Details

analyze162.0ms (8.2%)

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)

sample16.0ms (0.8%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 26 to 18 computations (30.8% saved)

simplify152.0ms (7.7%)

Algorithm

1×	egg-herbie

Rules

749×	`distribute-rgt-neg-in_binary64`
699×	`cube-prod_binary64`
690×	`sqr-pow_binary64`
575×	`cancel-sign-sub-inv_binary64`
556×	`distribute-lft-neg-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	20	13
2	47	13
3	97	13
4	139	13
5	233	13
6	390	13
7	813	13
8	1208	13
9	1810	13
10	2073	13
11	2193	13
12	2400	13
13	2596	13
14	2784	13
15	2281	13
16	2880	13
17	3866	13
18	4751	13
19	4816	13

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (.f64 2150310427208497/2251799813685248 x) (.f64 4647935950575487/36028797018963968 (.f64 (.f64 x x) x)))

Compiler

Compiled 34 to 24 computations (29.4% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b

(-.f64 (*.f64 2150310427208497/2251799813685248 x) (*.f64 4647935950575487/36028797018963968 (*.f64 (*.f64 x x) x)))

0.1b

(*.f64 (*.f64 x x) x)

0.2b

(*.f64 4647935950575487/36028797018963968 (*.f64 (*.f64 x x) x))

rewrite64.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

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

Counts

3 → 62

Calls

3 calls:

7.0ms

(*.f64 4647935950575487/36028797018963968 (*.f64 (*.f64 x x) x))

4.0ms

(*.f64 (*.f64 x x) x)

3.0ms

(-.f64 (*.f64 2150310427208497/2251799813685248 x) (*.f64 4647935950575487/36028797018963968 (*.f64 (*.f64 x x) x)))

Compiler

Compiled 866 to 441 computations (49.1% saved)

series22.0ms (1.1%)

Error

0.1b

Counts

3 → 12

Calls

3 calls:

10.0ms

(-.f64 (*.f64 2150310427208497/2251799813685248 x) (*.f64 4647935950575487/36028797018963968 (*.f64 (*.f64 x x) x)))

6.0ms

(*.f64 4647935950575487/36028797018963968 (*.f64 (*.f64 x x) x))

5.0ms

(*.f64 (*.f64 x x) x)

Compiler

Compiled 214 to 171 computations (20.1% saved)

simplify88.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

460×	`times-frac_binary64`
433×	`cancel-sign-sub-inv_binary64`
336×	`*-commutative_binary64`
311×	`distribute-rgt-neg-in_binary64`
293×	`distribute-lft-neg-in_binary64`

Counts

74 → 55

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	85	722
1	191	624
2	642	614
3	1427	593
4	3109	593
5	4801	593
6	5408	593

prune29.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	50	5	55
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	50	6	56

Error

0.0b

Counts

56 → 6

Alt Table

Status	Error	Program
	18.4b	(-.f64 (.f64 2150310427208497/2251799813685248 x) (.f64 (sqrt.f64 (.f64 4647935950575487/36028797018963968 (pow.f64 x 3))) (sqrt.f64 (.f64 4647935950575487/36028797018963968 (pow.f64 x 3)))))
	0.2b	(-.f64 (.f64 2150310427208497/2251799813685248 x) (.f64 (sqrt.f64 4647935950575487/36028797018963968) (*.f64 (pow.f64 x 3) (sqrt.f64 4647935950575487/36028797018963968))))
▶	0.1b	(-.f64 (.f64 x 2150310427208497/2251799813685248) (.f64 4647935950575487/36028797018963968 (pow.f64 x 3)))
✓	0.1b	(-.f64 (.f64 2150310427208497/2251799813685248 x) (.f64 4647935950575487/36028797018963968 (.f64 (.f64 x x) x)))
	32.4b	(-.f64 (.f64 2150310427208497/2251799813685248 x) (.f64 4647935950575487/36028797018963968 (*.f64 (pow.f64 x 3/2) (pow.f64 x 3/2))))
	29.6b	(/.f64 (+.f64 (.f64 x (.f64 x 4623834933361588875239908999009/5070602400912917605986812821504)) (.f64 (pow.f64 x 6) -21603308600652055932446485287169/1298074214633706907132624082305024)) (+.f64 (.f64 4647935950575487/36028797018963968 (pow.f64 x 3)) (*.f64 x 2150310427208497/2251799813685248)))

