Details

analyze1.2s (19.8%)

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

9.0ms	256×	body	128	valid
1.0ms	24×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify174.0ms (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

prune3.0ms (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

10.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	10.9b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Compiler

Compiled 48 to 30 computations (37.5% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 t (*.f64 a z))
10.7b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

rewrite61.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

10.7b

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 44

Calls

2 calls:

6.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
3.0ms	(-.f64 t (*.f64 a z))

Compiler

Compiled 941 to 165 computations (82.5% saved)

series136.0ms (2.3%)

Error

3.8b

Counts

2 → 49

Calls

2 calls:

96.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
23.0ms	(-.f64 t (*.f64 a z))

Compiler

Compiled 2010 to 1217 computations (39.5% saved)

simplify96.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

371×	`associate-l_binary64`
355×	`associate-/l*_binary64`
332×	`associate-r_binary64`
318×	`times-frac_binary64`
256×	`div-sub_binary64`

Counts

93 → 79

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	1819
1	372	1723
2	1172	1663
3	4642	1663
4	5195	1663

prune62.0ms (1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	70	9	79
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	70	10	80

Error

3.7b

Counts

80 → 10

Alt Table

Status	Error	Program
	39.8b	(.f64 (/.f64 (-.f64 x (.f64 z y)) (-.f64 (.f64 t t) (.f64 z (.f64 z (.f64 a a))))) (+.f64 t (*.f64 a z)))
▶	11.1b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
	11.7b	(.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 z y))) (cbrt.f64 (-.f64 x (.f64 z y)))) (/.f64 (cbrt.f64 (-.f64 x (.f64 z y))) (-.f64 t (.f64 z a))))
	11.2b	(/.f64 1 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 z y))))
	32.9b	(.f64 (sqrt.f64 (/.f64 (-.f64 x (.f64 z y)) (-.f64 t (.f64 z a)))) (sqrt.f64 (/.f64 (-.f64 x (.f64 z y)) (-.f64 t (*.f64 z a)))))
	11.7b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x (.f64 z y)) (-.f64 t (.f64 z a)))) (cbrt.f64 (/.f64 (-.f64 x (.f64 z y)) (-.f64 t (.f64 z a))))) (cbrt.f64 (/.f64 (-.f64 x (.f64 z y)) (-.f64 t (.f64 z a)))))
	38.6b	(+.f64 (/.f64 y a) (-.f64 (.f64 (/.f64 t (.f64 z (.f64 a a))) (-.f64 y (/.f64 x z))) (/.f64 x (.f64 z a))))
	27.2b	(/.f64 x (-.f64 t (*.f64 z a)))
	11.6b	(/.f64 (-.f64 x (.f64 y z)) (.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z a))) (cbrt.f64 (-.f64 t (.f64 z a)))) (cbrt.f64 (-.f64 t (.f64 z a)))))
✓	10.9b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Compiler

Compiled 1441 to 423 computations (70.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 t (*.f64 z a))
0.4b	(/.f64 1 (-.f64 t (*.f64 z a)))
10.5b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))

rewrite105.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

3.7b

Rules

26×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`
16×	`add-exp-log_binary64`

Counts

3 → 87

Calls

3 calls:

11.0ms	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
4.0ms	(/.f64 1 (-.f64 t (*.f64 z a)))
3.0ms	(-.f64 t (*.f64 z a))

Compiler

Compiled 1898 to 576 computations (69.7% saved)

series163.0ms (2.7%)

Error

3.7b

Counts

3 → 62

Calls

3 calls:

98.0ms	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
26.0ms	(-.f64 t (*.f64 z a))
25.0ms	(/.f64 1 (-.f64 t (*.f64 z a)))

Compiler

Compiled 2593 to 1633 computations (37% saved)

simplify112.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

396×	`associate-/l*_binary64`
345×	`times-frac_binary64`
245×	`distribute-rgt-in_binary64`
242×	`distribute-lft-in_binary64`
230×	`associate-/r*_binary64`

Counts

149 → 111

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	156	2625
1	418	2364
2	1371	2304
3	4403	2304
4	5004	2304

prune60.0ms (1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	4	4	8
Picked	0	1	1
Done	0	1	1
Total	113	8	121

