Details

analyze534.0ms (9.3%)

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
12.5%	87.3%	0.2%	5
12.5%	87.3%	0.2%	6
18.7%	81.1%	0.2%	7
28.1%	71.7%	0.2%	8
42.1%	57.7%	0.2%	9
42.1%	57.7%	0.2%	10
49.1%	50.7%	0.2%	11
57.3%	42.5%	0.2%	12
66.9%	32.9%	0.2%	13
66.9%	32.9%	0.2%	14

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample972.0ms (16.9%)

Infinites

76.5% of outputs are infinite.

Results

877.0ms

8256×

body

128

valid

Compiler

Compiled 65 to 47 computations (27.7% saved)

simplify105.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-neg_binary64`
614×	`times-frac_binary64`
480×	`neg-mul-1_binary64`
416×	`div-sub_binary64`
394×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	28	23
2	55	23
3	101	21
4	220	21
5	423	21
6	834	20
7	1845	19
8	3893	19
9	4281	19
10	4633	19
11	4956	19
12	4804	19

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	7.8b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
▶	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

Compiler

Compiled 110 to 79 computations (28.2% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)
✓	0.4b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

series46.0ms (0.8%)

Counts

2 → 72

Calls

2 calls:

32.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
14.0ms	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

rewrite43.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

103×	`*-un-lft-identity_binary64`
69×	`times-frac_binary64`
66×	`add-sqr-sqrt_binary64`
66×	`add-cube-cbrt_binary64`
65×	`associate-+r+_binary64`

Counts

2 → 132

Calls

2 calls:

21.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
7.0ms	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

simplify127.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

563×	`fma-def_binary64`
447×	`distribute-rgt-in_binary64`
425×	`distribute-lft-in_binary64`
234×	`fma-neg_binary64`
189×	`exp-prod_binary64`

Counts

204 → 178

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	235	4642
1	625	3549
2	1504	3327
3	4434	3327
4	4943	3327

prune282.0ms (4.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	172	6	178
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	173	7	180

Error

Counts

180 → 7

Alt Table

Status	Error	Program
	32.4b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) (sqrt.f64 t)) (sqrt.f64 t))))
	0.6b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	1.0b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (*.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (/.f64 t (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))))))
	23.4b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 (pow.f64 -2 3) (pow.f64 (/.f64 -2 z) 3)) (.f64 t (+.f64 (.f64 -2 -2) (-.f64 (.f64 (/.f64 -2 z) (/.f64 -2 z)) (.f64 -2 (/.f64 -2 z))))))))
▶	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
	7.8b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
	21.0b	(-.f64 (+.f64 (/.f64 2 t) (/.f64 x y)) 2)

Compiler

Compiled 6479 to 4505 computations (30.5% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))
✓	0.4b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))

series46.0ms (0.8%)

Counts

2 → 72

Calls

2 calls:

33.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
13.0ms	(*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
20×	`times-frac_binary64`
18×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`

Counts

2 → 79

Calls

2 calls:

12.0ms	(*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))
8.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))

simplify139.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

583×	`distribute-rgt-in_binary64`
562×	`distribute-lft-in_binary64`
452×	`fma-def_binary64`
260×	`times-frac_binary64`
226×	`associate-*l/_binary64`

Counts

151 → 130

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	159	2527
1	439	2344
2	1293	2210
3	4077	2210
4	4984	2210
5	4987	2210
6	4941	2210

prune135.0ms (2.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	130	7	137

Error

Counts

137 → 7

Alt Table

Status	Error	Program
	32.4b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) (sqrt.f64 t)) (sqrt.f64 t))))
▶	0.6b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	1.0b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (*.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (/.f64 t (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))))))
	23.4b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 (pow.f64 -2 3) (pow.f64 (/.f64 -2 z) 3)) (.f64 t (+.f64 (.f64 -2 -2) (-.f64 (.f64 (/.f64 -2 z) (/.f64 -2 z)) (.f64 -2 (/.f64 -2 z))))))))
✓	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
	7.8b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
	21.0b	(-.f64 (+.f64 (/.f64 2 t) (/.f64 x y)) 2)

Compiler

Compiled 3337 to 2323 computations (30.4% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.1b	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)
✓	0.5b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

series34.0ms (0.6%)

Counts

1 → 48

Calls

1 calls:

34.0ms

(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

simplify77.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

934×	`fma-def_binary64`
492×	`associate-l_binary64`
423×	`associate-+l+_binary64`
379×	`associate-r_binary64`
267×	`associate-*l/_binary64`