Compiler

Compiled 564 to 447 computations (20.7% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (.f64 x 2150310427208497/2251799813685248) (.f64 4647935950575487/36028797018963968 (pow.f64 x 3)))
0.2b	(*.f64 4647935950575487/36028797018963968 (pow.f64 x 3))

rewrite42.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

13×	`add-sqr-sqrt_binary64`
12×	`associate-r_binary64`
7×	`add-exp-log_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 43

Calls

2 calls:

6.0ms	(*.f64 4647935950575487/36028797018963968 (pow.f64 x 3))
3.0ms	(-.f64 (.f64 x 2150310427208497/2251799813685248) (.f64 4647935950575487/36028797018963968 (pow.f64 x 3)))

Compiler

Compiled 613 to 492 computations (19.7% saved)

series16.0ms (0.8%)

Error

0.0b

Counts

2 → 9

Calls

2 calls:

9.0ms	(-.f64 (.f64 x 2150310427208497/2251799813685248) (.f64 4647935950575487/36028797018963968 (pow.f64 x 3)))
6.0ms	(*.f64 4647935950575487/36028797018963968 (pow.f64 x 3))

Compiler

Compiled 163 to 130 computations (20.2% saved)

simplify85.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

428×	`unswap-sqr_binary64`
422×	`cancel-sign-sub-inv_binary64`
379×	`times-frac_binary64`
289×	`exp-prod_binary64`
286×	`*-commutative_binary64`

Counts

52 → 34

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	83	660
1	179	602
2	550	596
3	1243	596
4	3126	566
5	4459	566
6	5020	566

prune21.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	33	1	34
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	35	5	40

Error

0.0b

Counts

40 → 5

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (.f64 x 2150310427208497/2251799813685248) (.f64 (.f64 4647935950575487/36028797018963968 (.f64 x x)) (cbrt.f64 (pow.f64 x 3))))
	0.2b	(-.f64 (.f64 2150310427208497/2251799813685248 x) (.f64 (sqrt.f64 4647935950575487/36028797018963968) (*.f64 (pow.f64 x 3) (sqrt.f64 4647935950575487/36028797018963968))))
✓	0.1b	(-.f64 (.f64 2150310427208497/2251799813685248 x) (.f64 4647935950575487/36028797018963968 (.f64 (.f64 x x) x)))
	32.4b	(-.f64 (.f64 2150310427208497/2251799813685248 x) (.f64 4647935950575487/36028797018963968 (*.f64 (pow.f64 x 3/2) (pow.f64 x 3/2))))
	29.6b	(/.f64 (+.f64 (.f64 x (.f64 x 4623834933361588875239908999009/5070602400912917605986812821504)) (.f64 (pow.f64 x 6) -21603308600652055932446485287169/1298074214633706907132624082305024)) (+.f64 (.f64 4647935950575487/36028797018963968 (pow.f64 x 3)) (*.f64 x 2150310427208497/2251799813685248)))

Compiler

Compiled 395 to 305 computations (22.8% saved)

localize10.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 x 2150310427208497/2251799813685248) (.f64 (.f64 4647935950575487/36028797018963968 (.f64 x x)) (cbrt.f64 (pow.f64 x 3))))
0.1b	(.f64 (.f64 4647935950575487/36028797018963968 (*.f64 x x)) (cbrt.f64 (pow.f64 x 3)))
0.1b	(.f64 4647935950575487/36028797018963968 (.f64 x x))
27.7b	(cbrt.f64 (pow.f64 x 3))

rewrite102.0ms (5.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

24×	`cbrt-prod_binary64`
18×	`add-exp-log_binary64`
18×	`pow1_binary64`
16×	`associate-r_binary64`
15×	`add-cbrt-cube_binary64`

