Details

analyze5.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
62.5%	12.5%	25%	5
62.5%	6.2%	31.3%	6
65.6%	3.1%	31.3%	7
65.6%	1.6%	32.8%	8
66.4%	0.8%	32.8%	9
66.4%	0.4%	33.2%	10
66.6%	0.2%	33.2%	11
66.6%	0.1%	33.3%	12
66.6%	0%	33.3%	13
66.6%	0%	33.3%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample1.0s (44.4%)

Results

854.0ms

8256×

body

128

valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify147.0ms (6.4%)

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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(.f64 x (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))
	0.5b	(-.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))

0.5b

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

Compiler

Compiled 62 to 40 computations (35.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (*.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000)
✓	0.2b	(.f64 x (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))

series6.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

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

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

3.0ms	(.f64 x (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))
0.0ms	(fma.f64 (*.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000)

simplify41.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

907×	`distribute-rgt-in_binary64`
906×	`distribute-lft-in_binary64`
386×	`fma-def_binary64`
240×	`associate-l_binary64`
199×	`associate-r_binary64`

Counts

56 → 64

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	54	716
1	106	613
2	301	613
3	1063	613
4	5380	613

prune46.0ms (2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	59	5	64
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	61	5	66

Error

0.0b

Counts

66 → 5

Alt Table

Status	Error	Program
	32.8b	(.f64 (sqrt.f64 (.f64 x (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))) (sqrt.f64 (.f64 x (fma.f64 (*.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))
▶	0.2b	(.f64 x (-.f64 238732414637843/250000000000000 (.f64 6450306886639899/50000000000000000 (pow.f64 x 2))))
	0.4b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
	15.7b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))))
	33.1b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 (*.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000)))

Compiler

Compiled 958 to 573 computations (40.2% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 238732414637843/250000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 2)))
✓	0.2b	(.f64 x (-.f64 238732414637843/250000000000000 (.f64 6450306886639899/50000000000000000 (pow.f64 x 2))))
✓	0.2b	(*.f64 6450306886639899/50000000000000000 (pow.f64 x 2))

series9.0ms (0.4%)

Counts

3 → 15

Calls

3 calls:

4.0ms

(*.f64 x (-.f64 238732414637843/250000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 2))))

3.0ms

(*.f64 6450306886639899/50000000000000000 (pow.f64 x 2))

3.0ms

(-.f64 238732414637843/250000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 2)))

rewrite15.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
11×	`associate-r_binary64`
10×	`add-exp-log_binary64`

Counts

3 → 81

Calls

3 calls:

4.0ms

(*.f64 x (-.f64 238732414637843/250000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 2))))

4.0ms

(*.f64 6450306886639899/50000000000000000 (pow.f64 x 2))

3.0ms

(-.f64 238732414637843/250000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 2)))

simplify62.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

795×	`distribute-rgt-in_binary64`
737×	`distribute-lft-in_binary64`
584×	`fma-def_binary64`
209×	`*-commutative_binary64`
173×	`unswap-sqr_binary64`

Counts

96 → 136

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	1460
1	251	1152
2	731	1029
3	1675	1002
4	5249	1002

prune123.0ms (5.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	133	3	136
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	135	6	141

Error

Counts

141 → 6

Alt Table

Status	Error	Program
	0.4b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
	6.0b	(/.f64 (.f64 x (fma.f64 (pow.f64 x 4) -41606458931834106848498498730201/2500000000000000000000000000000000 56993165798814994692847692649/62500000000000000000000000000)) (+.f64 238732414637843/250000000000000 (.f64 6450306886639899/50000000000000000 (pow.f64 x 2))))
	8.8b	(/.f64 (.f64 x (-.f64 (pow.f64 238732414637843/250000000000000 3) (pow.f64 (.f64 6450306886639899/50000000000000000 (pow.f64 x 2)) 3))) (+.f64 (.f64 238732414637843/250000000000000 238732414637843/250000000000000) (+.f64 (.f64 (.f64 6450306886639899/50000000000000000 (pow.f64 x 2)) (.f64 6450306886639899/50000000000000000 (pow.f64 x 2))) (.f64 238732414637843/250000000000000 (.f64 6450306886639899/50000000000000000 (pow.f64 x 2))))))
▶	0.3b	(.f64 x (-.f64 238732414637843/250000000000000 (.f64 (.f64 x (sqrt.f64 6450306886639899/50000000000000000)) (.f64 x (sqrt.f64 6450306886639899/50000000000000000)))))
✓	0.2b	(.f64 x (-.f64 238732414637843/250000000000000 (.f64 6450306886639899/50000000000000000 (pow.f64 x 2))))
	33.1b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 (*.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000)))