Error

2.5b

Counts

121 → 8

Alt Table

Status	Error	Program
✓	11.1b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
	11.7b	(.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 z y))) (cbrt.f64 (-.f64 x (.f64 z y)))) (/.f64 (cbrt.f64 (-.f64 x (.f64 z y))) (-.f64 t (.f64 z a))))
▶	11.2b	(/.f64 1 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 z y))))
	33.7b	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 z (.f64 z y)))) (-.f64 t (.f64 z a))) (+.f64 x (.f64 y z)))
	32.9b	(.f64 (sqrt.f64 (/.f64 (-.f64 x (.f64 z y)) (-.f64 t (.f64 z a)))) (sqrt.f64 (/.f64 (-.f64 x (.f64 z y)) (-.f64 t (*.f64 z a)))))
	33.5b	(/.f64 (neg.f64 y) (-.f64 (/.f64 t z) a))
	11.6b	(/.f64 (-.f64 x (.f64 y z)) (.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z a))) (cbrt.f64 (-.f64 t (.f64 z a)))) (cbrt.f64 (-.f64 t (.f64 z a)))))
✓	10.9b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Compiler

Compiled 1480 to 463 computations (68.7% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 t (*.f64 z a))
0.6b	(/.f64 1 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 z y))))
10.4b	(/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 z y)))

rewrite137.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

2.5b

Rules

90×	`times-frac_binary64`
55×	`*-un-lft-identity_binary64`
55×	`add-sqr-sqrt_binary64`
55×	`add-cube-cbrt_binary64`
18×	`associate-/r*_binary64`

Counts

3 → 128

Calls

3 calls:

8.0ms	(/.f64 1 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 z y))))
6.0ms	(/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 z y)))
3.0ms	(-.f64 t (*.f64 z a))

Compiler

Compiled 3377 to 812 computations (76% saved)

series256.0ms (4.3%)

Error

2.5b

Counts

3 → 82

Calls

3 calls:

108.0ms	(/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 z y)))
99.0ms	(/.f64 1 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 z y))))
26.0ms	(-.f64 t (*.f64 z a))

Compiler

Compiled 3944 to 2455 computations (37.8% saved)

simplify186.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

396×	`cancel-sign-sub-inv_binary64`
281×	`distribute-rgt-in_binary64`
268×	`div-sub_binary64`
259×	`distribute-lft-in_binary64`
220×	`neg-mul-1_binary64`

Counts

210 → 171

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	222	5353
1	606	5012
2	2156	4838
3	4387	4838
4	5003	4838

prune86.0ms (1.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	168	3	171
Fresh	2	3	5
Picked	1	0	1
Done	0	2	2
Total	171	8	179

Error

1.1b

Counts

179 → 8

Alt Table

Status	Error	Program
	33.3b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x (.f64 z y)) (-.f64 t (.f64 a z))) 3))
	29.5b	(/.f64 1 (-.f64 (.f64 (+.f64 (/.f64 (.f64 z y) x) 1) (/.f64 t x)) (.f64 (/.f64 a x) (+.f64 z (/.f64 (.f64 z (*.f64 z y)) x)))))
✓	11.1b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
	33.7b	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 z (.f64 z y)))) (-.f64 t (.f64 z a))) (+.f64 x (.f64 y z)))
	31.9b	(/.f64 1 (/.f64 (/.f64 (-.f64 (.f64 t t) (.f64 z (.f64 a (.f64 a z)))) (+.f64 (.f64 a z) t)) (-.f64 x (.f64 z y))))
	33.5b	(/.f64 (neg.f64 y) (-.f64 (/.f64 t z) a))
▶	11.6b	(/.f64 (-.f64 x (.f64 y z)) (.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z a))) (cbrt.f64 (-.f64 t (.f64 z a)))) (cbrt.f64 (-.f64 t (.f64 z a)))))
✓	10.9b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Compiler

Compiled 2451 to 623 computations (74.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

10.0b	(cbrt.f64 (-.f64 t (*.f64 z a)))
10.0b	(cbrt.f64 (-.f64 t (*.f64 z a)))
10.0b	(cbrt.f64 (-.f64 t (*.f64 z a)))
10.7b	(/.f64 (-.f64 x (.f64 y z)) (.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z a))) (cbrt.f64 (-.f64 t (.f64 z a)))) (cbrt.f64 (-.f64 t (.f64 z a)))))

rewrite105.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

Rules

60×	`cbrt-div_binary64`
31×	`flip--_binary64`
31×	`flip3--_binary64`
28×	`frac-times_binary64`
26×	`associate-/r/_binary64`

Counts

4 → 91

Calls

4 calls:

