Details

analyze391.0ms (9.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
43.7%	56.2%	0.1%	8
62.4%	37.4%	0.1%	9
65.5%	34.3%	0.1%	10
71.8%	27.7%	0.5%	11
79.2%	19.7%	1.1%	12
80.2%	18.7%	1.1%	13
82.8%	15%	2.2%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample31.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	14×	body	128	invalid

Compiler

Compiled 32 to 24 computations (25% saved)

simplify11.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

37×	`associate-l_binary64`
36×	`associate-r_binary64`
20×	`*-commutative_binary64`
19×	`distribute-lft-in_binary64`
19×	`distribute-rgt-in_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	24	16
2	38	16
3	87	16
4	108	16
5	118	16
6	111	16

prune1.0ms (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

8.1b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	8.1b	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))

Compiler

Compiled 28 to 20 computations (28.6% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

3.1b	(.f64 y (+.f64 1 (.f64 z z)))
5.8b	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))

rewrite80.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

4.9b

Rules

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

Counts

2 → 74

Calls

2 calls:

6.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
4.0ms	(.f64 y (+.f64 1 (.f64 z z)))

Compiler

Compiled 1356 to 790 computations (41.7% saved)

series74.0ms (1.8%)

Error

4.9b

Counts

2 → 25

Calls

2 calls:

48.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
15.0ms	(.f64 y (+.f64 1 (.f64 z z)))

Compiler

Compiled 829 to 596 computations (28.1% saved)

simplify122.0ms (3%)

Algorithm

1×	egg-herbie

Rules

543×	`associate-/r*_binary64`
382×	`associate-/l*_binary64`
342×	`associate-/l/_binary64`
247×	`associate-*l/_binary64`
245×	`distribute-rgt-in_binary64`

Counts

99 → 85

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	154	1947
1	361	1692
2	1176	1690
3	3569	1690
4	4296	1690
5	4970	1690
6	4950	1690

prune49.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	78	7	85
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	78	8	86

Error

4.8b

Counts

86 → 8

Alt Table

Status	Error	Program
	21.3b	(/.f64 (/.f64 1 x) (.f64 (sqrt.f64 y) (.f64 (+.f64 1 (*.f64 z z)) (sqrt.f64 y))))
	8.7b	(/.f64 (/.f64 1 x) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (+.f64 1 (.f64 z z)) (cbrt.f64 y))))
	7.1b	(/.f64 (/.f64 1 (.f64 y x)) (+.f64 1 (.f64 z z)))
▶	6.0b	(.f64 (/.f64 1 y) (/.f64 1 (.f64 x (+.f64 1 (*.f64 z z)))))
	47.7b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 x)) y) (/.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 1 (.f64 z z))))
	26.8b	(.f64 (sqrt.f64 (/.f64 1 (.f64 (+.f64 y (.f64 y (.f64 z z))) x))) (sqrt.f64 (/.f64 1 (.f64 (+.f64 y (.f64 y (*.f64 z z))) x))))
✓	8.1b	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
	37.5b	(/.f64 1 (.f64 y (.f64 (*.f64 z z) x)))

Compiler

Compiled 1047 to 509 computations (51.4% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b	(/.f64 1 (.f64 x (+.f64 1 (.f64 z z))))
3.2b	(.f64 (/.f64 1 y) (/.f64 1 (.f64 x (+.f64 1 (*.f64 z z)))))
4.0b	(.f64 x (+.f64 1 (.f64 z z)))

rewrite116.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

4.8b

Rules

99×	`add-exp-log_binary64`
44×	`prod-exp_binary64`
34×	`div-exp_binary64`
31×	`add-cbrt-cube_binary64`
25×	`add-sqr-sqrt_binary64`

Counts

3 → 127

Calls

3 calls:

10.0ms	(.f64 (/.f64 1 y) (/.f64 1 (.f64 x (+.f64 1 (*.f64 z z)))))
4.0ms	(/.f64 1 (.f64 x (+.f64 1 (.f64 z z))))
4.0ms	(.f64 x (+.f64 1 (.f64 z z)))

Compiler

Compiled 2452 to 1537 computations (37.3% saved)

series95.0ms (2.3%)

Error

4.8b

Counts

3 → 38

Calls

3 calls:

43.0ms	(.f64 (/.f64 1 y) (/.f64 1 (.f64 x (+.f64 1 (*.f64 z z)))))
24.0ms	(/.f64 1 (.f64 x (+.f64 1 (.f64 z z))))
15.0ms	(.f64 x (+.f64 1 (.f64 z z)))

Compiler

Compiled 1326 to 987 computations (25.6% saved)

simplify136.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

563×	`associate-/r*_binary64`
422×	`associate-/l*_binary64`
373×	`associate-*l/_binary64`
303×	`unswap-sqr_binary64`
282×	`associate-/l/_binary64`

