Details

analyze160.0ms (2.5%)

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%	50%	50%	4
0%	50%	50%	5
12.5%	37.5%	50%	6
18.7%	31.2%	50%	7
28.1%	21.9%	50%	8
32.8%	17.2%	50%	9
38.2%	11.7%	50%	10
41%	9%	50%	11
43.9%	6%	50%	12
45.4%	4.6%	50%	13
46.9%	3.1%	50%	14

Compiler

Compiled 31 to 22 computations (29% saved)

sample1.5s (23.6%)

Results

1.5s	8256×	body	128	valid
1.0ms	10×	body	128	invalid

Compiler

Compiled 92 to 65 computations (29.3% saved)

simplify31.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

826×	`times-frac_binary64`
592×	`fma-def_binary64`
509×	`associate-/r*_binary64`
353×	`associate-/l*_binary64`
343×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	43
1	58	43
2	179	38
3	824	36
4	3882	36
5	5029	36

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))

Compiler

Compiled 106 to 73 computations (31.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 v (*.f64 -6 v) 2))
✓	0.2b	(*.f64 (PI.f64) t)
✓	0.3b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
✓	0.5b	(.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))

series224.0ms (3.5%)

Counts

4 → 60

Calls

4 calls:

179.0ms	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
37.0ms	(.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
6.0ms	(sqrt.f64 (fma.f64 v (*.f64 -6 v) 2))
2.0ms	(*.f64 (PI.f64) t)

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-cbrt-cube_binary64`
29×	`add-exp-log_binary64`
20×	`distribute-lft-in_binary64`
20×	`distribute-rgt-in_binary64`
18×	`add-sqr-sqrt_binary64`

Counts

4 → 112

Calls

4 calls:

9.0ms	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
8.0ms	(.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
3.0ms	(*.f64 (PI.f64) t)
1.0ms	(sqrt.f64 (fma.f64 v (*.f64 -6 v) 2))

simplify151.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

767×	`fma-def_binary64`
492×	`associate-l_binary64`
482×	`associate-/r*_binary64`
433×	`times-frac_binary64`
256×	`associate-/l*_binary64`

Counts

172 → 231

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	462	7020
1	1319	6443
2	4898	6428
3	5385	6428

prune297.0ms (4.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	225	6	231
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	226	6	232

Error

0.0b

Counts

232 → 6

Alt Table

Status	Error	Program
	0.7b	(.f64 (/.f64 (-.f64 1 (.f64 5 (pow.f64 v 2))) (.f64 (-.f64 (PI.f64) (.f64 (pow.f64 v 2) (PI.f64))) t)) (sqrt.f64 (/.f64 1 (-.f64 2 (*.f64 6 (pow.f64 v 2))))))
	1.0b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 v (.f64 -6 v) 2)) (cbrt.f64 (fma.f64 v (.f64 -6 v) 2)))) (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 v (.f64 -6 v) 2))) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v))))))
	0.5b	(.f64 (/.f64 1 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
	1.4b	(/.f64 (sqrt.f64 1/2) (*.f64 (PI.f64) t))
	0.4b	(/.f64 (fma.f64 v (.f64 v -5) 1) (/.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (pow.f64 v 6)))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 v v) (.f64 v v)) (.f64 1 (*.f64 v v))))))
▶	0.4b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))

Compiler

Compiled 9727 to 6221 computations (36% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (fma.f64 v (*.f64 -6 v) 2))
	0.2b	(*.f64 (PI.f64) t)
✓	0.4b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
✓	1.0b	(/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)))

series126.0ms (2%)

Counts

2 → 36

Calls

2 calls:

115.0ms

(/.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2))) (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))

10.0ms

(/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
43×	`add-cube-cbrt_binary64`
30×	`sqrt-prod_binary64`

Counts

2 → 113

Calls

2 calls:

10.0ms

(/.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2))) (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))

3.0ms

(/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)))

simplify150.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

879×	`fma-def_binary64`
419×	`associate-/r*_binary64`
279×	`times-frac_binary64`
276×	`associate-/l*_binary64`
250×	`associate-l_binary64`

Counts

149 → 220

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	436	7537
1	1236	6895
2	4807	6872
3	5527	6872

prune335.0ms (5.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	285	3	288
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	287	7	294