Compiler

Compiled 2287 to 1730 computations (24.4% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 238732414637843/250000000000000 (.f64 (.f64 x (sqrt.f64 6450306886639899/50000000000000000)) (*.f64 x (sqrt.f64 6450306886639899/50000000000000000))))
✓	0.2b	(.f64 x (-.f64 238732414637843/250000000000000 (.f64 (.f64 x (sqrt.f64 6450306886639899/50000000000000000)) (.f64 x (sqrt.f64 6450306886639899/50000000000000000)))))
✓	0.4b	(.f64 (.f64 x (sqrt.f64 6450306886639899/50000000000000000)) (*.f64 x (sqrt.f64 6450306886639899/50000000000000000)))
✓	0.4b	(*.f64 x (sqrt.f64 6450306886639899/50000000000000000))

series34.0ms (1.5%)

Counts

4 → 48

Calls

4 calls:

13.0ms	(.f64 x (-.f64 238732414637843/250000000000000 (.f64 (.f64 x (sqrt.f64 6450306886639899/50000000000000000)) (.f64 x (sqrt.f64 6450306886639899/50000000000000000)))))
8.0ms	(.f64 (.f64 x (sqrt.f64 6450306886639899/50000000000000000)) (*.f64 x (sqrt.f64 6450306886639899/50000000000000000)))
8.0ms	(-.f64 238732414637843/250000000000000 (.f64 (.f64 x (sqrt.f64 6450306886639899/50000000000000000)) (*.f64 x (sqrt.f64 6450306886639899/50000000000000000))))
4.0ms	(*.f64 x (sqrt.f64 6450306886639899/50000000000000000))

rewrite26.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`pow1_binary64`
21×	`add-sqr-sqrt_binary64`
20×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`
19×	`pow-prod-down_binary64`

Counts

4 → 114

Calls

4 calls:

6.0ms	(.f64 (.f64 x (sqrt.f64 6450306886639899/50000000000000000)) (*.f64 x (sqrt.f64 6450306886639899/50000000000000000)))
5.0ms	(*.f64 x (sqrt.f64 6450306886639899/50000000000000000))
5.0ms	(.f64 x (-.f64 238732414637843/250000000000000 (.f64 (.f64 x (sqrt.f64 6450306886639899/50000000000000000)) (.f64 x (sqrt.f64 6450306886639899/50000000000000000)))))
3.0ms	(-.f64 238732414637843/250000000000000 (.f64 (.f64 x (sqrt.f64 6450306886639899/50000000000000000)) (*.f64 x (sqrt.f64 6450306886639899/50000000000000000))))

simplify137.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

939×	`fma-def_binary64`
378×	`distribute-rgt-neg-in_binary64`
335×	`unswap-sqr_binary64`
288×	`*-commutative_binary64`
276×	`fma-neg_binary64`

Counts

162 → 168

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	143	1834
1	290	1598
2	974	1469
3	2363	1434
4	4903	1434
5	4710	1434

prune179.0ms (7.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	200	1	201
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	201	6	207

Error

Counts

207 → 6

Alt Table

Status	Error	Program
	6.0b	(/.f64 (.f64 x (fma.f64 (pow.f64 x 4) -41606458931834106848498498730201/2500000000000000000000000000000000 56993165798814994692847692649/62500000000000000000000000000)) (+.f64 238732414637843/250000000000000 (.f64 6450306886639899/50000000000000000 (pow.f64 x 2))))
	8.8b	(/.f64 (.f64 x (-.f64 (pow.f64 238732414637843/250000000000000 3) (pow.f64 (.f64 6450306886639899/50000000000000000 (pow.f64 x 2)) 3))) (+.f64 (.f64 238732414637843/250000000000000 238732414637843/250000000000000) (+.f64 (.f64 (.f64 6450306886639899/50000000000000000 (pow.f64 x 2)) (.f64 6450306886639899/50000000000000000 (pow.f64 x 2))) (.f64 238732414637843/250000000000000 (.f64 6450306886639899/50000000000000000 (pow.f64 x 2))))))
✓	0.3b	(.f64 x (-.f64 238732414637843/250000000000000 (.f64 (.f64 x (sqrt.f64 6450306886639899/50000000000000000)) (.f64 x (sqrt.f64 6450306886639899/50000000000000000)))))
✓	0.2b	(.f64 x (-.f64 238732414637843/250000000000000 (.f64 6450306886639899/50000000000000000 (pow.f64 x 2))))
	33.1b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 (*.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000)))
▶	0.4b	(fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 x 238732414637843/250000000000000))

