Details

analyze424.0ms (6.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 33 to 24 computations (27.3% saved)

sample57.0ms (0.9%)

Algorithm

1×

intervals

Results

15.0ms	123×	body	256	valid
11.0ms	52×	body	512	valid
9.0ms	290×	pre	128	true
5.0ms	81×	body	128	valid
2.0ms	34×	body	128	nan

Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify275.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

1743×	`fma-neg_binary64`
1393×	`fma-def_binary64`
800×	`div-sub_binary64`
619×	`times-frac_binary64`
473×	`associate-/r/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	33	22
2	67	22
3	138	22
4	204	22
5	338	22
6	558	22
7	924	22
8	1388	22
9	1604	22
10	2375	22
11	2742	22
12	2533	22
13	2621	22
14	3171	22
15	3313	22
16	3873	22
17	3679	22
18	4029	22
19	4317	22
20	4485	22
21	4561	22
22	4805	22
23	4793	22
24	4797	22
25	4797	22
26	4948	22

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

53.3b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	53.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	53.3b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))

Compiler

Compiled 94 to 64 computations (31.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
0.1b	(fma.f64 a (.f64 c -4) (.f64 b b))
0.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
25.2b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)

rewrite100.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

50.0b

Rules

42×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
17×	`sqrt-prod_binary64`

Counts

4 → 109

Calls

4 calls:

8.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
5.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
1.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
0.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

Compiler

Compiled 2813 to 1478 computations (47.5% saved)

series160.0ms (2.5%)

Error

0.3b

Counts

4 → 72

Calls

4 calls:

45.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
38.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
30.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))
27.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 2658 to 1932 computations (27.3% saved)

simplify172.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

730×	`fma-def_binary64`
406×	`fma-neg_binary64`
337×	`distribute-rgt-in_binary64`
207×	`exp-prod_binary64`
176×	`cancel-sign-sub-inv_binary64`

Counts

181 → 152

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	239	4650
1	572	3736
2	2171	3587
3	4521	3587
4	4917	3587
5	4879	3587

prune63.0ms (1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	148	4	152
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	150	4	154

Error

0.0b

Counts

154 → 4

Alt Table

Status	Error	Program
	1.8b	(-.f64 (.f64 -2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))) (fma.f64 5 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))
	53.3b	(.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))) b) (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (sqrt.f64 a))) (/.f64 (cbrt.f64 1/2) (sqrt.f64 a)))
▶	0.4b	(/.f64 (.f64 1/2 (fma.f64 a (.f64 c -4) 0)) (.f64 a (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (*.f64 b b))))))
	0.4b	(.f64 (/.f64 (fma.f64 a (.f64 c -4) 0) (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))) (/.f64 1/2 a))

Compiler

Compiled 2065 to 1206 computations (41.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 a (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (*.f64 b b)))))
0.1b	(fma.f64 c (.f64 a -4) (.f64 b b))
0.1b	(+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))
0.3b	(/.f64 (.f64 1/2 (fma.f64 a (.f64 c -4) 0)) (.f64 a (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (*.f64 b b))))))

rewrite107.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

18×	`add-cbrt-cube_binary64`
18×	`add-exp-log_binary64`
11×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`

Counts

4 → 77

Calls

4 calls:

7.0ms	(.f64 a (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (*.f64 b b)))))
6.0ms	(/.f64 (.f64 1/2 (fma.f64 a (.f64 c -4) 0)) (.f64 a (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (*.f64 b b))))))
3.0ms	(+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))
0.0ms	(fma.f64 c (.f64 a -4) (.f64 b b))

Compiler

Compiled 2495 to 1475 computations (40.9% saved)

series181.0ms (2.9%)

Error

0.0b

Counts

4 → 72

Calls

4 calls:

60.0ms	(/.f64 (.f64 1/2 (fma.f64 a (.f64 c -4) 0)) (.f64 a (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (*.f64 b b))))))
41.0ms	(.f64 a (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (*.f64 b b)))))
33.0ms	(+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))
31.0ms	(fma.f64 c (.f64 a -4) (.f64 b b))

Compiler

Compiled 3266 to 2367 computations (27.5% saved)

simplify97.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

555×	`fma-def_binary64`
378×	`distribute-rgt-in_binary64`
315×	`distribute-lft-in_binary64`
241×	`times-frac_binary64`
156×	`cancel-sign-sub-inv_binary64`

Counts

149 → 111

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	202	3718
1	590	3188
2	2442	3119
3	5013	3119

prune55.0ms (0.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	105	6	111
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	109	6	115

