886639899/50000000000000000) 238732414637843/250000000000000))
✓	0.2b	(fma.f64 238732414637843/250000000000000 x (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))

Compiler

Compiled 1163 to 881 computations (24.2% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 x -6450306886639899/50000000000000000)
✓	0.1b	(fma.f64 238732414637843/250000000000000 x (.f64 (.f64 x x) (*.f64 x -6450306886639899/50000000000000000)))
✓	0.1b	(.f64 (.f64 x x) (*.f64 x -6450306886639899/50000000000000000))

series8.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

3.0ms

(fma.f64 238732414637843/250000000000000 x (*.f64 (*.f64 x x) (*.f64 x -6450306886639899/50000000000000000)))

3.0ms

(*.f64 (*.f64 x x) (*.f64 x -6450306886639899/50000000000000000))

2.0ms

(*.f64 x -6450306886639899/50000000000000000)

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
17×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

3 → 54

Calls

3 calls:

5.0ms

(*.f64 (*.f64 x x) (*.f64 x -6450306886639899/50000000000000000))

3.0ms

(*.f64 x -6450306886639899/50000000000000000)

0.0ms

(fma.f64 238732414637843/250000000000000 x (*.f64 (*.f64 x x) (*.f64 x -6450306886639899/50000000000000000)))

simplify76.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1001×	`fma-def_binary64`
337×	`distribute-rgt-neg-out_binary64`
318×	`distribute-lft-neg-out_binary64`
296×	`unswap-sqr_binary64`
282×	`distribute-rgt-neg-in_binary64`

Counts

90 → 83

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	78	834
1	152	724
2	523	724
3	931	724
4	1972	709
5	4434	709
6	4873	709

prune73.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	83	9	92

Error

0.0b

Counts

92 → 9

Alt Table

Status	Error	Program
	1.2b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 238732414637843/250000000000000 x)) (cbrt.f64 (.f64 238732414637843/250000000000000 x))) (cbrt.f64 (.f64 238732414637843/250000000000000 x))) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
	31.3b	(/.f64 (fma.f64 (pow.f64 x 6) -41606458931834106848498498730201/2500000000000000000000000000000000 (.f64 x (.f64 x 56993165798814994692847692649/62500000000000000000000000000))) (fma.f64 6450306886639899/50000000000000000 (pow.f64 x 3) (*.f64 x 238732414637843/250000000000000)))
	1.1b	(-.f64 (.f64 (.f64 238732414637843/250000000000000 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
	0.2b	(fma.f64 238732414637843/250000000000000 x (.f64 (.f64 x x) (cbrt.f64 (pow.f64 (*.f64 -6450306886639899/50000000000000000 x) 3))))
▶	0.2b	(fma.f64 238732414637843/250000000000000 x (.f64 (.f64 x x) (.f64 1 (.f64 x -6450306886639899/50000000000000000))))
	31.2b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 238732414637843/250000000000000 x) (.f64 238732414637843/250000000000000 x)) (.f64 238732414637843/250000000000000 x))) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
	0.3b	(-.f64 (.f64 (sqrt.f64 238732414637843/250000000000000) (.f64 (sqrt.f64 238732414637843/250000000000000) x)) (.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x)))
	33.8b	(-.f64 (.f64 (.f64 (sqrt.f64 238732414637843/250000000000000) (sqrt.f64 x)) (.f64 (sqrt.f64 238732414637843/250000000000000) (sqrt.f64 x))) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
✓	0.2b	(fma.f64 238732414637843/250000000000000 x (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))

Compiler

Compiled 1500 to 933 computations (37.8% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(*.f64 x -6450306886639899/50000000000000000)
✓	0.1b	(fma.f64 238732414637843/250000000000000 x (.f64 (.f64 x x) (.f64 1 (.f64 x -6450306886639899/50000000000000000))))
✓	0.1b	(.f64 (.f64 x x) (.f64 1 (.f64 x -6450306886639899/50000000000000000)))

series6.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(fma.f64 238732414637843/250000000000000 x (.f64 (.f64 x x) (.f64 1 (.f64 x -6450306886639899/50000000000000000))))
3.0ms	(.f64 (.f64 x x) (.f64 1 (.f64 x -6450306886639899/50000000000000000)))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-exp-log_binary64`
27×	`prod-exp_binary64`
23×	`add-cbrt-cube_binary64`
23×	`pow1_binary64`
15×	`cbrt-unprod_binary64`

