Details

analyze1.1s (23%)

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
9.4%	90.4%	0.2%	8
9.4%	90.4%	0.2%	9
10.9%	88.9%	0.2%	10
25.9%	73.9%	0.2%	11
47.1%	52.7%	0.2%	12
55.3%	44.5%	0.2%	13
59.2%	40.6%	0.2%	14

Compiler

Compiled 22 to 15 computations (31.8% saved)

sample65.0ms (1.4%)

Algorithm

1×

intervals

Results

54.0ms

256×

body

128

valid

Compiler

Compiled 47 to 33 computations (29.8% saved)

simplify61.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

504×	`associate-*l/_binary64`
495×	`div-sub_binary64`
454×	`cancel-sign-sub-inv_binary64`
429×	`sub-neg_binary64`
348×	`associate-l_binary64`

Counts

1 → 1

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	29	25
2	68	25
3	167	22
4	460	19
5	999	19
6	2280	19
7	4268	19
8	5059	19

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

3.5b

Counts

2 → 2

Alt Table

Status	Error	Program
	11.0b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
▶	3.8b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))

Compiler

Compiled 93 to 61 computations (34.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))
0.0b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
5.4b	(/.f64 (.f64 y t) (.f64 2 z))
5.5b	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))

rewrite140.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

0.9b

Rules

45×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
33×	`times-frac_binary64`
26×	`cancel-sign-sub-inv_binary64`
24×	`add-cube-cbrt_binary64`

Counts

4 → 111

Calls

4 calls:

9.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
6.0ms	(/.f64 (.f64 y t) (.f64 2 z))
5.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
4.0ms	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))

Compiler

Compiled 2586 to 1313 computations (49.2% saved)

series176.0ms (3.7%)

Error

0.0b

Counts

4 → 83

Calls

4 calls:

68.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
45.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
29.0ms	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))
23.0ms	(/.f64 (.f64 y t) (.f64 2 z))

Compiler

Compiled 2582 to 1810 computations (29.9% saved)

simplify183.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

263×	`distribute-rgt-neg-in_binary64`
255×	`cancel-sign-sub-inv_binary64`
243×	`distribute-neg-frac_binary64`
233×	`distribute-lft-neg-in_binary64`
204×	`exp-prod_binary64`

Counts

194 → 155

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	239	4148
1	665	4063
2	2411	3867
3	4429	3867
4	4985	3867
5	4987	3867

prune67.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	151	4	155
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	151	6	157

Error

0.6b

Counts

157 → 6

Alt Table

Status	Error	Program
▶	2.4b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (.f64 1/2 (*.f64 (/.f64 y z) t))))))
	11.0b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
✓	3.8b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
	48.8b	(neg.f64 (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))
	3.6b	(.f64 (.f64 (cbrt.f64 (-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))) (cbrt.f64 (-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))))))) (cbrt.f64 (-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))))
	37.8b	(-.f64 x (-.f64 (.f64 -2 (/.f64 z t)) (.f64 4 (/.f64 (pow.f64 z 3) (.f64 y (.f64 t t))))))

Compiler

Compiled 1970 to 926 computations (53% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (.f64 1/2 (*.f64 (/.f64 y z) t))))))
0.4b	(/.f64 1 (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))))
5.3b	(.f64 y (/.f64 1 (-.f64 z (.f64 1/2 (*.f64 (/.f64 y z) t)))))
5.8b	(*.f64 (/.f64 y z) t)

rewrite112.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

40×	`add-sqr-sqrt_binary64`
30×	`times-frac_binary64`
29×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
22×	`add-exp-log_binary64`

Counts

4 → 115

Calls

4 calls:

7.0ms	(.f64 y (/.f64 1 (-.f64 z (.f64 1/2 (*.f64 (/.f64 y z) t)))))
5.0ms	(*.f64 (/.f64 y z) t)
4.0ms	(/.f64 1 (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))))
2.0ms	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (.f64 1/2 (*.f64 (/.f64 y z) t))))))

Compiler

Compiled 2844 to 1446 computations (49.2% saved)

series192.0ms (4%)

Error

Counts

4 → 87

Calls

4 calls:

60.0ms	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (.f64 1/2 (*.f64 (/.f64 y z) t))))))
48.0ms	(/.f64 1 (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))))
45.0ms	(.f64 y (/.f64 1 (-.f64 z (.f64 1/2 (*.f64 (/.f64 y z) t)))))
20.0ms	(*.f64 (/.f64 y z) t)

Compiler

Compiled 3206 to 2302 computations (28.2% saved)

simplify140.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

929×	`times-frac_binary64`
671×	`associate-/l*_binary64`
219×	`distribute-rgt-neg-in_binary64`
193×	`distribute-lft-neg-in_binary64`
181×	`cancel-sign-sub-inv_binary64`

Counts

202 → 142

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	213	3853
1	514	3662
2	1665	3662
3	4780	3662
4	5048	3662

prune68.0ms (1.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	142	6	148

Error

0.6b

Counts

148 → 6

Alt Table

Status	Error	Program
✓	2.4b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (.f64 1/2 (*.f64 (/.f64 y z) t))))))
	11.0b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
✓	3.8b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
	48.8b	(neg.f64 (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))
▶	3.6b	(.f64 (.f64 (cbrt.f64 (-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))) (cbrt.f64 (-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))))))) (cbrt.f64 (-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))))
	37.8b	(-.f64 x (-.f64 (.f64 -2 (/.f64 z t)) (.f64 4 (/.f64 (pow.f64 z 3) (.f64 y (.f64 t t))))))