Counts

165 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	3091
1	436	2693
2	1404	2667
3	4264	2667
4	4466	2667
5	5132	2667

prune68.0ms (1.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	148	8	156

Error

4.8b

Counts

156 → 8

Alt Table

Status	Error	Program
▶	6.0b	(/.f64 (/.f64 1 (.f64 (+.f64 1 (.f64 z z)) x)) y)
	21.3b	(/.f64 (/.f64 1 x) (.f64 (sqrt.f64 y) (.f64 (+.f64 1 (*.f64 z z)) (sqrt.f64 y))))
	36.6b	(/.f64 1 (.f64 (.f64 z z) (*.f64 x y)))
	7.1b	(/.f64 (/.f64 1 (.f64 y x)) (+.f64 1 (.f64 z z)))
✓	6.0b	(.f64 (/.f64 1 y) (/.f64 1 (.f64 x (+.f64 1 (*.f64 z z)))))
	26.8b	(.f64 (sqrt.f64 (/.f64 1 (.f64 (+.f64 y (.f64 y (.f64 z z))) x))) (sqrt.f64 (/.f64 1 (.f64 (+.f64 y (.f64 y (*.f64 z z))) x))))
✓	8.1b	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
	37.5b	(/.f64 1 (.f64 y (.f64 (*.f64 z z) x)))

Compiler

Compiled 1536 to 942 computations (38.7% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b	(/.f64 1 (.f64 (+.f64 1 (.f64 z z)) x))
3.1b	(/.f64 (/.f64 1 (.f64 (+.f64 1 (.f64 z z)) x)) y)
4.0b	(.f64 (+.f64 1 (.f64 z z)) x)

rewrite129.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

4.8b

Rules

42×	`times-frac_binary64`
35×	`add-exp-log_binary64`
27×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
25×	`add-cube-cbrt_binary64`

Counts

3 → 110

Calls

3 calls:

6.0ms	(/.f64 (/.f64 1 (.f64 (+.f64 1 (.f64 z z)) x)) y)
4.0ms	(/.f64 1 (.f64 (+.f64 1 (.f64 z z)) x))
4.0ms	(.f64 (+.f64 1 (.f64 z z)) x)

Compiler

Compiled 2073 to 1187 computations (42.7% saved)

series95.0ms (2.3%)

Error

4.8b

Counts

3 → 38

Calls

3 calls:

41.0ms	(/.f64 (/.f64 1 (.f64 (+.f64 1 (.f64 z z)) x)) y)
23.0ms	(/.f64 1 (.f64 (+.f64 1 (.f64 z z)) x))
16.0ms	(.f64 (+.f64 1 (.f64 z z)) x)

Compiler

Compiled 1244 to 905 computations (27.3% saved)

simplify162.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

526×	`associate-/r*_binary64`
443×	`times-frac_binary64`
313×	`associate-/l/_binary64`
291×	`distribute-rgt-in_binary64`
270×	`distribute-lft-in_binary64`

Counts

148 → 136

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	196	3034
1	456	2750
2	1367	2748
3	4298	2748
4	4618	2748
5	4984	2748
6	4909	2748

prune75.0ms (1.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	136	8	144

Error

4.8b

Counts

144 → 8

Alt Table

Status	Error	Program
	21.3b	(/.f64 (/.f64 1 x) (.f64 (sqrt.f64 y) (.f64 (+.f64 1 (*.f64 z z)) (sqrt.f64 y))))
	19.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 (+.f64 x (.f64 x (.f64 z z))))) (cbrt.f64 (/.f64 1 (+.f64 x (.f64 x (.f64 z z)))))) (sqrt.f64 y)) (/.f64 (cbrt.f64 (/.f64 1 (+.f64 x (.f64 x (.f64 z z))))) (sqrt.f64 y)))
▶	6.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 (+.f64 x (.f64 x (.f64 z z))))) (cbrt.f64 (/.f64 1 (+.f64 x (.f64 x (.f64 z z)))))) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 (/.f64 1 (+.f64 x (.f64 x (*.f64 z z))))) (cbrt.f64 y)))
	7.1b	(/.f64 (/.f64 1 (.f64 y x)) (+.f64 1 (.f64 z z)))
✓	6.0b	(.f64 (/.f64 1 y) (/.f64 1 (.f64 x (+.f64 1 (*.f64 z z)))))
	26.8b	(.f64 (sqrt.f64 (/.f64 1 (.f64 (+.f64 y (.f64 y (.f64 z z))) x))) (sqrt.f64 (/.f64 1 (.f64 (+.f64 y (.f64 y (*.f64 z z))) x))))
✓	8.1b	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
	37.5b	(/.f64 1 (.f64 y (.f64 (*.f64 z z) x)))

Compiler

Compiled 1777 to 832 computations (53.2% saved)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

9.4b	(.f64 x (.f64 z z))
14.1b	(cbrt.f64 (/.f64 1 (+.f64 x (.f64 x (.f64 z z)))))
14.1b	(cbrt.f64 (/.f64 1 (+.f64 x (.f64 x (.f64 z z)))))
14.1b	(cbrt.f64 (/.f64 1 (+.f64 x (.f64 x (.f64 z z)))))

rewrite115.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

4.8b

Rules

45×	`cbrt-prod_binary64`
27×	`times-frac_binary64`
27×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`