Error

Counts

115 → 6

Alt Table

Status	Error	Program
	0.6b	(.f64 (/.f64 (.f64 (.f64 c (.f64 a -4)) 1/2) (.f64 a (+.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))) 3)))) (+.f64 (.f64 b b) (-.f64 (.f64 (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))) (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))) (.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))))))
	1.5b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 (.f64 c (.f64 a -4)) 1/2) (.f64 a (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))))) (cbrt.f64 (/.f64 (.f64 (.f64 c (.f64 a -4)) 1/2) (.f64 a (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))))))) (cbrt.f64 (/.f64 (.f64 (.f64 c (.f64 a -4)) 1/2) (.f64 a (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))))))
	0.7b	(cbrt.f64 (pow.f64 (/.f64 (.f64 (.f64 c (.f64 a -4)) 1/2) (.f64 a (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))))) 3))
	0.4b	(.f64 (/.f64 1/2 a) (/.f64 (.f64 c (.f64 a -4)) (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (*.f64 b b))))))
	2.1b	(-.f64 (.f64 (/.f64 (.f64 (pow.f64 c 3) (.f64 a a)) (pow.f64 b 5)) -2) (fma.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a (/.f64 c b)))
▶	0.4b	(/.f64 (.f64 1/2 (fma.f64 a (.f64 c -4) 0)) (+.f64 (.f64 b a) (.f64 a (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))))

Compiler

Compiled 1734 to 1036 computations (40.3% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (.f64 b a) (.f64 a (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))))
0.1b	(.f64 a (sqrt.f64 (fma.f64 c (.f64 a -4) (*.f64 b b))))
0.1b	(fma.f64 c (.f64 a -4) (.f64 b b))
0.3b	(/.f64 (.f64 1/2 (fma.f64 a (.f64 c -4) 0)) (+.f64 (.f64 b a) (.f64 a (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))))

rewrite95.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

13×	`add-sqr-sqrt_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

4 → 73

Calls

4 calls:

5.0ms	(/.f64 (.f64 1/2 (fma.f64 a (.f64 c -4) 0)) (+.f64 (.f64 b a) (.f64 a (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))))
4.0ms	(.f64 a (sqrt.f64 (fma.f64 c (.f64 a -4) (*.f64 b b))))
3.0ms	(+.f64 (.f64 b a) (.f64 a (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))))
1.0ms	(fma.f64 c (.f64 a -4) (.f64 b b))

Compiler

Compiled 2554 to 1401 computations (45.1% saved)

series192.0ms (3%)

Error

Counts

4 → 73

Calls

4 calls:

59.0ms	(/.f64 (.f64 1/2 (fma.f64 a (.f64 c -4) 0)) (+.f64 (.f64 b a) (.f64 a (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))))
41.0ms	(+.f64 (.f64 b a) (.f64 a (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))))
41.0ms	(.f64 a (sqrt.f64 (fma.f64 c (.f64 a -4) (*.f64 b b))))
32.0ms	(fma.f64 c (.f64 a -4) (.f64 b b))

Compiler

Compiled 3501 to 2493 computations (28.8% saved)

simplify131.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

600×	`fma-def_binary64`
352×	`fma-neg_binary64`
227×	`distribute-rgt-in_binary64`
185×	`cancel-sign-sub-inv_binary64`
184×	`associate-/r/_binary64`

Counts

146 → 114

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	199	3701
1	544	3325
2	1884	3250
3	4686	3250
4	4954	3250

prune61.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	115	5	120

Error

Counts

120 → 5

Alt Table

Status	Error	Program
	0.6b	(/.f64 (.f64 (/.f64 1/2 (sqrt.f64 (.f64 a (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))))) (.f64 c (.f64 a -4))) (sqrt.f64 (+.f64 (.f64 b a) (.f64 a (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))))))
	0.6b	(.f64 (/.f64 (.f64 (.f64 c (.f64 a -4)) 1/2) (.f64 a (+.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))) 3)))) (+.f64 (.f64 b b) (-.f64 (.f64 (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))) (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))) (.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))))))
	1.5b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 (.f64 c (.f64 a -4)) 1/2) (.f64 a (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))))) (cbrt.f64 (/.f64 (.f64 (.f64 c (.f64 a -4)) 1/2) (.f64 a (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))))))) (cbrt.f64 (/.f64 (.f64 (.f64 c (.f64 a -4)) 1/2) (.f64 a (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))))))
▶	0.4b	(.f64 (/.f64 1/2 a) (/.f64 (.f64 c (.f64 a -4)) (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (*.f64 b b))))))
	2.1b	(-.f64 (.f64 (/.f64 (.f64 (pow.f64 c 3) (.f64 a a)) (pow.f64 b 5)) -2) (fma.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a (/.f64 c b)))