Counts

2 → 44

Calls

2 calls:

9.0ms	(.f64 (.f64 x x) (.f64 1 (.f64 x -6450306886639899/50000000000000000)))
0.0ms	(fma.f64 238732414637843/250000000000000 x (.f64 (.f64 x x) (.f64 1 (.f64 x -6450306886639899/50000000000000000))))

simplify87.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

587×	`fma-def_binary64`
476×	`neg-mul-1_binary64`
338×	`distribute-rgt-neg-out_binary64`
318×	`distribute-lft-neg-out_binary64`
269×	`unsub-neg_binary64`

Counts

68 → 61

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	76	894
1	150	634
2	473	634
3	820	634
4	1785	634
5	4241	634
6	4996	634
7	4865	634

prune77.0ms (1.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	91	9	100

Error

0.0b

Counts

100 → 9

Alt Table

Status	Error	Program
	1.2b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 238732414637843/250000000000000 x)) (cbrt.f64 (.f64 238732414637843/250000000000000 x))) (cbrt.f64 (.f64 238732414637843/250000000000000 x))) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
	31.3b	(/.f64 (fma.f64 (pow.f64 x 6) -41606458931834106848498498730201/2500000000000000000000000000000000 (.f64 x (.f64 x 56993165798814994692847692649/62500000000000000000000000000))) (fma.f64 6450306886639899/50000000000000000 (pow.f64 x 3) (*.f64 x 238732414637843/250000000000000)))
	1.1b	(-.f64 (.f64 (.f64 238732414637843/250000000000000 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
	0.2b	(fma.f64 238732414637843/250000000000000 x (.f64 (.f64 x x) (cbrt.f64 (pow.f64 (*.f64 -6450306886639899/50000000000000000 x) 3))))
✓	0.2b	(fma.f64 238732414637843/250000000000000 x (.f64 (.f64 x x) (.f64 1 (.f64 x -6450306886639899/50000000000000000))))
	31.2b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 238732414637843/250000000000000 x) (.f64 238732414637843/250000000000000 x)) (.f64 238732414637843/250000000000000 x))) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
	0.3b	(-.f64 (.f64 (sqrt.f64 238732414637843/250000000000000) (.f64 (sqrt.f64 238732414637843/250000000000000) x)) (.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x)))
	33.8b	(-.f64 (.f64 (.f64 (sqrt.f64 238732414637843/250000000000000) (sqrt.f64 x)) (.f64 (sqrt.f64 238732414637843/250000000000000) (sqrt.f64 x))) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
✓	0.2b	(fma.f64 238732414637843/250000000000000 x (*.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))

Compiler

Compiled 1681 to 1084 computations (35.5% saved)

regimes115.0ms (2.6%)

Accuracy

Total 0.1b remaining (79%)

Threshold costs 0.1b (79%)

Counts

53 → 1

Compiler

Compiled 1672 to 1192 computations (28.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	10	14
2	10	14

end130.0ms (2.9%)

Compiler: Compiled 177 to 124 computations (29.9% saved)

Details

analyze1.2s (27.3%)

sample2.1s (46.7%)

simplify149.0ms (3.3%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series15.0ms (0.3%)

rewrite23.0ms (0.5%)

simplify78.0ms (1.7%)

prune124.0ms (2.8%)

localize5.0ms (0.1%)

series7.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify71.0ms (1.6%)

prune70.0ms (1.6%)

localize7.0ms (0.1%)

series8.0ms (0.2%)

rewrite11.0ms (0.2%)

simplify76.0ms (1.7%)

prune73.0ms (1.6%)

localize7.0ms (0.2%)

series6.0ms (0.1%)

rewrite13.0ms (0.3%)

simplify87.0ms (1.9%)

prune77.0ms (1.7%)

regimes115.0ms (2.6%)

simplify2.0ms (0%)

end130.0ms (2.9%)

Profiling