17.0ms	(/.f64 (-.f64 x (.f64 y z)) (.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z a))) (cbrt.f64 (-.f64 t (.f64 z a)))) (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)))
2.0ms	(cbrt.f64 (-.f64 t (*.f64 z a)))

Compiler

Compiled 4034 to 551 computations (86.3% saved)

series358.0ms (6%)

Error

1.1b

Counts

4 → 85

Calls

4 calls:

109.0ms	(/.f64 (-.f64 x (.f64 y z)) (.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z a))) (cbrt.f64 (-.f64 t (.f64 z a)))) (cbrt.f64 (-.f64 t (.f64 z a)))))
70.0ms	(cbrt.f64 (-.f64 t (*.f64 z a)))
68.0ms	(cbrt.f64 (-.f64 t (*.f64 z a)))
66.0ms	(cbrt.f64 (-.f64 t (*.f64 z a)))

Compiler

Compiled 7384 to 4287 computations (41.9% saved)

simplify199.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

922×	`times-frac_binary64`
372×	`cancel-sign-sub-inv_binary64`
236×	`associate-/r*_binary64`
195×	`distribute-neg-frac_binary64`
142×	`associate-/l*_binary64`

Counts

176 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	279	4688
1	735	4506
2	2524	4470
3	4950	4434
4	5000	4434
5	4960	4434

prune79.0ms (1.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	142	8	150

Error

1.1b

Counts

150 → 8

Alt Table

Status	Error	Program
	33.3b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x (.f64 z y)) (-.f64 t (.f64 a z))) 3))
	29.5b	(/.f64 1 (-.f64 (.f64 (+.f64 (/.f64 (.f64 z y) x) 1) (/.f64 t x)) (.f64 (/.f64 a x) (+.f64 z (/.f64 (.f64 z (*.f64 z y)) x)))))
	11.1b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
	33.7b	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 z (.f64 z y)))) (-.f64 t (.f64 z a))) (+.f64 x (.f64 y z)))
	31.9b	(/.f64 1 (/.f64 (/.f64 (-.f64 (.f64 t t) (.f64 z (.f64 a (.f64 a z)))) (+.f64 (.f64 a z) t)) (-.f64 x (.f64 z y))))
	33.5b	(/.f64 (neg.f64 y) (-.f64 (/.f64 t z) a))
	11.6b	(/.f64 (-.f64 x (.f64 y z)) (.f64 (.f64 (cbrt.f64 (-.f64 t (.f64 z a))) (cbrt.f64 (-.f64 t (.f64 z a)))) (cbrt.f64 (-.f64 t (.f64 z a)))))
	10.9b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Compiler

Compiled 3548 to 910 computations (74.4% saved)

regimes1.5s (25%)

Accuracy

Total 1.3b remaining (71.9%)

Threshold costs 0b (0%)

Compiler

Compiled 19040 to 10308 computations (45.9% saved)

bsearch4.0ms (0.1%)

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

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	28	142
1	48	128
2	69	118
3	86	116
4	95	116
5	99	116
6	99	116
7	100	116
8	100	116

end1.0ms (0%)

Compiler: Compiled 82 to 28 computations (65.9% saved)

sample835.0ms (14%)

Algorithm

1×

intervals

Results

289.0ms	8000×	body	128	valid
23.0ms	690×	body	128	invalid

Compiler

Compiled 291 to 153 computations (47.4% saved)

Details

analyze1.2s (19.8%)

sample24.0ms (0.4%)

simplify174.0ms (2.9%)

prune3.0ms (0%)

localize11.0ms (0.2%)

rewrite61.0ms (1%)

series136.0ms (2.3%)

simplify96.0ms (1.6%)

prune62.0ms (1%)

localize9.0ms (0.1%)

rewrite105.0ms (1.8%)

series163.0ms (2.7%)

simplify112.0ms (1.9%)

prune60.0ms (1%)

localize12.0ms (0.2%)

rewrite137.0ms (2.3%)

series256.0ms (4.3%)

simplify186.0ms (3.1%)

prune86.0ms (1.4%)

localize12.0ms (0.2%)

rewrite105.0ms (1.8%)

series358.0ms (6%)

simplify199.0ms (3.3%)

prune79.0ms (1.3%)

regimes1.5s (25%)

bsearch4.0ms (0.1%)

simplify9.0ms (0.2%)

end1.0ms (0%)

sample835.0ms (14%)

Profiling