Details

analyze3.5s (31.6%)

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
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)

sample69.0ms (0.6%)

Algorithm

1×

intervals

Results

30.0ms	256×	body	128	valid
9.0ms	79×	body	128	invalid

Compiler

Compiled 47 to 35 computations (25.5% saved)

simplify158.0ms (1.4%)

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

prune8.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	9.4b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))

Compiler

Compiled 110 to 79 computations (28.2% saved)

localize20.0ms (0.2%)

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)

series102.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

73.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
29.0ms	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

rewrite99.0ms (0.9%)

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:

39.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
13.0ms	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

simplify220.0ms (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 → 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

prune380.0ms (3.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	173	4	177
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	173	6	179

Error

0.0b

Counts

179 → 6

Alt Table

Status	Error	Program
	33.8b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) (sqrt.f64 t)) (sqrt.f64 t))))
	9.4b	(+.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)))
	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)))))
▶	0.6b	(+.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)))))
	10.4b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (-.f64 (.f64 -2 -2) (.f64 (/.f64 -2 z) (/.f64 -2 z))) (*.f64 t (-.f64 -2 (/.f64 -2 z))))))

Compiler

Compiled 6374 to 4421 computations (30.6% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (*.f64 (cbrt.f64 t) (cbrt.f64 t)))
✓	0.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (+.f64 -2 (/.f64 -2 z)) (cbrt.f64 t)))
✓	0.5b	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
✓	0.6b	(cbrt.f64 t)

series337.0ms (3.1%)

Counts

4 → 60

Calls

4 calls:

123.0ms	(/.f64 1 (*.f64 (cbrt.f64 t) (cbrt.f64 t)))
78.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (+.f64 -2 (/.f64 -2 z)) (cbrt.f64 t)))
67.0ms	(cbrt.f64 t)
67.0ms	(*.f64 (cbrt.f64 t) (cbrt.f64 t))

rewrite77.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`add-exp-log_binary64`
61×	`add-sqr-sqrt_binary64`
47×	`*-un-lft-identity_binary64`
42×	`times-frac_binary64`
34×	`associate-r_binary64`

Counts

4 → 170

Calls

4 calls:

34.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (+.f64 -2 (/.f64 -2 z)) (cbrt.f64 t)))
10.0ms	(/.f64 1 (*.f64 (cbrt.f64 t) (cbrt.f64 t)))
8.0ms	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
1.0ms	(cbrt.f64 t)

simplify239.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

569×	`fma-def_binary64`
557×	`associate-/r/_binary64`
388×	`unswap-sqr_binary64`
386×	`*-commutative_binary64`
278×	`fma-neg_binary64`

Counts

230 → 242

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	193	4033
1	451	2821
2	1729	2642
3	3067	2455
4	4474	2443
5	4979	2443
6	4933	2443

prune333.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	278	2	280
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	279	7	286

Error

Counts

286 → 7

Alt Table

Status	Error	Program
	33.8b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) (sqrt.f64 t)) (sqrt.f64 t))))
	9.4b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
	10.4b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (-.f64 (.f64 -2 -2) (.f64 (/.f64 -2 z) (/.f64 -2 z))) (*.f64 t (-.f64 -2 (/.f64 -2 z))))))
▶	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (/.f64 (/.f64 1 (cbrt.f64 t)) (cbrt.f64 t)) (/.f64 (+.f64 -2 (/.f64 -2 z)) (cbrt.f64 t)))))
✓	0.1b	(+.f64 (/.f64 x 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)))))
	1.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cbrt.f64 t)) 8)) (/.f64 (+.f64 -2 (/.f64 -2 z)) (cbrt.f64 (cbrt.f64 t))))))

Compiler

Compiled 8035 to 4565 computations (43.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (+.f64 -2 (/.f64 -2 z)) (cbrt.f64 t))
✓	0.3b	(*.f64 (/.f64 (/.f64 1 (cbrt.f64 t)) (cbrt.f64 t)) (/.f64 (+.f64 -2 (/.f64 -2 z)) (cbrt.f64 t)))
✓	0.3b	(/.f64 (/.f64 1 (cbrt.f64 t)) (cbrt.f64 t))
	0.6b	(cbrt.f64 t)

series235.0ms (2.2%)

Counts

3 → 60

Calls

3 calls:

122.0ms	(/.f64 (+.f64 -2 (/.f64 -2 z)) (cbrt.f64 t))
72.0ms	(/.f64 (/.f64 1 (cbrt.f64 t)) (cbrt.f64 t))
41.0ms	(*.f64 (/.f64 (/.f64 1 (cbrt.f64 t)) (cbrt.f64 t)) (/.f64 (+.f64 -2 (/.f64 -2 z)) (cbrt.f64 t)))

rewrite141.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

624×	`times-frac_binary64`
430×	`add-sqr-sqrt_binary64`
333×	`*-un-lft-identity_binary64`
318×	`cbrt-prod_binary64`
295×	`add-cube-cbrt_binary64`