Error

Counts

294 → 7

Alt Table

Status	Error	Program
	0.7b	(.f64 (/.f64 (-.f64 1 (.f64 5 (pow.f64 v 2))) (.f64 (-.f64 (PI.f64) (.f64 (pow.f64 v 2) (PI.f64))) t)) (sqrt.f64 (/.f64 1 (-.f64 2 (*.f64 6 (pow.f64 v 2))))))
	1.0b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 v (.f64 -6 v) 2)) (cbrt.f64 (fma.f64 v (.f64 -6 v) 2)))) (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 v (.f64 -6 v) 2))) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v))))))
	1.4b	(/.f64 (sqrt.f64 1/2) (*.f64 (PI.f64) t))
	0.5b	(.f64 (/.f64 (sqrt.f64 (fma.f64 v (.f64 v -5) 1)) (.f64 (PI.f64) t)) (/.f64 (/.f64 (sqrt.f64 (fma.f64 v (.f64 v -5) 1)) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) (-.f64 1 (.f64 v v))))
	0.5b	(.f64 (/.f64 (sqrt.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)))) (.f64 (PI.f64) t)) (/.f64 (sqrt.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)))) (-.f64 1 (*.f64 v v))))
▶	0.4b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))
✓	0.4b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))

Compiler

Compiled 12282 to 8240 computations (32.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 v (*.f64 v -6) 2))
	0.2b	(*.f64 (PI.f64) t)
✓	0.3b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))
✓	0.5b	(.f64 (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

series160.0ms (2.5%)

Counts

3 → 60

Calls

3 calls:

118.0ms

(/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))

37.0ms

(*.f64 (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

4.0ms

(sqrt.f64 (fma.f64 v (*.f64 v -6) 2))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-cbrt-cube_binary64`
26×	`add-exp-log_binary64`
13×	`pow1_binary64`
12×	`cbrt-unprod_binary64`
12×	`prod-exp_binary64`

Counts

3 → 72

Calls

3 calls:

9.0ms

(/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))

8.0ms

(*.f64 (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

1.0ms

(sqrt.f64 (fma.f64 v (*.f64 v -6) 2))

simplify127.0ms (2%)

Algorithm

1×	egg-herbie

Rules

694×	`fma-def_binary64`
413×	`associate-/r*_binary64`
405×	`associate-l_binary64`
386×	`associate-r_binary64`
350×	`times-frac_binary64`

Counts

132 → 176

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	410	5873
1	1253	5288
2	4867	5265
3	5287	5265

prune213.0ms (3.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	199	7	206

Error

Counts

206 → 7

Alt Table

Status	Error	Program
	0.7b	(.f64 (/.f64 (-.f64 1 (.f64 5 (pow.f64 v 2))) (.f64 (-.f64 (PI.f64) (.f64 (pow.f64 v 2) (PI.f64))) t)) (sqrt.f64 (/.f64 1 (-.f64 2 (*.f64 6 (pow.f64 v 2))))))
	1.0b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 v (.f64 -6 v) 2)) (cbrt.f64 (fma.f64 v (.f64 -6 v) 2)))) (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 v (.f64 -6 v) 2))) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v))))))
	1.4b	(/.f64 (sqrt.f64 1/2) (*.f64 (PI.f64) t))
▶	0.5b	(.f64 (/.f64 (sqrt.f64 (fma.f64 v (.f64 v -5) 1)) (.f64 (PI.f64) t)) (/.f64 (/.f64 (sqrt.f64 (fma.f64 v (.f64 v -5) 1)) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) (-.f64 1 (.f64 v v))))
	0.5b	(.f64 (/.f64 (sqrt.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)))) (.f64 (PI.f64) t)) (/.f64 (sqrt.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)))) (-.f64 1 (*.f64 v v))))
✓	0.4b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))
✓	0.4b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))

Compiler

Compiled 8421 to 5485 computations (34.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (PI.f64) t)
✓	0.3b	(/.f64 (sqrt.f64 (fma.f64 v (.f64 v -5) 1)) (.f64 (PI.f64) t))
✓	0.4b	(.f64 (/.f64 (sqrt.f64 (fma.f64 v (.f64 v -5) 1)) (.f64 (PI.f64) t)) (/.f64 (/.f64 (sqrt.f64 (fma.f64 v (.f64 v -5) 1)) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) (-.f64 1 (.f64 v v))))
✓	1.0b	(/.f64 (sqrt.f64 (fma.f64 v (.f64 v -5) 1)) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))

series153.0ms (2.4%)

