Details

analyze95.0ms (1.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample28.0ms (0.5%)

Algorithm

1×

intervals

Results

8.0ms	39×	body	512	valid
7.0ms	57×	body	1024	valid
5.0ms	141×	body	128	valid
1.0ms	6×	body	2048	valid
1.0ms	13×	body	256	valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify78.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

335×	`div-sub_binary64`
178×	`associate-/l*_binary64`
162×	`sub-neg_binary64`
146×	`times-frac_binary64`
139×	`cancel-sign-sub-inv_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	33	19
4	55	19
5	85	19
6	165	19
7	242	19
8	538	19
9	578	19
10	658	19
11	835	19
12	780	19
13	770	19
14	764	19
15	766	19
16	768	19
17	770	19
18	770	19
19	681	19

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

28.6b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	28.6b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 28 to 20 computations (28.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
2.8b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite190.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

28.1b

Rules

130×	`*-un-lft-identity_binary64`
76×	`times-frac_binary64`
75×	`add-sqr-sqrt_binary64`
34×	`cancel-sign-sub-inv_binary64`
27×	`add-cube-cbrt_binary64`

Counts

2 → 114

Calls

2 calls:

43.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
8.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

Compiler

Compiled 1887 to 1386 computations (26.6% saved)

series47.0ms (0.8%)

Error

0.0b

Counts

2 → 24

Calls

2 calls:

15.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
14.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

Compiler

Compiled 600 to 488 computations (18.7% saved)

simplify119.0ms (2%)

Algorithm

1×	egg-herbie

Rules

448×	`associate-/l*_binary64`
442×	`div-sub_binary64`
392×	`times-frac_binary64`
323×	`distribute-rgt-in_binary64`
299×	`associate-*l/_binary64`

Counts

138 → 128

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	194	2893
1	551	2776
2	1689	2527
3	4197	2527
4	5295	2527

prune75.0ms (1.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	125	3	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	126	3	129

Error

0.0b

Counts

129 → 3

Alt Table

Status	Error	Program
▶	28.6b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)) (+.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (/.f64 (+.f64 x (.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))))
	28.6b	(-.f64 (/.f64 x (+.f64 x 1)) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)))
	32.8b	(-.f64 (-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x))) (+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 4))))

Compiler

Compiled 1458 to 1052 computations (27.8% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x)))
0.0b	(pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)
0.1b	(pow.f64 (/.f64 x (+.f64 1 x)) 3)
2.7b	(-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3))

rewrite590.0ms (9.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

411×	`*-un-lft-identity_binary64`
256×	`times-frac_binary64`
211×	`add-sqr-sqrt_binary64`
130×	`cube-prod_binary64`
130×	`unpow-prod-down_binary64`

Counts

4 → 360

Calls

4 calls:

118.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3))
22.0ms	(*.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x)))
11.0ms	(pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)
7.0ms	(pow.f64 (/.f64 x (+.f64 1 x)) 3)

Compiler

Compiled 11507 to 8421 computations (26.8% saved)

series140.0ms (2.3%)

Error

0.0b

Counts

4 → 48

Calls

4 calls:

28.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3))
21.0ms	(pow.f64 (/.f64 x (+.f64 1 x)) 3)
21.0ms	(pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)
20.0ms	(*.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x)))

Compiler

Compiled 3884 to 2936 computations (24.4% saved)

simplify259.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

443×	`associate-l_binary64`
313×	`associate-*l/_binary64`
310×	`associate-*r/_binary64`
234×	`associate-/l*_binary64`
149×	`sqr-pow_binary64`

Counts

408 → 302

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	450	10458
1	1382	9536
2	4868	9536
3	5027	9536

prune241.0ms (4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	300	2	302
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	300	5	305

Error

0.0b

Counts

305 → 5

Alt Table

Status	Error	Program
	33.1b	(/.f64 (+.f64 (/.f64 -9 x) (/.f64 -12 (.f64 x x))) (+.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (/.f64 (+.f64 x (*.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))))
▶	28.6b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (cbrt.f64 (pow.f64 (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3) 3))) (+.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (/.f64 (+.f64 x (.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))))
✓	28.6b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)) (+.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (/.f64 (+.f64 x (.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))))
	28.6b	(-.f64 (/.f64 x (+.f64 x 1)) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)))
	32.8b	(-.f64 (-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x))) (+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 4))))

Compiler

Compiled 7653 to 5553 computations (27.4% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)
0.0b	(pow.f64 (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3) 3)
0.1b	(pow.f64 (/.f64 x (+.f64 1 x)) 3)
2.7b	(-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (cbrt.f64 (pow.f64 (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3) 3)))

rewrite991.0ms (16.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

370×	`add-sqr-sqrt_binary64`
354×	`cube-prod_binary64`
354×	`unpow-prod-down_binary64`
323×	`*-un-lft-identity_binary64`
278×	`times-frac_binary64`

Counts

4 → 493

Calls

4 calls:

241.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (cbrt.f64 (pow.f64 (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3) 3)))
233.0ms	(pow.f64 (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3) 3)
11.0ms	(pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)
7.0ms	(pow.f64 (/.f64 x (+.f64 1 x)) 3)

Compiler

Compiled 11932 to 9088 computations (23.8% saved)

series159.0ms (2.6%)

Error

0.0b

Counts

4 → 48

Calls

4 calls:

35.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (cbrt.f64 (pow.f64 (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3) 3)))
23.0ms	(pow.f64 (/.f64 x (+.f64 1 x)) 3)
23.0ms	(pow.f64 (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3) 3)
21.0ms	(pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)

