Details

analyze1.3s (20.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
13.2%	86.5%	0.2%	10
17%	82.8%	0.2%	11
18.2%	81.5%	0.2%	12
21.7%	78.1%	0.2%	13
32.9%	66.9%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample24.0ms (0.4%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	21×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify178.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

1133×	`div-sub_binary64`
860×	`sub-neg_binary64`
750×	`associate-/r/_binary64`
699×	`cancel-sign-sub-inv_binary64`
610×	`distribute-rgt-neg-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	26	16
2	49	16
3	86	16
4	166	16
5	293	16
6	570	16
7	1559	16
8	2366	16
9	2268	16
10	2532	16
11	2753	16
12	2839	16
13	3034	16
14	4109	16
15	4495	16
16	4543	16
17	4973	16

prune2.0ms (0%)

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

7.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	7.9b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Compiler

Compiled 48 to 30 computations (37.5% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 t (*.f64 a z))
0.0b	(-.f64 x (*.f64 y z))
7.8b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

rewrite66.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

7.8b

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-log-exp_binary64`

Counts

3 → 56

Calls

3 calls:

6.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
2.0ms	(-.f64 x (*.f64 y z))
2.0ms	(-.f64 t (*.f64 a z))

Compiler

Compiled 1156 to 203 computations (82.4% saved)

series149.0ms (2.4%)

Error

2.9b

Counts

3 → 70

Calls

3 calls:

92.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
23.0ms	(-.f64 x (*.f64 y z))
18.0ms	(-.f64 t (*.f64 a z))

Compiler

Compiled 2693 to 1660 computations (38.4% saved)

simplify118.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

995×	`times-frac_binary64`
390×	`cancel-sign-sub-inv_binary64`
229×	`div-sub_binary64`
199×	`neg-mul-1_binary64`
192×	`distribute-rgt-in_binary64`

Counts

126 → 105

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	152	2799
1	443	2703
2	1635	2607
3	4543	2607
4	5017	2607

prune46.0ms (0.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	97	8	105
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	8	106

Error

2.8b

Counts

106 → 8

Alt Table

Status	Error	Program
	8.0b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
	29.0b	(/.f64 x (-.f64 t (*.f64 z a)))
▶	7.9b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 (.f64 y z) (-.f64 t (*.f64 z a))))
	33.1b	(.f64 (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 z a)))) (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (*.f64 z a)))))
	40.0b	(/.f64 (/.f64 (-.f64 x (.f64 y z)) (sqrt.f64 (-.f64 t (.f64 z a)))) (sqrt.f64 (-.f64 t (*.f64 a z))))
	8.8b	(/.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (.f64 y z)))) (/.f64 (-.f64 t (.f64 z a)) (cbrt.f64 (-.f64 x (*.f64 y z)))))
	43.4b	(-.f64 (+.f64 (/.f64 y a) (.f64 (/.f64 t (.f64 a a)) (-.f64 (/.f64 y z) (/.f64 x (.f64 z z))))) (/.f64 x (.f64 z a)))
	44.9b	(.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 (pow.f64 t 3) (pow.f64 (.f64 z a) 3))) (+.f64 (.f64 t t) (+.f64 (.f64 (.f64 a z) (.f64 a z)) (.f64 t (*.f64 a z)))))

Compiler

Compiled 1528 to 442 computations (71.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 t (*.f64 z a))
0.0b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 (.f64 y z) (-.f64 t (*.f64 z a))))
3.1b	(/.f64 x (-.f64 t (*.f64 z a)))
7.3b	(/.f64 (.f64 y z) (-.f64 t (.f64 z a)))

rewrite126.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

1.3b

Rules

21×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
16×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
11×	`add-cbrt-cube_binary64`

Counts

4 → 92

Calls

4 calls:

12.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 (.f64 y z) (-.f64 t (*.f64 z a))))
7.0ms	(/.f64 (.f64 y z) (-.f64 t (.f64 z a)))
3.0ms	(/.f64 x (-.f64 t (*.f64 z a)))
2.0ms	(-.f64 t (*.f64 z a))

Compiler

Compiled 2486 to 381 computations (84.7% saved)

series245.0ms (4%)

Error

1.6b

Counts

4 → 95

Calls

4 calls:

107.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 (.f64 y z) (-.f64 t (*.f64 z a))))
55.0ms	(/.f64 x (-.f64 t (*.f64 z a)))
42.0ms	(/.f64 (.f64 y z) (-.f64 t (.f64 z a)))
19.0ms	(-.f64 t (*.f64 z a))