Compiler

Compiled 3933 to 3043 computations (22.6% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 x 238732414637843/250000000000000)
✓	0.3b	(fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 x 238732414637843/250000000000000))

series6.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 x 238732414637843/250000000000000))
1.0ms	(*.f64 x 238732414637843/250000000000000)

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

3.0ms	(*.f64 x 238732414637843/250000000000000)
0.0ms	(fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 x 238732414637843/250000000000000))

simplify61.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

714×	`fma-def_binary64`
600×	`distribute-rgt-in_binary64`
563×	`distribute-lft-in_binary64`
228×	`times-frac_binary64`
218×	`exp-prod_binary64`

Counts

54 → 51

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	54	488
1	92	435
2	229	435
3	580	435
4	1300	435
5	4704	435
6	5233	435

prune43.0ms (1.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	51	6	57

Error

Counts

57 → 6

Alt Table

Status	Error	Program
	6.0b	(/.f64 (.f64 x (fma.f64 (pow.f64 x 4) -41606458931834106848498498730201/2500000000000000000000000000000000 56993165798814994692847692649/62500000000000000000000000000)) (+.f64 238732414637843/250000000000000 (.f64 6450306886639899/50000000000000000 (pow.f64 x 2))))
	8.8b	(/.f64 (.f64 x (-.f64 (pow.f64 238732414637843/250000000000000 3) (pow.f64 (.f64 6450306886639899/50000000000000000 (pow.f64 x 2)) 3))) (+.f64 (.f64 238732414637843/250000000000000 238732414637843/250000000000000) (+.f64 (.f64 (.f64 6450306886639899/50000000000000000 (pow.f64 x 2)) (.f64 6450306886639899/50000000000000000 (pow.f64 x 2))) (.f64 238732414637843/250000000000000 (.f64 6450306886639899/50000000000000000 (pow.f64 x 2))))))
✓	0.3b	(.f64 x (-.f64 238732414637843/250000000000000 (.f64 (.f64 x (sqrt.f64 6450306886639899/50000000000000000)) (.f64 x (sqrt.f64 6450306886639899/50000000000000000)))))
✓	0.2b	(.f64 x (-.f64 238732414637843/250000000000000 (.f64 6450306886639899/50000000000000000 (pow.f64 x 2))))
	33.1b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 (*.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000)))
✓	0.4b	(fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 x 238732414637843/250000000000000))

Compiler

Compiled 732 to 558 computations (23.8% saved)

regimes151.0ms (6.5%)

Accuracy

Total 0.2b remaining (92.2%)

Threshold costs 0.2b (92.2%)

Counts

73 → 1

Compiler

Compiled 2112 to 1580 computations (25.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`distribute-lft-neg-in_binary64`
2×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	17	13
2	25	13
3	29	13
4	32	13
5	33	13
6	32	13

end159.0ms (6.9%)

Compiler: Compiled 121 to 97 computations (19.8% saved)

Details

analyze5.0ms (0.2%)

sample1.0s (44.4%)

simplify147.0ms (6.4%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series6.0ms (0.3%)

rewrite4.0ms (0.2%)

simplify41.0ms (1.8%)

prune46.0ms (2%)

localize5.0ms (0.2%)

series9.0ms (0.4%)

rewrite15.0ms (0.6%)

simplify62.0ms (2.7%)

prune123.0ms (5.3%)

localize7.0ms (0.3%)

series34.0ms (1.5%)

rewrite26.0ms (1.1%)

simplify137.0ms (5.9%)

prune179.0ms (7.7%)

localize5.0ms (0.2%)

series6.0ms (0.3%)

rewrite4.0ms (0.2%)

simplify61.0ms (2.7%)

prune43.0ms (1.8%)

regimes151.0ms (6.5%)

simplify3.0ms (0.1%)

end159.0ms (6.9%)

Profiling