Compiler

Compiled 4305 to 3275 computations (23.9% saved)

simplify314.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

410×	`associate-l_binary64`
221×	`sqr-pow_binary64`
218×	`associate-*r/_binary64`
215×	`associate-*l/_binary64`
126×	`cancel-sign-sub-inv_binary64`

Counts

541 → 466

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	534	16474
1	1491	15503
2	4984	15503

prune228.0ms (3.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	466	0	466
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	466	5	471

Error

0.0b

Counts

471 → 5

Alt Table

Status	Error	Program
	33.1b	(/.f64 (+.f64 (/.f64 -9 x) (/.f64 -12 (.f64 x x))) (+.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (/.f64 (+.f64 x (*.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))))
✓	28.6b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (cbrt.f64 (pow.f64 (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3) 3))) (+.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (/.f64 (+.f64 x (.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))))
✓	28.6b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)) (+.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (/.f64 (+.f64 x (.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))))
▶	28.6b	(-.f64 (/.f64 x (+.f64 x 1)) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)))
	32.8b	(-.f64 (-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x))) (+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 4))))

Compiler

Compiled 7531 to 5582 computations (25.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 1 x) (+.f64 x -1))
0.0b	(pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)
0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3))
2.8b	(-.f64 (/.f64 x (+.f64 x 1)) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)))

rewrite347.0ms (5.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

211×	`*-un-lft-identity_binary64`
151×	`times-frac_binary64`
145×	`add-sqr-sqrt_binary64`
128×	`cbrt-prod_binary64`
82×	`cube-prod_binary64`

Counts

4 → 273

Calls

4 calls:

70.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)))
12.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3))
11.0ms	(pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)
8.0ms	(/.f64 (+.f64 1 x) (+.f64 x -1))

Compiler

Compiled 4364 to 3406 computations (22% saved)

series106.0ms (1.8%)

Error

0.0b

Counts

4 → 48

Calls

4 calls:

20.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)))
18.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3))
15.0ms	(/.f64 (+.f64 1 x) (+.f64 x -1))
14.0ms	(pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)

Compiler

Compiled 1595 to 1315 computations (17.6% saved)

simplify249.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

384×	`unswap-sqr_binary64`
286×	`log-prod_binary64`
204×	`exp-prod_binary64`
201×	`div-sub_binary64`
147×	`sqr-pow_binary64`

Counts

321 → 273

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	374	7036
1	981	6488
2	3028	6423
3	4475	6423
4	5060	6423

prune131.0ms (2.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	273	0	273
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	273	5	278

Error

0.0b

Counts

278 → 5

Alt Table

Status	Error	Program
	33.1b	(/.f64 (+.f64 (/.f64 -9 x) (/.f64 -12 (.f64 x x))) (+.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (/.f64 (+.f64 x (*.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))))
	28.6b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (cbrt.f64 (pow.f64 (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3) 3))) (+.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (/.f64 (+.f64 x (.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))))
	28.6b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)) (+.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (/.f64 (+.f64 x (.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))))
	28.6b	(-.f64 (/.f64 x (+.f64 x 1)) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)))
	32.8b	(-.f64 (-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x))) (+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 4))))

Compiler

Compiled 2599 to 1923 computations (26% saved)

regimes640.0ms (10.6%)

Accuracy

Total 0.1b remaining (79.5%)

Threshold costs 0.1b (79.5%)

Compiler

Compiled 9365 to 7063 computations (24.6% saved)

bsearch8.0ms (0.1%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`+-commutative_binary64`
13×	`sub-neg_binary64`
9×	`*-commutative_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	115
1	48	115
2	67	115
3	89	115
4	102	115
5	107	115
6	108	115
7	105	115

end2.0ms (0%)

Compiler: Compiled 77 to 60 computations (22.1% saved)

sample937.0ms (15.5%)

Algorithm

1×

intervals

Results

245.0ms	2031×	body	1024	valid
136.0ms	4305×	body	128	valid
91.0ms	1009×	body	512	valid
30.0ms	190×	body	2048	valid
27.0ms	465×	body	256	valid

Compiler

Compiled 271 to 203 computations (25.1% saved)

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	33	19
4	55	19
5	85	19
6	165	19
7	242	19
8	538	19
9	578	19
10	658	19
11	835	19
12	780	19
13	770	19
14	764	19
15	766	19
16	768	19
17	770	19
18	770	19
19	681	19

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	33	19
4	55	19
5	85	19
6	165	19
7	242	19
8	538	19
9	578	19
10	658	19
11	835	19
12	780	19
13	770	19
14	764	19
15	766	19
16	768	19
17	770	19
18	770	19
19	681	19

Details

analyze95.0ms (1.6%)

sample28.0ms (0.5%)

simplify78.0ms (1.3%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite190.0ms (3.2%)

series47.0ms (0.8%)

simplify119.0ms (2%)

prune75.0ms (1.2%)

localize16.0ms (0.3%)

rewrite590.0ms (9.8%)

series140.0ms (2.3%)

simplify259.0ms (4.3%)

prune241.0ms (4%)

localize20.0ms (0.3%)

rewrite991.0ms (16.4%)

series159.0ms (2.6%)

simplify314.0ms (5.2%)

prune228.0ms (3.8%)

localize10.0ms (0.2%)

rewrite347.0ms (5.8%)

series106.0ms (1.8%)

simplify249.0ms (4.1%)

prune131.0ms (2.2%)

regimes640.0ms (10.6%)

bsearch8.0ms (0.1%)

simplify7.0ms (0.1%)

end2.0ms (0%)

sample937.0ms (15.5%)

Profiling

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	33	19
4	55	19
5	85	19
6	165	19
7	242	19
8	538	19
9	578	19
10	658	19
11	835	19
12	780	19
13	770	19
14	764	19
15	766	19
16	768	19
17	770	19
18	770	19
19	681	19