Details

analyze1.8s (22.9%)

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)

sample1.8s (23.1%)

Results

1.2s	8256×	body	128	valid
509.0ms	2402×	body	128	invalid

Compiler

Compiled 65 to 47 computations (27.7% saved)

simplify101.0ms (1.3%)

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 (0.1%)

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)))
	10.1b	(+.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)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series22.0ms (0.3%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)
10.0ms	(-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

94×	`*-un-lft-identity_binary64`
65×	`add-sqr-sqrt_binary64`
61×	`times-frac_binary64`
60×	`add-cube-cbrt_binary64`
48×	`prod-diff_binary64`

Counts

2 → 118

Calls

2 calls:

12.0ms	(-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))
6.0ms	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

simplify296.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

430×	`fma-def_binary64`
402×	`associate-/l*_binary64`
281×	`distribute-rgt-in_binary64`
257×	`distribute-lft-in_binary64`
198×	`exp-prod_binary64`

Counts

166 → 140

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	216	5034
1	550	3207
2	1310	2469
3	4369	2461
4	4996	2461
5	4985	2461
6	4763	2461

prune191.0ms (2.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	136	4	140
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	136	6	142

Error

0.0b

Counts

142 → 6

Alt Table

Status	Error	Program
	16.0b	(+.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))))))))
	0.7b	(+.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)))))
	0.6b	(+.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)))))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
▶	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
	10.1b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))

Compiler

Compiled 5027 to 3556 computations (29.3% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t)))
✓	0.1b	(*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))

series23.0ms (0.3%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))
10.0ms	(-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t)))

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64`
12×	`add-cube-cbrt_binary64`
11×	`times-frac_binary64`

Counts

2 → 63

Calls

2 calls:

15.0ms	(*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))
3.0ms	(-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t)))

simplify113.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

548×	`fma-neg_binary64`
394×	`associate-l_binary64`
362×	`distribute-rgt-in_binary64`
350×	`associate-r_binary64`
339×	`distribute-lft-in_binary64`

Counts

111 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	129	1711
1	313	1512
2	915	1410
3	3218	1410
4	4914	1410
5	5000	1410
6	4870	1410

prune153.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	110	5	115

Error

0.0b

Counts

115 → 5

Alt Table

Status	Error	Program
▶	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)))))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	10.1b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
	11.5b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (-.f64 4 (/.f64 4 (.f64 z z))) (.f64 t (+.f64 -2 (/.f64 2 z))))))

Compiler

Compiled 2628 to 1858 computations (29.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)
✓	0.4b	(.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)))
✓	0.5b	(cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))

series929.0ms (12%)

Counts

3 → 72

Calls

3 calls:

483.0ms

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

386.0ms

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

61.0ms

(*.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)))

rewrite78.0ms (1%)

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:

24.0ms

(*.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)))

23.0ms

(*.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))

simplify227.0ms (2.9%)

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

prune686.0ms (8.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	516	2	518
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	518	5	523

Error

Counts

523 → 5

Alt Table

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

Compiler

Compiled 22204 to 16357 computations (26.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 -2 (+.f64 (/.f64 -2 t) (/.f64 -2 (*.f64 t z))))
✓	0.0b	(+.f64 (/.f64 -2 t) (/.f64 -2 (*.f64 t z)))
✓	0.6b	(/.f64 -2 (*.f64 t z))

series33.0ms (0.4%)

Counts

3 → 48

Calls

3 calls:

12.0ms	(-.f64 -2 (+.f64 (/.f64 -2 t) (/.f64 -2 (*.f64 t z))))
11.0ms	(/.f64 -2 (*.f64 t z))
11.0ms	(+.f64 (/.f64 -2 t) (/.f64 -2 (*.f64 t z)))

rewrite33.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
24×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
15×	`prod-diff_binary64`
13×	`fma-def_binary64`

Counts

3 → 93

Calls

3 calls:

11.0ms	(-.f64 -2 (+.f64 (/.f64 -2 t) (/.f64 -2 (*.f64 t z))))
8.0ms	(+.f64 (/.f64 -2 t) (/.f64 -2 (*.f64 t z)))
3.0ms	(/.f64 -2 (*.f64 t z))

simplify83.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

736×	`fma-neg_binary64`
430×	`fma-def_binary64`
212×	`distribute-rgt-in_binary64`
186×	`distribute-lft-in_binary64`
175×	`*-commutative_binary64`

Counts

141 → 141

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	151	2395
1	347	2092
2	997	1840
3	3690	1840
4	4922	1840

prune145.0ms (1.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	141	5	146

Error

Counts

146 → 5

Alt Table

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

Compiler

Compiled 3691 to 2277 computations (38.3% saved)

regimes881.0ms (11.3%)

Accuracy

Total 0.1b remaining (73%)

Threshold costs 0.1b (73%)

Counts

99 → 1

Compiler

Compiled 23112 to 18038 computations (22% 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

end108.0ms (1.4%)

Compiler: Compiled 189 to 144 computations (23.8% saved)

Details

analyze1.8s (22.9%)

sample1.8s (23.1%)

simplify101.0ms (1.3%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

series22.0ms (0.3%)

rewrite30.0ms (0.4%)

simplify296.0ms (3.8%)

prune191.0ms (2.5%)

localize9.0ms (0.1%)

series23.0ms (0.3%)

rewrite21.0ms (0.3%)

simplify113.0ms (1.5%)

prune153.0ms (2%)

localize12.0ms (0.2%)

series929.0ms (12%)

rewrite78.0ms (1%)

simplify227.0ms (2.9%)

prune686.0ms (8.8%)

localize9.0ms (0.1%)

series33.0ms (0.4%)

rewrite33.0ms (0.4%)

simplify83.0ms (1.1%)

prune145.0ms (1.9%)

regimes881.0ms (11.3%)

simplify3.0ms (0%)

end108.0ms (1.4%)

Profiling