Counts

58 → 29

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	43	1177
1	83	1126
2	164	1126
3	357	1126
4	1233	1009
5	4295	1009
6	5040	1009

prune246.0ms (4.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	73	7	80

Error

Counts

80 → 7

Alt Table

Status	Error	Program
	32.4b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) (sqrt.f64 t)) (sqrt.f64 t))))
✓	0.6b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
▶	1.0b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (*.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (/.f64 t (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))))))
	23.4b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 (pow.f64 -2 3) (pow.f64 (/.f64 -2 z) 3)) (.f64 t (+.f64 (.f64 -2 -2) (-.f64 (.f64 (/.f64 -2 z) (/.f64 -2 z)) (.f64 -2 (/.f64 -2 z))))))))
✓	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
	7.8b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
	21.0b	(-.f64 (+.f64 (/.f64 2 t) (/.f64 x y)) 2)

Compiler

Compiled 1782 to 1302 computations (26.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z))))
✓	0.3b	(/.f64 (*.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (/.f64 t (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))))
✓	0.4b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (*.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (/.f64 t (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))))))
✓	0.7b	(cbrt.f64 (+.f64 -2 (/.f64 -2 z)))

series389.0ms (6.8%)

Counts

4 → 96

Calls

4 calls:

262.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (*.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (/.f64 t (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))))))
81.0ms	(/.f64 (*.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (/.f64 t (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))))
29.0ms	(*.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z))))
16.0ms	(cbrt.f64 (+.f64 -2 (/.f64 -2 z)))

rewrite135.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

270×	`times-frac_binary64`
197×	`*-un-lft-identity_binary64`
148×	`add-sqr-sqrt_binary64`
140×	`add-cube-cbrt_binary64`
129×	`associate-+r+_binary64`

Counts

4 → 316

Calls

4 calls:

33.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (*.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (/.f64 t (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))))))
25.0ms	(/.f64 (*.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (/.f64 t (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))))
14.0ms	(*.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z))))
4.0ms	(cbrt.f64 (+.f64 -2 (/.f64 -2 z)))

simplify327.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

446×	`fma-def_binary64`
373×	`associate-l_binary64`
310×	`associate-/l*_binary64`
255×	`associate-*l/_binary64`
251×	`associate-*r/_binary64`

Counts

412 → 496

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	579	13041
1	1498	11640
2	4550	11600
3	4988	11600
4	4984	11600

prune973.0ms (16.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	579	1	580
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	580	7	587

Error

Counts

587 → 7

Alt Table

Status	Error	Program
	32.4b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) (sqrt.f64 t)) (sqrt.f64 t))))
✓	0.6b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
✓	1.0b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (*.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (/.f64 t (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))))))
	23.4b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 (pow.f64 -2 3) (pow.f64 (/.f64 -2 z) 3)) (.f64 t (+.f64 (.f64 -2 -2) (-.f64 (.f64 (/.f64 -2 z) (/.f64 -2 z)) (.f64 -2 (/.f64 -2 z))))))))
✓	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
	21.0b	(-.f64 (+.f64 (/.f64 2 t) (/.f64 x y)) 2)
	0.6b	(+.f64 (+.f64 (/.f64 2 t) (+.f64 (/.f64 2 (*.f64 z t)) (/.f64 x y))) -2)

Compiler

Compiled 32121 to 24948 computations (22.3% saved)

regimes941.0ms (16.4%)

Accuracy

Total 0.5b remaining (97.9%)

Threshold costs 0.5b (97.9%)

Counts

104 → 1

Compiler

Compiled 22939 to 18176 computations (20.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
5×	`*-commutative_binary64`
5×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	24	22
2	38	22
3	50	22
4	56	22
5	58	22
6	55	22

end120.0ms (2.1%)

Compiler: Compiled 199 to 156 computations (21.6% saved)

Details

analyze534.0ms (9.3%)

sample972.0ms (16.9%)

simplify105.0ms (1.8%)

prune5.0ms (0.1%)

localize10.0ms (0.2%)

series46.0ms (0.8%)

rewrite43.0ms (0.8%)

simplify127.0ms (2.2%)

prune282.0ms (4.9%)

localize11.0ms (0.2%)

series46.0ms (0.8%)

rewrite25.0ms (0.4%)

simplify139.0ms (2.4%)

prune135.0ms (2.3%)

localize10.0ms (0.2%)

series34.0ms (0.6%)

rewrite1.0ms (0%)

simplify77.0ms (1.3%)

prune246.0ms (4.3%)

localize14.0ms (0.2%)

series389.0ms (6.8%)

rewrite135.0ms (2.4%)

simplify327.0ms (5.7%)

prune973.0ms (16.9%)

regimes941.0ms (16.4%)

simplify3.0ms (0.1%)

end120.0ms (2.1%)

Profiling