Counts

3 → 462

Calls

3 calls:

59.0ms	(*.f64 (/.f64 (/.f64 1 (cbrt.f64 t)) (cbrt.f64 t)) (/.f64 (+.f64 -2 (/.f64 -2 z)) (cbrt.f64 t)))
8.0ms	(/.f64 (/.f64 1 (cbrt.f64 t)) (cbrt.f64 t))
7.0ms	(/.f64 (+.f64 -2 (/.f64 -2 z)) (cbrt.f64 t))

simplify431.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

892×	`fma-def_binary64`
385×	`distribute-rgt-in_binary64`
374×	`distribute-lft-in_binary64`
354×	`associate-*l/_binary64`
348×	`associate-/r/_binary64`

Counts

522 → 651

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	300	14564
1	858	12912
2	2383	11817
3	4054	11621
4	4979	11621
5	4938	11621

prune843.0ms (7.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	707	1	708
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	708	7	715

Error

Counts

715 → 7

Alt Table

Status	Error	Program
	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (*.f64 (/.f64 (/.f64 1 (cbrt.f64 t)) (cbrt.f64 t)) (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 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)))))
	10.4b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (-.f64 (.f64 -2 -2) (.f64 (/.f64 -2 z) (/.f64 -2 z))) (*.f64 t (-.f64 -2 (/.f64 -2 z))))))
✓	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (/.f64 (/.f64 1 (cbrt.f64 t)) (cbrt.f64 t)) (/.f64 (+.f64 -2 (/.f64 -2 z)) (cbrt.f64 t)))))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	9.4b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
	1.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cbrt.f64 t)) 8)) (/.f64 (+.f64 -2 (/.f64 -2 z)) (cbrt.f64 (cbrt.f64 t))))))

Compiler

Compiled 23832 to 12979 computations (45.5% saved)

localize14.0ms (0.1%)

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))

series904.0ms (8.3%)

Counts

3 → 72

Calls

3 calls:

487.0ms

(*.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))

57.0ms

(*.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)))

rewrite72.0ms (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:

22.0ms

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

22.0ms

(*.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)))

5.0ms

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

simplify231.0ms (2.1%)

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

prune771.0ms (7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	517	1	518
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	518	7	525

Error

Counts

525 → 7

Alt Table

Status	Error	Program
	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (*.f64 (/.f64 (/.f64 1 (cbrt.f64 t)) (cbrt.f64 t)) (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 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)))))
	10.4b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (-.f64 (.f64 -2 -2) (.f64 (/.f64 -2 z) (/.f64 -2 z))) (*.f64 t (-.f64 -2 (/.f64 -2 z))))))
✓	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (/.f64 (/.f64 1 (cbrt.f64 t)) (cbrt.f64 t)) (/.f64 (+.f64 -2 (/.f64 -2 z)) (cbrt.f64 t)))))
	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (+.f64 (/.f64 -2 t) (/.f64 -2 (*.f64 t z)))))
	1.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cbrt.f64 t)) 8)) (/.f64 (+.f64 -2 (/.f64 -2 z)) (cbrt.f64 (cbrt.f64 t))))))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

Compiler

Compiled 22127 to 16296 computations (26.4% saved)

regimes553.0ms (5.1%)

Accuracy

Total 0.1b remaining (71.9%)

Threshold costs 0.1b (71.9%)

Counts

71 → 1

Compiler

Compiled 12425 to 9377 computations (24.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	16	19
2	23	19
3	32	19
4	39	19
5	42	19
6	43	19
7	42	19

end1.0ms (0%)

Compiler: Compiled 17 to 13 computations (23.5% saved)

sample1.2s (10.9%)

Algorithm

1×

intervals

Results

528.0ms	8000×	body	128	valid
156.0ms	2331×	body	128	invalid

Compiler

Compiled 223 to 167 computations (25.1% saved)

Details

analyze3.5s (31.6%)

sample69.0ms (0.6%)

simplify158.0ms (1.4%)

prune8.0ms (0.1%)

localize20.0ms (0.2%)

series102.0ms (0.9%)

rewrite99.0ms (0.9%)

simplify220.0ms (2%)

prune380.0ms (3.5%)

localize28.0ms (0.3%)

series337.0ms (3.1%)

rewrite77.0ms (0.7%)

simplify239.0ms (2.2%)

prune333.0ms (3%)

localize15.0ms (0.1%)

series235.0ms (2.2%)

rewrite141.0ms (1.3%)

simplify431.0ms (3.9%)

prune843.0ms (7.7%)

localize14.0ms (0.1%)

series904.0ms (8.3%)

rewrite72.0ms (0.7%)

simplify231.0ms (2.1%)

prune771.0ms (7%)

regimes553.0ms (5.1%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.2s (10.9%)

Profiling