Compiler

Compiled 2188 to 1083 computations (50.5% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

5.5b	(/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))))
5.8b	(*.f64 (/.f64 y z) t)
5.8b	(*.f64 (/.f64 y z) t)
5.8b	(*.f64 (/.f64 y z) t)

rewrite125.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

51×	`add-sqr-sqrt_binary64`
39×	`associate-l_binary64`
39×	`times-frac_binary64`
36×	`*-un-lft-identity_binary64`
36×	`add-cube-cbrt_binary64`

Counts

4 → 125

Calls

4 calls:

5.0ms	(/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))))
5.0ms	(*.f64 (/.f64 y z) t)
5.0ms	(*.f64 (/.f64 y z) t)
5.0ms	(*.f64 (/.f64 y z) t)

Compiler

Compiled 6183 to 2699 computations (56.3% saved)

series146.0ms (3.1%)

Error

0.6b

Counts

4 → 49

Calls

4 calls:

63.0ms	(/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))))
28.0ms	(*.f64 (/.f64 y z) t)
25.0ms	(*.f64 (/.f64 y z) t)
23.0ms	(*.f64 (/.f64 y z) t)

Compiler

Compiled 4745 to 2826 computations (40.4% saved)

simplify126.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

539×	`associate-/l*_binary64`
502×	`times-frac_binary64`
457×	`associate-*l/_binary64`
396×	`associate-*r/_binary64`
263×	`associate-/r*_binary64`

Counts

174 → 115

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	146	2537
1	352	2317
2	1112	2317
3	4570	2317
4	4972	2317
5	4970	2317

prune75.0ms (1.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	115	6	121

Error

0.6b

Counts

121 → 6

Alt Table

Status	Error	Program
✓	2.4b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (.f64 1/2 (*.f64 (/.f64 y z) t))))))
▶	11.0b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
✓	3.8b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
	48.8b	(neg.f64 (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))
✓	3.6b	(.f64 (.f64 (cbrt.f64 (-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))) (cbrt.f64 (-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))))))) (cbrt.f64 (-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))))
	37.8b	(-.f64 x (-.f64 (.f64 -2 (/.f64 z t)) (.f64 4 (/.f64 (pow.f64 z 3) (.f64 y (.f64 t t))))))

Compiler

Compiled 4783 to 2156 computations (54.9% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
1.3b	(-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))
19.4b	(/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t)))

rewrite76.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

12×	`add-cbrt-cube_binary64`
12×	`add-exp-log_binary64`
10×	`cancel-sign-sub-inv_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`

Counts

3 → 59

Calls

3 calls:

9.0ms	(/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t)))
7.0ms	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
4.0ms	(-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))

Compiler

Compiled 1833 to 1030 computations (43.8% saved)

series191.0ms (4%)

Error

0.6b

Counts

3 → 74

Calls

3 calls:

82.0ms	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
70.0ms	(/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t)))
27.0ms	(-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))

Compiler

Compiled 2454 to 1776 computations (27.6% saved)

simplify118.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

519×	`associate-/l/_binary64`
235×	`distribute-rgt-neg-in_binary64`
217×	`distribute-lft-neg-in_binary64`
193×	`cancel-sign-sub-inv_binary64`
191×	`distribute-neg-frac_binary64`

Counts

133 → 100

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	179	3075
1	518	2944
2	2072	2939
3	4709	2939
4	4951	2939

prune66.0ms (1.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	1	1	2
Picked	0	1	1
Done	1	2	3
Total	101	5	106

Error

Counts

106 → 5

Alt Table

Status	Error	Program
	2.4b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (.f64 1/2 (*.f64 (/.f64 y z) t))))))
	11.0b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
	0.1b	(-.f64 x (/.f64 1 (+.f64 (.f64 (/.f64 z y) 1) (.f64 -1 (/.f64 t (*.f64 z 2))))))
	3.8b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
	37.8b	(-.f64 x (-.f64 (.f64 -2 (/.f64 z t)) (.f64 4 (/.f64 (pow.f64 z 3) (.f64 y (.f64 t t))))))

Compiler

Compiled 1438 to 728 computations (49.4% saved)

regimes489.0ms (10.2%)

Accuracy

Total 0.1b remaining (92%)

Threshold costs 0.1b (92%)

Compiler

Compiled 9124 to 5842 computations (36% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
5×	`*-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
2×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	21
1	25	19
2	34	19
3	39	19
4	43	19
5	44	19
6	42	19

end1.0ms (0%)

Compiler: Compiled 17 to 12 computations (29.4% saved)

sample1.0s (21.3%)

Algorithm

1×

intervals

Results

593.0ms

8000×

body

128

valid

Compiler

Compiled 144 to 101 computations (29.9% saved)

Details

analyze1.1s (23%)

sample65.0ms (1.4%)

simplify61.0ms (1.3%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

rewrite140.0ms (2.9%)

series176.0ms (3.7%)

simplify183.0ms (3.8%)

prune67.0ms (1.4%)

localize12.0ms (0.3%)

rewrite112.0ms (2.3%)

series192.0ms (4%)

simplify140.0ms (2.9%)

prune68.0ms (1.4%)

localize17.0ms (0.4%)

rewrite125.0ms (2.6%)

series146.0ms (3.1%)

simplify126.0ms (2.6%)

prune75.0ms (1.6%)

localize11.0ms (0.2%)

rewrite76.0ms (1.6%)

series191.0ms (4%)

simplify118.0ms (2.5%)

prune66.0ms (1.4%)

regimes489.0ms (10.2%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.0s (21.3%)

Profiling