Details

analyze1.7s (18.5%)

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
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
3.7%	96.1%	0.2%	13
4.2%	94.5%	1.3%	14

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample1.7s (18.5%)

Results

1.3s	8256×	body	128	valid
350.0ms	2487×	body	128	invalid

Compiler

Compiled 65 to 47 computations (27.7% saved)

simplify99.0ms (1.1%)

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

prune4.0ms (0%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	9.1b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
▶	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

Compiler

Compiled 110 to 79 computations (28.2% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
✓	0.1b	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

series48.0ms (0.5%)

Counts

2 → 72

Calls

2 calls:

35.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
12.0ms	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

rewrite45.0ms (0.5%)

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:

22.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
6.0ms	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

simplify126.0ms (1.4%)

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 → 177

Iterations

Useful iterations: 2 (0.0ms)

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

prune208.0ms (2.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	172	5	177
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	173	6	179

Error

0.0b

Counts

179 → 6

Alt Table

Status	Error	Program
	9.1b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
	30.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (sqrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (sqrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
▶	0.1b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
	0.7b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (/.f64 1 (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (+.f64 -2 (/.f64 -2 z)) (cbrt.f64 t)))))
	0.7b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (/.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) t))))

Compiler

Compiled 6411 to 4454 computations (30.5% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series85.0ms (0.9%)

Counts

1 → 48

Calls

1 calls:

85.0ms

(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)))

simplify71.0ms (0.8%)

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

prune75.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	71	6	77

Error

0.0b

Counts

77 → 6

Alt Table

Status	Error	Program
	9.1b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
	30.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (sqrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (sqrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
✓	0.1b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
▶	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
	0.7b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (/.f64 1 (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (+.f64 -2 (/.f64 -2 z)) (cbrt.f64 t)))))
	0.7b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (/.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) t))))

Compiler

Compiled 1726 to 1258 computations (27.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
✓	0.6b	(cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))

series901.0ms (9.7%)

Counts

3 → 72

Calls

3 calls:

481.0ms

(*.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

360.0ms

(cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))

58.0ms

(*.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

rewrite70.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`cbrt-prod_binary64`
114×	`*-un-lft-identity_binary64`
91×	`times-frac_binary64`
88×	`add-sqr-sqrt_binary64`
60×	`add-cube-cbrt_binary64`

Counts

3 → 181

Calls

3 calls:

23.0ms

(*.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

19.0ms

(*.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

5.0ms

(cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))

simplify254.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

793×	`fma-def_binary64`
506×	`times-frac_binary64`
279×	`associate-r_binary64`
275×	`cancel-sign-sub-inv_binary64`
272×	`associate-l_binary64`

Counts

253 → 276

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	323	7739
1	734	7358
2	2319	6759
3	4761	6652
4	4989	6652
5	4963	6652

prune942.0ms (10.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	516	2	518
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	519	5	524

Error

Counts

524 → 5

Alt Table

Status	Error	Program
	9.1b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
✓	0.1b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	0.9b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (.f64 (.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (cbrt.f64 t)))))
	14.0b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 -2 (*.f64 t z)))) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
▶	0.7b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (/.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) t))))

Compiler

Compiled 22217 to 16368 computations (26.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z))))
✓	0.2b	(/.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) t)
✓	0.4b	(.f64 (.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (/.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) t))
✓	0.8b	(cbrt.f64 (+.f64 -2 (/.f64 -2 z)))

series564.0ms (6.1%)

Counts

4 → 72

Calls

4 calls:

442.0ms	(/.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) t)
71.0ms	(.f64 (.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (/.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) t))
28.0ms	(*.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z))))
23.0ms	(cbrt.f64 (+.f64 -2 (/.f64 -2 z)))

rewrite108.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`*-un-lft-identity_binary64`
57×	`cbrt-prod_binary64`
56×	`add-sqr-sqrt_binary64`
44×	`times-frac_binary64`
43×	`add-cube-cbrt_binary64`

Counts

4 → 184

Calls

4 calls:

67.0ms	(.f64 (.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (/.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) t))
11.0ms	(*.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z))))
8.0ms	(/.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) t)
4.0ms	(cbrt.f64 (+.f64 -2 (/.f64 -2 z)))

simplify247.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

387×	`associate-l_binary64`
337×	`associate-r_binary64`
335×	`fma-neg_binary64`
326×	`cancel-sign-sub-inv_binary64`
234×	`*-commutative_binary64`

Counts

256 → 323

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	356	6911
1	935	6474
2	3240	5896
3	4605	5701
4	4980	5701
5	4988	5701

prune533.0ms (5.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	408	1	409
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	409	5	414

Error

Counts

414 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	0.9b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (.f64 (.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (cbrt.f64 t)))))
	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (-.f64 (/.f64 -2 (*.f64 z t)) (/.f64 2 t))))
	14.0b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 -2 (*.f64 t z)))) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
✓	0.7b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (/.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) t))))

Compiler

Compiled 16421 to 12785 computations (22.1% saved)

regimes1.3s (14%)

Accuracy

Total 0.1b remaining (75%)

Threshold costs 0.1b (75%)

Counts

129 → 1

Compiler

Compiled 22358 to 17735 computations (20.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	19
1	21	19
2	20	19

end120.0ms (1.3%)

Compiler: Compiled 176 to 135 computations (23.3% saved)

Details

analyze1.7s (18.5%)

sample1.7s (18.5%)

simplify99.0ms (1.1%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series48.0ms (0.5%)

rewrite45.0ms (0.5%)

simplify126.0ms (1.4%)

prune208.0ms (2.2%)

localize10.0ms (0.1%)

series85.0ms (0.9%)

rewrite1.0ms (0%)

simplify71.0ms (0.8%)

prune75.0ms (0.8%)

localize15.0ms (0.2%)

series901.0ms (9.7%)

rewrite70.0ms (0.7%)

simplify254.0ms (2.7%)

prune942.0ms (10.1%)

localize12.0ms (0.1%)

series564.0ms (6.1%)

rewrite108.0ms (1.2%)

simplify247.0ms (2.7%)

prune533.0ms (5.7%)

regimes1.3s (14%)

simplify2.0ms (0%)

end120.0ms (1.3%)

Profiling