Compiler

Compiled 4709 to 2843 computations (39.6% saved)

simplify188.0ms (3%)

Algorithm

1×	egg-herbie

Rules

495×	`cancel-sign-sub-inv_binary64`
403×	`associate-/l/_binary64`
202×	`distribute-rgt-in_binary64`
202×	`distribute-rgt-neg-in_binary64`
179×	`distribute-lft-neg-in_binary64`

Counts

187 → 148

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	239	4918
1	655	4778
2	2377	4620
3	4747	4601
4	4992	4601
5	4962	4601

prune61.0ms (1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	144	4	148
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	148	8	156

Error

0.0b

Counts

156 → 8

Alt Table

Status	Error	Program
✓	7.9b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 (.f64 y z) (-.f64 t (*.f64 z a))))
	24.9b	(+.f64 (/.f64 x (-.f64 t (*.f64 z a))) (/.f64 y a))
	33.1b	(.f64 (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 z a)))) (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (*.f64 z a)))))
	8.1b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))
	8.8b	(/.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (.f64 y z)))) (/.f64 (-.f64 t (.f64 z a)) (cbrt.f64 (-.f64 x (*.f64 y z)))))
	40.7b	(+.f64 (/.f64 (.f64 t y) (.f64 z (*.f64 a a))) (/.f64 (-.f64 y (/.f64 x z)) a))
▶	7.2b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 (.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 t (.f64 z a))) (cbrt.f64 (-.f64 t (.f64 z a))))) z) (cbrt.f64 (-.f64 t (.f64 z a)))))
	8.0b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))

Compiler

Compiled 2026 to 476 computations (76.5% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

5.4b	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 t (.f64 z a))) (cbrt.f64 (-.f64 t (.f64 z a))))) z)
7.9b	(cbrt.f64 (-.f64 t (*.f64 z a)))
7.9b	(cbrt.f64 (-.f64 t (*.f64 z a)))
7.9b	(cbrt.f64 (-.f64 t (*.f64 z a)))

rewrite90.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

18×	`cbrt-div_binary64`
15×	`associate-l_binary64`
14×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`

Counts

4 → 75

Calls

4 calls:

13.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 t (.f64 z a))) (cbrt.f64 (-.f64 t (.f64 z a))))) z)
2.0ms	(cbrt.f64 (-.f64 t (*.f64 z a)))
2.0ms	(cbrt.f64 (-.f64 t (*.f64 z a)))
2.0ms	(cbrt.f64 (-.f64 t (*.f64 z a)))

Compiler

Compiled 3207 to 470 computations (85.3% saved)

series330.0ms (5.3%)

Error

0.0b

Counts

4 → 68

Calls

4 calls:

109.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 t (.f64 z a))) (cbrt.f64 (-.f64 t (.f64 z a))))) z)
59.0ms	(cbrt.f64 (-.f64 t (*.f64 z a)))
58.0ms	(cbrt.f64 (-.f64 t (*.f64 z a)))
56.0ms	(cbrt.f64 (-.f64 t (*.f64 z a)))

Compiler

Compiled 8044 to 4450 computations (44.7% saved)

simplify197.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

477×	`distribute-neg-frac_binary64`
242×	`cancel-sign-sub-inv_binary64`
232×	`associate-/l*_binary64`
186×	`*-commutative_binary64`
161×	`sub-neg_binary64`

Counts

143 → 107

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	414	5942
1	950	5631
2	3091	5547
3	4901	5503
4	4967	5503

prune64.0ms (1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	107	8	115

Error

0.0b

Counts

115 → 8

Alt Table

Status	Error	Program
✓	7.9b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 (.f64 y z) (-.f64 t (*.f64 z a))))
	24.9b	(+.f64 (/.f64 x (-.f64 t (*.f64 z a))) (/.f64 y a))
	33.1b	(.f64 (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 z a)))) (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (*.f64 z a)))))
	8.1b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))
	8.8b	(/.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (.f64 y z)))) (/.f64 (-.f64 t (.f64 z a)) (cbrt.f64 (-.f64 x (*.f64 y z)))))
	40.7b	(+.f64 (/.f64 (.f64 t y) (.f64 z (*.f64 a a))) (/.f64 (-.f64 y (/.f64 x z)) a))
✓	7.2b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 (.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 t (.f64 z a))) (cbrt.f64 (-.f64 t (.f64 z a))))) z) (cbrt.f64 (-.f64 t (.f64 z a)))))
▶	8.0b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))