Counts

4 → 85

Calls

4 calls:

10.0ms	(.f64 (.f64 4647935950575487/36028797018963968 (*.f64 x x)) (cbrt.f64 (pow.f64 x 3)))
4.0ms	(.f64 4647935950575487/36028797018963968 (.f64 x x))
3.0ms	(-.f64 (.f64 x 2150310427208497/2251799813685248) (.f64 (.f64 4647935950575487/36028797018963968 (.f64 x x)) (cbrt.f64 (pow.f64 x 3))))
2.0ms	(cbrt.f64 (pow.f64 x 3))

Compiler

Compiled 1582 to 1048 computations (33.8% saved)

series41.0ms (2%)

Error

Counts

4 → 15

Calls

4 calls:

15.0ms	(-.f64 (.f64 x 2150310427208497/2251799813685248) (.f64 (.f64 4647935950575487/36028797018963968 (.f64 x x)) (cbrt.f64 (pow.f64 x 3))))
8.0ms	(.f64 (.f64 4647935950575487/36028797018963968 (*.f64 x x)) (cbrt.f64 (pow.f64 x 3)))
6.0ms	(.f64 4647935950575487/36028797018963968 (.f64 x x))
6.0ms	(cbrt.f64 (pow.f64 x 3))

Compiler

Compiled 423 to 331 computations (21.7% saved)

simplify165.0ms (8.3%)

Algorithm

1×	egg-herbie

Rules

489×	`exp-prod_binary64`
349×	`unswap-sqr_binary64`
282×	`log-prod_binary64`
264×	`associate-l_binary64`
263×	`cube-prod_binary64`

Counts

100 → 76

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	129	1018
1	276	928
2	1278	919
3	3332	894
4	4419	877
5	5091	877

prune38.0ms (1.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	1	2	3
Picked	0	1	1
Done	1	0	1
Total	76	5	81

Error

Counts

81 → 5

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (.f64 x 2150310427208497/2251799813685248) (.f64 (.f64 4647935950575487/36028797018963968 (.f64 x x)) (cbrt.f64 (pow.f64 x 3))))
	0.1b	(-.f64 (.f64 x 2150310427208497/2251799813685248) (.f64 (.f64 4647935950575487/36028797018963968 (.f64 x x)) (*.f64 1 x)))
▶	0.1b	(-.f64 (.f64 x 2150310427208497/2251799813685248) (pow.f64 (.f64 4647935950575487/36028797018963968 (pow.f64 x 3)) 1))
	32.4b	(-.f64 (.f64 2150310427208497/2251799813685248 x) (.f64 4647935950575487/36028797018963968 (*.f64 (pow.f64 x 3/2) (pow.f64 x 3/2))))
	29.6b	(/.f64 (+.f64 (.f64 x (.f64 x 4623834933361588875239908999009/5070602400912917605986812821504)) (.f64 (pow.f64 x 6) -21603308600652055932446485287169/1298074214633706907132624082305024)) (+.f64 (.f64 4647935950575487/36028797018963968 (pow.f64 x 3)) (*.f64 x 2150310427208497/2251799813685248)))

Compiler

Compiled 751 to 560 computations (25.4% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (.f64 x 2150310427208497/2251799813685248) (pow.f64 (.f64 4647935950575487/36028797018963968 (pow.f64 x 3)) 1))
0.2b	(*.f64 4647935950575487/36028797018963968 (pow.f64 x 3))

rewrite51.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

14×	`add-sqr-sqrt_binary64`
12×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`
7×	`add-exp-log_binary64`

Counts

2 → 47

Calls

2 calls:

5.0ms	(*.f64 4647935950575487/36028797018963968 (pow.f64 x 3))
5.0ms	(-.f64 (.f64 x 2150310427208497/2251799813685248) (pow.f64 (.f64 4647935950575487/36028797018963968 (pow.f64 x 3)) 1))

