Details

analyze1.4s (21.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
3.1%	96.7%	0.1%	9
4.7%	95.2%	0.1%	10
7.8%	92.1%	0.1%	11
11.4%	88.4%	0.1%	12
14.7%	85.1%	0.2%	13
17%	82.9%	0.2%	14

Compiler

Compiled 16 to 9 computations (43.8% saved)

sample1.1s (17%)

Results

928.0ms	8256×	body	128	valid
75.0ms	134×	body	8192	exit
14.0ms	131×	body	128	invalid

Compiler

Compiled 47 to 26 computations (44.7% saved)

simplify73.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-def_binary64`
505×	`times-frac_binary64`
497×	`div-sub_binary64`
469×	`neg-mul-1_binary64`
463×	`neg-sub0_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	30	18
2	83	18
3	193	18
4	334	18
5	435	18
6	600	18
7	871	18
8	1369	16
9	3594	16
10	4298	16
11	4856	16

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	17.1b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))

Compiler

Compiled 84 to 47 computations (44% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 v (+.f64 t1 u))
✓	0.0b	(-.f64 -1 (/.f64 u t1))
✓	0.3b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

series95.0ms (1.4%)

Counts

3 → 84

Calls

3 calls:

73.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
17.0ms	(/.f64 v (+.f64 t1 u))
6.0ms	(-.f64 -1 (/.f64 u t1))

rewrite53.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

260×	`times-frac_binary64`
229×	`add-sqr-sqrt_binary64`
219×	`*-un-lft-identity_binary64`
129×	`add-cube-cbrt_binary64`
40×	`difference-of-squares_binary64`

Counts

3 → 257

Calls

3 calls:

12.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
7.0ms	(-.f64 -1 (/.f64 u t1))
4.0ms	(/.f64 v (+.f64 t1 u))

simplify229.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

817×	`fma-def_binary64`
310×	`associate-/l/_binary64`
233×	`associate-/l*_binary64`
223×	`div-sub_binary64`
212×	`fma-neg_binary64`

Counts

341 → 304

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	465	9966
1	1202	8417
2	3569	8323
3	4946	8323
4	5008	8323

prune265.0ms (4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	298	6	304
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	300	6	306

Error

Counts

306 → 6

Alt Table

Status	Error	Program
	2.7b	(/.f64 v (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 1 (+.f64 t1 u))))
	1.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))) (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))))
	0.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (neg.f64 (/.f64 u (pow.f64 (cbrt.f64 t1) 3)))))
	9.9b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 (fma.f64 1 -1 (neg.f64 (.f64 (/.f64 1 t1) u))) (fma.f64 (neg.f64 (/.f64 1 t1)) u (.f64 (/.f64 1 t1) u))))
	7.0b	(.f64 -1 (/.f64 v (+.f64 t1 (+.f64 (/.f64 (pow.f64 u 2) t1) (.f64 2 u)))))
▶	0.4b	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))

Compiler

Compiled 8221 to 2960 computations (64% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 v (+.f64 t1 u))
	0.0b	(-.f64 -1 (/.f64 u t1))
✓	0.2b	(/.f64 1 (-.f64 -1 (/.f64 u t1)))
✓	0.3b	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))

series79.0ms (1.2%)

Counts

2 → 60

Calls

2 calls:

70.0ms	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))
9.0ms	(/.f64 1 (-.f64 -1 (/.f64 u t1)))

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

83×	`add-sqr-sqrt_binary64`
62×	`times-frac_binary64`
53×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
28×	`add-exp-log_binary64`

Counts

2 → 122

Calls

2 calls:

18.0ms	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))
6.0ms	(/.f64 1 (-.f64 -1 (/.f64 u t1)))

simplify116.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

766×	`associate-/l*_binary64`
478×	`associate-*l/_binary64`
442×	`associate-/r*_binary64`
294×	`fma-neg_binary64`
258×	`fma-def_binary64`

Counts

182 → 202

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	214	3921
1	576	3621
2	1776	3532
3	4978	3523
4	5138	3523

prune302.0ms (4.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	334	1	335
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	335	6	341

Error

Counts

341 → 6

Alt Table

Status	Error	Program
▶	0.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (neg.f64 (/.f64 u (pow.f64 (cbrt.f64 t1) 3)))))
	9.9b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 (fma.f64 1 -1 (neg.f64 (.f64 (/.f64 1 t1) u))) (fma.f64 (neg.f64 (/.f64 1 t1)) u (.f64 (/.f64 1 t1) u))))
	7.0b	(.f64 -1 (/.f64 v (+.f64 t1 (+.f64 (/.f64 (pow.f64 u 2) t1) (.f64 2 u)))))
✓	0.4b	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))
	0.7b	(/.f64 (*.f64 v (/.f64 1 (-.f64 -1 (/.f64 u t1)))) (+.f64 t1 u))
	1.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))) (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))))

Compiler

Compiled 8590 to 3658 computations (57.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 -1 (neg.f64 (/.f64 u (pow.f64 (cbrt.f64 t1) 3))))
✓	0.3b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (neg.f64 (/.f64 u (pow.f64 (cbrt.f64 t1) 3)))))
✓	0.6b	(cbrt.f64 t1)
✓	0.7b	(pow.f64 (cbrt.f64 t1) 3)

series183.0ms (2.8%)

Counts

4 → 84

Calls

4 calls:

74.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (neg.f64 (/.f64 u (pow.f64 (cbrt.f64 t1) 3)))))
59.0ms	(pow.f64 (cbrt.f64 t1) 3)
29.0ms	(cbrt.f64 t1)
20.0ms	(+.f64 -1 (neg.f64 (/.f64 u (pow.f64 (cbrt.f64 t1) 3))))

rewrite72.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

194×	`*-un-lft-identity_binary64`
162×	`times-frac_binary64`
78×	`add-sqr-sqrt_binary64`
78×	`add-cube-cbrt_binary64`
58×	`distribute-lft-out_binary64`