Compiler

Compiled 2112 to 1210 computations (42.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(fma.f64 c (.f64 a -4) (.f64 b b))
0.1b	(+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))
0.3b	(/.f64 (.f64 c (.f64 a -4)) (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))))
0.3b	(.f64 (/.f64 1/2 a) (/.f64 (.f64 c (.f64 a -4)) (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (*.f64 b b))))))

rewrite138.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

45×	`add-cbrt-cube_binary64`
45×	`add-exp-log_binary64`
24×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
18×	`times-frac_binary64`

Counts

4 → 111

Calls

4 calls:

11.0ms	(.f64 (/.f64 1/2 a) (/.f64 (.f64 c (.f64 a -4)) (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (*.f64 b b))))))
8.0ms	(/.f64 (.f64 c (.f64 a -4)) (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))))
3.0ms	(+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))
1.0ms	(fma.f64 c (.f64 a -4) (.f64 b b))

Compiler

Compiled 3663 to 2127 computations (41.9% saved)

series187.0ms (2.9%)

Error

Counts

4 → 72

Calls

4 calls:

56.0ms	(/.f64 (.f64 c (.f64 a -4)) (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))))
50.0ms	(.f64 (/.f64 1/2 a) (/.f64 (.f64 c (.f64 a -4)) (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (*.f64 b b))))))
33.0ms	(+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))
29.0ms	(fma.f64 c (.f64 a -4) (.f64 b b))

Compiler

Compiled 3216 to 2282 computations (29% saved)

simplify190.0ms (3%)

Algorithm

1×	egg-herbie

Rules

493×	`fma-def_binary64`
298×	`associate-r_binary64`
250×	`associate-/l*_binary64`
204×	`associate-*r/_binary64`
198×	`associate-l_binary64`

Counts

183 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	259	5459
1	740	4462
2	3296	4402
3	4590	4402
4	4984	4402
5	4933	4402

prune99.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	167	2	169
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	169	5	174

Error

Counts

174 → 5

Alt Table

Status	Error	Program
	0.2b	(.f64 1/2 (/.f64 (.f64 (/.f64 c (+.f64 b (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b))))) (*.f64 a -4)) a))
	0.6b	(/.f64 (.f64 (/.f64 1/2 (sqrt.f64 (.f64 a (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))))) (.f64 c (.f64 a -4))) (sqrt.f64 (+.f64 (.f64 b a) (.f64 a (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))))))
	0.4b	(.f64 (/.f64 1/2 a) (/.f64 (.f64 c (.f64 a -4)) (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (*.f64 b b))))))
	2.1b	(-.f64 (.f64 (/.f64 (.f64 (pow.f64 c 3) (.f64 a a)) (pow.f64 b 5)) -2) (fma.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a (/.f64 c b)))
	1.5b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 -2 (.f64 c a)) (.f64 a (+.f64 b (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b))))))) (cbrt.f64 (/.f64 (.f64 -2 (.f64 c a)) (.f64 a (+.f64 b (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b)))))))) (cbrt.f64 (/.f64 (.f64 -2 (.f64 c a)) (.f64 a (+.f64 b (sqrt.f64 (fma.f64 (.f64 c a) -4 (*.f64 b b))))))))

Compiler

Compiled 2782 to 1501 computations (46% saved)

regimes1.7s (27.5%)

Accuracy

Total 0.2b remaining (89.6%)

Threshold costs 0.2b (89.6%)

Compiler

Compiled 41000 to 26526 computations (35.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	28
1	19	28
2	19	28

end1.0ms (0%)

Compiler: Compiled 22 to 14 computations (36.4% saved)

sample1.8s (27.6%)

Algorithm

1×

intervals

Results

482.0ms	3749×	body	256	valid
284.0ms	1495×	body	512	valid
278.0ms	8829×	pre	128	true
182.0ms	2756×	body	128	valid
54.0ms	829×	body	128	nan

Compiler

Compiled 242 to 152 computations (37.2% saved)

Details

analyze424.0ms (6.7%)

sample57.0ms (0.9%)

simplify275.0ms (4.3%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

rewrite100.0ms (1.6%)

series160.0ms (2.5%)

simplify172.0ms (2.7%)

prune63.0ms (1%)

localize16.0ms (0.2%)

rewrite107.0ms (1.7%)

series181.0ms (2.9%)

simplify97.0ms (1.5%)

prune55.0ms (0.9%)

localize17.0ms (0.3%)

rewrite95.0ms (1.5%)

series192.0ms (3%)

simplify131.0ms (2.1%)

prune61.0ms (1%)

localize15.0ms (0.2%)

rewrite138.0ms (2.2%)

series187.0ms (2.9%)

simplify190.0ms (3%)

prune99.0ms (1.6%)

regimes1.7s (27.5%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.8s (27.6%)

Profiling