Details

analyze817.0ms (15.6%)

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)

sample24.0ms (0.4%)

Algorithm

1×

intervals

Results

12.0ms

256×

body

128

valid

Compiler

Compiled 47 to 33 computations (29.8% saved)

simplify62.0ms (1.2%)

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

prune6.0ms (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

1.5b

Counts

2 → 2

Alt Table

Status	Error	Program
	10.9b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
▶	2.2b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))

Compiler

Compiled 93 to 61 computations (34.4% saved)

localize13.0ms (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)))))
5.2b	(/.f64 (.f64 y t) (.f64 2 z))
5.9b	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))

rewrite187.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

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:

12.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
6.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
5.0ms	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))
5.0ms	(/.f64 (.f64 y t) (.f64 2 z))

Compiler

Compiled 2586 to 1313 computations (49.2% saved)

series177.0ms (3.4%)

Error

0.0b

Counts

4 → 65

Calls

4 calls:

66.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
40.0ms	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))
35.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
29.0ms	(/.f64 (.f64 y t) (.f64 2 z))

Compiler

Compiled 1825 to 1251 computations (31.5% saved)

simplify136.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

476×	`associate-/l/_binary64`
240×	`distribute-rgt-neg-in_binary64`
228×	`cancel-sign-sub-inv_binary64`
223×	`distribute-neg-frac_binary64`
211×	`distribute-lft-neg-in_binary64`

Counts

176 → 137

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	216	3517
1	606	3442
2	2186	3246
3	4631	3246
4	4968	3246

prune76.0ms (1.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	134	3	137
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	135	4	139

Error

0.6b

Counts

139 → 4

Alt Table

Status	Error	Program
▶	1.4b	(-.f64 x (/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t))))))
	10.9b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
	2.8b	(.f64 (.f64 (cbrt.f64 (-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (/.f64 y (/.f64 z t))))))) (cbrt.f64 (-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (/.f64 y (/.f64 z t)))))))) (cbrt.f64 (-.f64 x (/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t))))))))
	36.1b	(cbrt.f64 (pow.f64 (-.f64 x (/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t)))))) 3))

Compiler

Compiled 1842 to 851 computations (53.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t))))
0.0b	(-.f64 x (/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t))))))
4.4b	(/.f64 y (/.f64 z t))
5.9b	(/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t)))))

rewrite168.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

94×	`times-frac_binary64`
66×	`add-sqr-sqrt_binary64`
63×	`*-un-lft-identity_binary64`
61×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64` `cancel-sign-sub-inv_binary64`

Counts

4 → 140

Calls

4 calls:

10.0ms	(/.f64 y (/.f64 z t))
9.0ms	(-.f64 x (/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t))))))
6.0ms	(/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t)))))
3.0ms	(-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t))))

Compiler

Compiled 3391 to 1425 computations (58% saved)

series176.0ms (3.4%)

Error

0.0b

Counts

4 → 65

Calls

4 calls:

69.0ms	(-.f64 x (/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t))))))
40.0ms	(-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t))))
35.0ms	(/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t)))))
24.0ms	(/.f64 y (/.f64 z t))

Compiler

Compiled 1825 to 1251 computations (31.5% saved)

simplify196.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

554×	`times-frac_binary64`
477×	`associate-/r/_binary64`
465×	`associate-/l/_binary64`
167×	`associate-*l/_binary64`
160×	`distribute-rgt-in_binary64`

Counts

205 → 145

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	277	3962
1	698	3836
2	2170	3674
3	4718	3668
4	4995	3668
5	4962	3668

prune96.0ms (1.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	145	4	149

Error

0.6b

Counts

149 → 4

Alt Table

Status	Error	Program
✓	1.4b	(-.f64 x (/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t))))))
	10.9b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
▶	2.8b	(.f64 (.f64 (cbrt.f64 (-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (/.f64 y (/.f64 z t))))))) (cbrt.f64 (-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (/.f64 y (/.f64 z t)))))))) (cbrt.f64 (-.f64 x (/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t))))))))
	36.1b	(cbrt.f64 (pow.f64 (-.f64 x (/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t)))))) 3))

Compiler

Compiled 2193 to 959 computations (56.3% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

4.4b	(/.f64 y (/.f64 z t))
5.9b	(/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t)))))
5.9b	(/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t)))))
5.9b	(/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t)))))

rewrite220.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

102×	`times-frac_binary64`
70×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
22×	`associate-/r*_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`associate-/l*_binary64`

Counts

4 → 157

Calls

4 calls:

6.0ms	(/.f64 y (/.f64 z t))
5.0ms	(/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t)))))
5.0ms	(/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t)))))
5.0ms	(/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t)))))

Compiler

Compiled 8475 to 3846 computations (54.6% saved)

series193.0ms (3.7%)

Error

0.5b

Counts

4 → 48

Calls

4 calls:

49.0ms	(/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t)))))
48.0ms	(/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t)))))
47.0ms	(/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t)))))
36.0ms	(/.f64 y (/.f64 z t))

Compiler

Compiled 4629 to 2752 computations (40.5% saved)

simplify204.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

466×	`associate-/l*_binary64`
439×	`times-frac_binary64`
434×	`associate-/r/_binary64`
412×	`associate-*l/_binary64`
404×	`associate-/l/_binary64`