Counts

4 → 197

Calls

4 calls:

28.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (neg.f64 (/.f64 u (pow.f64 (cbrt.f64 t1) 3)))))
20.0ms	(+.f64 -1 (neg.f64 (/.f64 u (pow.f64 (cbrt.f64 t1) 3))))
2.0ms	(pow.f64 (cbrt.f64 t1) 3)
1.0ms	(cbrt.f64 t1)

simplify167.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

588×	`fma-def_binary64`
471×	`div-sub_binary64`
201×	`fma-neg_binary64`
185×	`associate-/l/_binary64`
182×	`cancel-sign-sub-inv_binary64`

Counts

281 → 260

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	306	5679
1	768	5482
2	2613	5482
3	4408	5478
4	4917	5478

prune231.0ms (3.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	259	1	260
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	260	6	266

Error

Counts

266 → 6

Alt Table

Status	Error	Program
✓	0.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (neg.f64 (/.f64 u (pow.f64 (cbrt.f64 t1) 3)))))
	9.9b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 (fma.f64 1 -1 (neg.f64 (.f64 (/.f64 1 t1) u))) (fma.f64 (neg.f64 (/.f64 1 t1)) u (.f64 (/.f64 1 t1) u))))
	7.0b	(neg.f64 (/.f64 v (+.f64 t1 (fma.f64 u 2 (/.f64 (*.f64 u u) t1)))))
✓	0.4b	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))
▶	0.7b	(/.f64 (*.f64 v (/.f64 1 (-.f64 -1 (/.f64 u t1)))) (+.f64 t1 u))
	1.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))) (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))))

Compiler

Compiled 6710 to 3148 computations (53.1% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 -1 (/.f64 u t1))
	0.2b	(/.f64 1 (-.f64 -1 (/.f64 u t1)))
✓	0.7b	(/.f64 (*.f64 v (/.f64 1 (-.f64 -1 (/.f64 u t1)))) (+.f64 t1 u))
✓	3.1b	(*.f64 v (/.f64 1 (-.f64 -1 (/.f64 u t1))))

series99.0ms (1.5%)

Counts

2 → 72

Calls

2 calls:

70.0ms	(/.f64 (*.f64 v (/.f64 1 (-.f64 -1 (/.f64 u t1)))) (+.f64 t1 u))
28.0ms	(*.f64 v (/.f64 1 (-.f64 -1 (/.f64 u t1))))

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
27×	`times-frac_binary64`
26×	`*-un-lft-identity_binary64`
26×	`add-exp-log_binary64`
24×	`associate-r_binary64`

Counts

2 → 82

Calls

2 calls:

12.0ms	(/.f64 (*.f64 v (/.f64 1 (-.f64 -1 (/.f64 u t1)))) (+.f64 t1 u))
11.0ms	(*.f64 v (/.f64 1 (-.f64 -1 (/.f64 u t1))))

simplify102.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

604×	`associate-/r*_binary64`
446×	`associate-/r/_binary64`
440×	`associate-/l/_binary64`
316×	`fma-neg_binary64`
262×	`fma-def_binary64`

Counts

154 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	202	3190
1	531	2931
2	1891	2834
3	4572	2834
4	4974	2834

prune299.0ms (4.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	313	0	313
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	313	6	319

Error

Counts

319 → 6

Alt Table

Status	Error	Program
✓	0.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (neg.f64 (/.f64 u (pow.f64 (cbrt.f64 t1) 3)))))
	9.9b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 (fma.f64 1 -1 (neg.f64 (.f64 (/.f64 1 t1) u))) (fma.f64 (neg.f64 (/.f64 1 t1)) u (.f64 (/.f64 1 t1) u))))
	7.0b	(neg.f64 (/.f64 v (+.f64 t1 (fma.f64 u 2 (/.f64 (*.f64 u u) t1)))))
✓	0.4b	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))
✓	0.7b	(/.f64 (*.f64 v (/.f64 1 (-.f64 -1 (/.f64 u t1)))) (+.f64 t1 u))
	1.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))) (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))))

Compiler

Compiled 7673 to 3565 computations (53.5% saved)

regimes1.5s (22.6%)

Accuracy

Total 0.7b remaining (52.9%)

Threshold costs 0.7b (52.9%)

Counts

265 → 1

Compiler

Compiled 22306 to 14134 computations (36.6% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	18	16
2	23	16
3	27	16
4	30	16
5	31	16
6	30	16

end96.0ms (1.5%)

Compiler: Compiled 165 to 104 computations (37% saved)

Details

analyze1.4s (21.5%)

sample1.1s (17%)

simplify73.0ms (1.1%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series95.0ms (1.4%)

rewrite53.0ms (0.8%)

simplify229.0ms (3.5%)

prune265.0ms (4%)

localize8.0ms (0.1%)

series79.0ms (1.2%)

rewrite36.0ms (0.5%)

simplify116.0ms (1.8%)

prune302.0ms (4.6%)

localize10.0ms (0.2%)

series183.0ms (2.8%)

rewrite72.0ms (1.1%)

simplify167.0ms (2.5%)

prune231.0ms (3.5%)

localize8.0ms (0.1%)

series99.0ms (1.5%)

rewrite29.0ms (0.4%)

simplify102.0ms (1.6%)

prune299.0ms (4.5%)

regimes1.5s (22.6%)

simplify4.0ms (0.1%)

end96.0ms (1.5%)

Profiling