Counts

4 → 91

Calls

4 calls:

8.0ms	(.f64 x (.f64 z z))
3.0ms	(cbrt.f64 (/.f64 1 (+.f64 x (.f64 x (.f64 z z)))))
3.0ms	(cbrt.f64 (/.f64 1 (+.f64 x (.f64 x (.f64 z z)))))
3.0ms	(cbrt.f64 (/.f64 1 (+.f64 x (.f64 x (.f64 z z)))))

Compiler

Compiled 4474 to 1548 computations (65.4% saved)

series165.0ms (4%)

Error

4.8b

Counts

4 → 24

Calls

4 calls:

44.0ms	(cbrt.f64 (/.f64 1 (+.f64 x (.f64 x (.f64 z z)))))
41.0ms	(cbrt.f64 (/.f64 1 (+.f64 x (.f64 x (.f64 z z)))))
40.0ms	(cbrt.f64 (/.f64 1 (+.f64 x (.f64 x (.f64 z z)))))
19.0ms	(.f64 x (.f64 z z))

Compiler

Compiled 3254 to 1928 computations (40.7% saved)

simplify185.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

359×	`cancel-sign-sub-inv_binary64`
350×	`*-commutative_binary64`
297×	`associate-l_binary64`
259×	`exp-prod_binary64`
244×	`unsub-neg_binary64`

Counts

115 → 103

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	110	2586
1	232	2532
2	536	2472
3	1446	2307
4	2927	2151
5	4655	2133
6	4743	2133
7	4966	2133
8	4898	2133

prune71.0ms (1.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	103	8	111

Error

4.8b

Counts

111 → 8

Alt Table

Status	Error	Program
	21.3b	(/.f64 (/.f64 1 x) (.f64 (sqrt.f64 y) (.f64 (+.f64 1 (*.f64 z z)) (sqrt.f64 y))))
	19.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 (+.f64 x (.f64 x (.f64 z z))))) (cbrt.f64 (/.f64 1 (+.f64 x (.f64 x (.f64 z z)))))) (sqrt.f64 y)) (/.f64 (cbrt.f64 (/.f64 1 (+.f64 x (.f64 x (.f64 z z))))) (sqrt.f64 y)))
	6.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 (+.f64 x (.f64 x (.f64 z z))))) (cbrt.f64 (/.f64 1 (+.f64 x (.f64 x (.f64 z z)))))) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 (/.f64 1 (+.f64 x (.f64 x (*.f64 z z))))) (cbrt.f64 y)))
	7.1b	(/.f64 (/.f64 1 (.f64 y x)) (+.f64 1 (.f64 z z)))
	6.0b	(.f64 (/.f64 1 y) (/.f64 1 (.f64 x (+.f64 1 (*.f64 z z)))))
	26.8b	(.f64 (sqrt.f64 (/.f64 1 (.f64 (+.f64 y (.f64 y (.f64 z z))) x))) (sqrt.f64 (/.f64 1 (.f64 (+.f64 y (.f64 y (*.f64 z z))) x))))
	8.1b	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
	37.5b	(/.f64 1 (.f64 y (.f64 (*.f64 z z) x)))

Compiler

Compiled 3123 to 1134 computations (63.7% saved)

regimes913.0ms (22.2%)

Accuracy

Total 1.5b remaining (23.6%)

Threshold costs 0b (0%)

Compiler

Compiled 20208 to 13808 computations (31.7% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	13	16
2	12	16

end6.0ms (0.1%)

Compiler: Compiled 42 to 30 computations (28.6% saved)

sample965.0ms (23.5%)

Algorithm

1×

intervals

Results

378.0ms	8000×	body	128	valid
18.0ms	429×	body	128	invalid

Compiler

Compiled 219 to 131 computations (40.2% saved)

Details

analyze391.0ms (9.5%)

sample31.0ms (0.7%)

simplify11.0ms (0.3%)

prune1.0ms (0%)

localize8.0ms (0.2%)

rewrite80.0ms (2%)

series74.0ms (1.8%)

simplify122.0ms (3%)

prune49.0ms (1.2%)

localize10.0ms (0.2%)

rewrite116.0ms (2.8%)

series95.0ms (2.3%)

simplify136.0ms (3.3%)

prune68.0ms (1.7%)

localize7.0ms (0.2%)

rewrite129.0ms (3.2%)

series95.0ms (2.3%)

simplify162.0ms (3.9%)

prune75.0ms (1.8%)

localize22.0ms (0.5%)

rewrite115.0ms (2.8%)

series165.0ms (4%)

simplify185.0ms (4.5%)

prune71.0ms (1.7%)

regimes913.0ms (22.2%)

simplify5.0ms (0.1%)

end6.0ms (0.1%)

sample965.0ms (23.5%)

Profiling