Compiler

Compiled 3125 to 840 computations (73.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 t (*.f64 z a))
0.0b	(-.f64 x (*.f64 y z))
0.8b	(/.f64 1 (-.f64 t (*.f64 z a)))
7.2b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))

rewrite98.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

27×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
20×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`
17×	`add-exp-log_binary64`

Counts

4 → 99

Calls

4 calls:

9.0ms	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
3.0ms	(/.f64 1 (-.f64 t (*.f64 z a)))
2.0ms	(-.f64 t (*.f64 z a))
2.0ms	(-.f64 x (*.f64 y z))

Compiler

Compiled 2137 to 638 computations (70.1% saved)

series176.0ms (2.9%)

Error

0.0b

Counts

4 → 93

Calls

4 calls:

82.0ms	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
38.0ms	(/.f64 1 (-.f64 t (*.f64 z a)))
20.0ms	(-.f64 x (*.f64 y z))
19.0ms	(-.f64 t (*.f64 z a))

Compiler

Compiled 3867 to 2497 computations (35.4% saved)

simplify182.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

409×	`distribute-rgt-in_binary64`
393×	`distribute-lft-in_binary64`
375×	`cancel-sign-sub-inv_binary64`
248×	`neg-mul-1_binary64`
150×	`associate-/l/_binary64`

Counts

192 → 152

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	4272
1	521	3829
2	1989	3728
3	4515	3728
4	4976	3728
5	4974	3728

prune44.0ms (0.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	152	8	160

Error

0.0b

Counts

160 → 8

Alt Table

Status	Error	Program
✓	7.9b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 (.f64 y z) (-.f64 t (*.f64 z a))))
	24.9b	(+.f64 (/.f64 x (-.f64 t (*.f64 z a))) (/.f64 y a))
	33.1b	(.f64 (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 z a)))) (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (*.f64 z a)))))
	8.1b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))
	8.8b	(/.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (.f64 y z)))) (/.f64 (-.f64 t (.f64 z a)) (cbrt.f64 (-.f64 x (*.f64 y z)))))
	40.7b	(+.f64 (/.f64 (.f64 t y) (.f64 z (*.f64 a a))) (/.f64 (-.f64 y (/.f64 x z)) a))
✓	7.2b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 (.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 t (.f64 z a))) (cbrt.f64 (-.f64 t (.f64 z a))))) z) (cbrt.f64 (-.f64 t (.f64 z a)))))
✓	8.0b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))

Compiler

Compiled 1456 to 406 computations (72.1% saved)

regimes1.6s (25.3%)

Accuracy

Total 2.5b remaining (97.9%)

Threshold costs 0b (0%)

Compiler

Compiled 20810 to 11106 computations (46.6% saved)

bsearch8.0ms (0.1%)

Compiler: Compiled 16 to 10 computations (37.5% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

20×	`sub-neg_binary64`
19×	`+-commutative_binary64`
17×	`*-commutative_binary64`
12×	`neg-sub0_binary64`
12×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	222
1	79	222
2	115	222
3	139	222
4	152	222
5	154	222
6	153	222

end1.0ms (0%)

Compiler: Compiled 155 to 43 computations (72.3% saved)

sample905.0ms (14.7%)

Algorithm

1×

intervals

Results

398.0ms	8000×	body	128	valid
32.0ms	760×	body	128	invalid

Compiler

Compiled 375 to 155 computations (58.7% saved)

Details

analyze1.3s (20.4%)

sample24.0ms (0.4%)

simplify178.0ms (2.9%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite66.0ms (1.1%)

series149.0ms (2.4%)

simplify118.0ms (1.9%)

prune46.0ms (0.7%)

localize11.0ms (0.2%)

rewrite126.0ms (2%)

series245.0ms (4%)

simplify188.0ms (3%)

prune61.0ms (1%)

localize15.0ms (0.2%)

rewrite90.0ms (1.5%)

series330.0ms (5.3%)

simplify197.0ms (3.2%)

prune64.0ms (1%)

localize9.0ms (0.1%)

rewrite98.0ms (1.6%)

series176.0ms (2.9%)

simplify182.0ms (2.9%)

prune44.0ms (0.7%)

regimes1.6s (25.3%)

bsearch8.0ms (0.1%)

simplify11.0ms (0.2%)

end1.0ms (0%)

sample905.0ms (14.7%)

Profiling