Counts

3 → 60

Calls

3 calls:

116.0ms

(*.f64 (/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -5) 1)) (*.f64 (PI.f64) t)) (/.f64 (/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -5) 1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (-.f64 1 (*.f64 v v))))

26.0ms

(/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -5) 1)) (*.f64 (PI.f64) t))

10.0ms

(/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -5) 1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

rewrite145.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

437×	`times-frac_binary64`
267×	`add-sqr-sqrt_binary64`
244×	`*-un-lft-identity_binary64`
235×	`sqrt-prod_binary64`
206×	`associate-r_binary64`

Counts

3 → 347

Calls

3 calls:

55.0ms

(*.f64 (/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -5) 1)) (*.f64 (PI.f64) t)) (/.f64 (/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -5) 1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (-.f64 1 (*.f64 v v))))

4.0ms

(/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -5) 1)) (*.f64 (PI.f64) t))

4.0ms

(/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -5) 1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

simplify293.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

652×	`associate-/r*_binary64`
515×	`times-frac_binary64`
478×	`associate-/l*_binary64`
307×	`associate-/l/_binary64`
228×	`fma-def_binary64`

Counts

407 → 457

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	651	19583
1	1946	18575
2	5332	18575

prune699.0ms (11%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	476	4	480
Fresh	4	0	4
Picked	1	0	1
Done	0	2	2
Total	481	6	487

Error

Counts

487 → 6

Alt Table

Status	Error	Program
	0.2b	(.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 v (.f64 v -5) 1)) (PI.f64)) t) (/.f64 (/.f64 (sqrt.f64 (fma.f64 v (.f64 v -5) 1)) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) (-.f64 1 (*.f64 v v))))
✓	0.4b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
	0.6b	(.f64 (/.f64 (sqrt.f64 (fma.f64 v (.f64 v -5) 1)) (.f64 (PI.f64) t)) (/.f64 (sqrt.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v (.f64 v -6) 2))) (-.f64 1 (.f64 v v))))
	0.3b	(.f64 (/.f64 1 (PI.f64)) (/.f64 (/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) (-.f64 1 (.f64 v v))) t))
✓	0.4b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))
	0.4b	(.f64 (/.f64 1 (PI.f64)) (.f64 (/.f64 (sqrt.f64 (fma.f64 v (.f64 v -5) 1)) t) (/.f64 (/.f64 (sqrt.f64 (fma.f64 v (.f64 v -5) 1)) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) (-.f64 1 (.f64 v v)))))

Compiler

Compiled 25690 to 17766 computations (30.8% saved)

regimes1.3s (20.6%)

Accuracy

Total 0.3b remaining (96.3%)

Threshold costs 0.3b (96.3%)

Counts

188 → 1

Compiler

Compiled 35254 to 26015 computations (26.2% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-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	21	50
1	31	50
2	37	50
3	41	50
4	43	50
5	42	50

end142.0ms (2.2%)

Compiler: Compiled 256 to 190 computations (25.8% saved)

Details

analyze160.0ms (2.5%)

sample1.5s (23.6%)

simplify31.0ms (0.5%)

prune3.0ms (0.1%)

localize14.0ms (0.2%)

series224.0ms (3.5%)

rewrite30.0ms (0.5%)

simplify151.0ms (2.4%)

prune297.0ms (4.7%)

localize16.0ms (0.2%)

series126.0ms (2%)

rewrite27.0ms (0.4%)

simplify150.0ms (2.4%)

prune335.0ms (5.3%)

localize15.0ms (0.2%)

series160.0ms (2.5%)

rewrite24.0ms (0.4%)

simplify127.0ms (2%)

prune213.0ms (3.3%)

localize15.0ms (0.2%)

series153.0ms (2.4%)

rewrite145.0ms (2.3%)

simplify293.0ms (4.6%)

prune699.0ms (11%)

regimes1.3s (20.6%)

simplify4.0ms (0.1%)

end142.0ms (2.2%)

Profiling