Compiler

Compiled 800 to 667 computations (16.6% saved)

series18.0ms (0.9%)

Error

Counts

2 → 9

Calls

2 calls:

10.0ms	(-.f64 (.f64 x 2150310427208497/2251799813685248) (pow.f64 (.f64 4647935950575487/36028797018963968 (pow.f64 x 3)) 1))
6.0ms	(*.f64 4647935950575487/36028797018963968 (pow.f64 x 3))

Compiler

Compiled 177 to 144 computations (18.6% saved)

simplify89.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

351×	`exp-prod_binary64`
344×	`*-commutative_binary64`
289×	`sqr-pow_binary64`
283×	`distribute-rgt-neg-in_binary64`
276×	`distribute-lft-neg-in_binary64`

Counts

56 → 42

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	104	688
1	206	630
2	662	624
3	1423	624
4	3417	594
5	4674	594
6	4852	594

prune21.0ms (1.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	42	5	47

Error

Counts

47 → 5

Alt Table

Status	Error	Program
	0.1b	(-.f64 (.f64 x 2150310427208497/2251799813685248) (.f64 (.f64 4647935950575487/36028797018963968 (.f64 x x)) (cbrt.f64 (pow.f64 x 3))))
	0.1b	(-.f64 (.f64 x 2150310427208497/2251799813685248) (.f64 (.f64 4647935950575487/36028797018963968 (.f64 x x)) (*.f64 1 x)))
	0.1b	(-.f64 (.f64 x 2150310427208497/2251799813685248) (pow.f64 (.f64 4647935950575487/36028797018963968 (pow.f64 x 3)) 1))
	32.4b	(-.f64 (.f64 2150310427208497/2251799813685248 x) (.f64 4647935950575487/36028797018963968 (*.f64 (pow.f64 x 3/2) (pow.f64 x 3/2))))
	29.6b	(/.f64 (+.f64 (.f64 x (.f64 x 4623834933361588875239908999009/5070602400912917605986812821504)) (.f64 (pow.f64 x 6) -21603308600652055932446485287169/1298074214633706907132624082305024)) (+.f64 (.f64 4647935950575487/36028797018963968 (pow.f64 x 3)) (*.f64 x 2150310427208497/2251799813685248)))

Compiler

Compiled 427 to 339 computations (20.6% saved)

regimes186.0ms (9.4%)

Accuracy

Total 0.1b remaining (84.3%)

Threshold costs 0.1b (84.3%)

Compiler

Compiled 2630 to 1922 computations (26.9% saved)

simplify4.0ms (0.2%)

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	11	13
1	17	13
2	28	13
3	32	13
4	35	13
5	36	13
6	34	13

end1.0ms (0%)

Compiler: Compiled 10 to 8 computations (20% saved)

sample543.0ms (27.4%)

Algorithm

1×

intervals

Results

296.0ms	8000×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 101 to 77 computations (23.8% saved)

Details

analyze162.0ms (8.2%)

sample16.0ms (0.8%)

simplify152.0ms (7.7%)

prune3.0ms (0.1%)

localize6.0ms (0.3%)

rewrite64.0ms (3.2%)

series22.0ms (1.1%)

simplify88.0ms (4.4%)

prune29.0ms (1.5%)

localize5.0ms (0.2%)

rewrite42.0ms (2.1%)

series16.0ms (0.8%)

simplify85.0ms (4.3%)

prune21.0ms (1%)

localize10.0ms (0.5%)

rewrite102.0ms (5.1%)

series41.0ms (2%)

simplify165.0ms (8.3%)

prune38.0ms (1.9%)

localize7.0ms (0.3%)

rewrite51.0ms (2.6%)

series18.0ms (0.9%)

simplify89.0ms (4.5%)

prune21.0ms (1.1%)

regimes186.0ms (9.4%)

simplify4.0ms (0.2%)

end1.0ms (0%)

sample543.0ms (27.4%)

Profiling