Counts

205 → 148

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	201	4163
1	449	3905
2	1369	3902
3	4371	3878
4	4799	3878
5	4980	3878

prune132.0ms (2.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	149	3	152

Error

0.6b

Counts

152 → 3

Alt Table

Status	Error	Program
▶	2.7b	(.f64 (.f64 (cbrt.f64 (-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (/.f64 y (/.f64 z t))))))) (cbrt.f64 (-.f64 x (/.f64 1 (+.f64 (/.f64 z y) (/.f64 -1/2 (/.f64 z t))))))) (cbrt.f64 (-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (/.f64 y (/.f64 z t))))))))
✓	1.4b	(-.f64 x (/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t))))))
	10.9b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))

Compiler

Compiled 6150 to 2825 computations (54.1% saved)

localize27.0ms (0.5%)

Local error

Found 4 expressions with local error:

4.4b	(/.f64 y (/.f64 z t))
4.4b	(/.f64 y (/.f64 z t))
5.9b	(/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t)))))
5.9b	(/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t)))))

rewrite282.0ms (5.4%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

168×	`times-frac_binary64`
104×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
32×	`associate-/r*_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`div-inv_binary64` `associate-/l*_binary64`

Counts

4 → 198

Calls

4 calls:

6.0ms	(/.f64 y (/.f64 z t))
6.0ms	(/.f64 y (/.f64 z t))
5.0ms	(/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t)))))
5.0ms	(/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t)))))

Compiler

Compiled 10578 to 4840 computations (54.2% saved)

series187.0ms (3.6%)

Error

0.6b

Counts

4 → 44

Calls

4 calls:

53.0ms	(/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t)))))
49.0ms	(/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t)))))
37.0ms	(/.f64 y (/.f64 z t))
35.0ms	(/.f64 y (/.f64 z t))

Compiler

Compiled 4298 to 2706 computations (37% saved)

simplify218.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

466×	`associate-/l*_binary64`
439×	`times-frac_binary64`
434×	`associate-/r/_binary64`
412×	`associate-*l/_binary64`
404×	`associate-/l/_binary64`

Counts

242 → 172

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	201	4518
1	449	4266
2	1369	4260
3	4371	4244
4	4799	4244
5	4980	4244

prune148.0ms (2.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	171	4	175

Error

0.6b

Counts

175 → 4

Alt Table

Status	Error	Program
	2.7b	(.f64 (.f64 (cbrt.f64 (-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (/.f64 y (/.f64 z t))))))) (cbrt.f64 (-.f64 x (/.f64 1 (+.f64 (/.f64 z y) (/.f64 -1/2 (/.f64 z t))))))) (cbrt.f64 (-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (/.f64 y (/.f64 z t))))))))
	1.4b	(-.f64 x (/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t))))))
	10.9b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
	2.8b	(.f64 (.f64 (cbrt.f64 (-.f64 x (/.f64 y (-.f64 z (*.f64 1/2 (/.f64 y (/.f64 z t))))))) (cbrt.f64 (-.f64 x (/.f64 1 (+.f64 (/.f64 z y) (/.f64 -1/2 (/.f64 z t))))))) (cbrt.f64 (-.f64 x (/.f64 1 (+.f64 (/.f64 z y) (/.f64 -1/2 (/.f64 z t)))))))

Compiler

Compiled 6664 to 3076 computations (53.8% saved)

regimes631.0ms (12%)

Accuracy

Total 0.5b remaining (57.6%)

Threshold costs 0.5b (57.6%)

Compiler

Compiled 10888 to 6946 computations (36.2% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`sub-neg_binary64` `+-commutative_binary64`
5×	`*-commutative_binary64`
4×	`neg-mul-1_binary64` `neg-sub0_binary64`
2×	`cancel-sign-sub-inv_binary64` `distribute-neg-frac_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	21	19
2	34	19
3	43	19
4	49	19
5	51	19
6	50	19

end1.0ms (0%)

Compiler: Compiled 17 to 11 computations (35.3% saved)

sample841.0ms (16%)

Algorithm

1×

intervals

Results

403.0ms

8000×

body

128

valid

Compiler

Compiled 177 to 112 computations (36.7% saved)

Details

analyze817.0ms (15.6%)

sample24.0ms (0.4%)

simplify62.0ms (1.2%)

prune6.0ms (0.1%)

localize13.0ms (0.2%)

rewrite187.0ms (3.6%)

series177.0ms (3.4%)

simplify136.0ms (2.6%)

prune76.0ms (1.4%)

localize9.0ms (0.2%)

rewrite168.0ms (3.2%)

series176.0ms (3.4%)

simplify196.0ms (3.7%)

prune96.0ms (1.8%)

localize20.0ms (0.4%)

rewrite220.0ms (4.2%)

series193.0ms (3.7%)

simplify204.0ms (3.9%)

prune132.0ms (2.5%)

localize27.0ms (0.5%)

rewrite282.0ms (5.4%)

series187.0ms (3.6%)

simplify218.0ms (4.2%)

prune148.0ms (2.8%)

regimes631.0ms (12%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample841.0ms (16%)

Profiling