Details

analyze419.0ms (6.3%)

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)

sample55.0ms (0.8%)

Algorithm

1×

intervals

Results

16.0ms	127×	body	256	valid
10.0ms	286×	pre	128	true
9.0ms	46×	body	512	valid
5.0ms	83×	body	128	valid
2.0ms	30×	body	128	nan

Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify274.0ms (4.1%)

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

prune4.0ms (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

53.1b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	53.1b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	53.1b	(/.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 (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
0.0b	(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))
27.6b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)

rewrite184.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

49.9b

Rules

32×	`add-cube-cbrt_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`pow1_binary64`
14×	`add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`

Counts

4 → 162

Calls

4 calls:

15.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
15.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
13.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))
10.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 3930 to 2088 computations (46.9% saved)

series156.0ms (2.3%)

Error

0.2b

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))
36.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
28.0ms	(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)

simplify119.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

878×	`times-frac_binary64`
332×	`fma-neg_binary64`
247×	`unswap-sqr_binary64`
163×	`associate-r_binary64`
160×	`associate-l_binary64`

Counts

234 → 120

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	246	4482
1	656	4168
2	2499	4099
3	5036	4099

prune60.0ms (0.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	114	6	120
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	116	6	122

Error

0.0b

Counts

122 → 6

Alt Table

Status	Error	Program
	53.0b	(.f64 (-.f64 (cbrt.f64 (pow.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)) 3/2)) b) (/.f64 1/2 a))
	1.5b	(neg.f64 (fma.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)) (+.f64 (/.f64 c b) (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))
	52.6b	(/.f64 (.f64 1/2 (-.f64 (pow.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) 3/2) (pow.f64 b 3))) (.f64 a (fma.f64 b (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (fma.f64 a (.f64 c -4) (.f64 b b)))))
	1.8b	(.f64 (-.f64 (.f64 -2 (+.f64 (/.f64 (.f64 c a) b) (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)))) (fma.f64 4 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 10 (/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))))) (/.f64 1/2 a))
	53.4b	(.f64 (.f64 (+.f64 (pow.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) 1/4) (sqrt.f64 b)) (-.f64 (pow.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) 1/4) (sqrt.f64 b))) (/.f64 1/2 a))
▶	0.4b	(.f64 (/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) (/.f64 1/2 a))

Compiler

Compiled 2122 to 1213 computations (42.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(fma.f64 a (.f64 c -4) (.f64 b b))
0.1b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
0.3b	(/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
0.3b	(.f64 (/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) (/.f64 1/2 a))

rewrite213.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

32×	`add-cube-cbrt_binary64`
23×	`pow1_binary64`
20×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`add-cbrt-cube_binary64`

Counts

4 → 170

Calls

4 calls:

20.0ms	(/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
17.0ms	(.f64 (/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) (/.f64 1/2 a))
12.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
12.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

Compiler

Compiled 5059 to 3135 computations (38% saved)

series183.0ms (2.7%)

Error

0.0b

Counts

4 → 72

Calls

4 calls:

56.0ms	(/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
49.0ms	(.f64 (/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) (/.f64 1/2 a))
34.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
30.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

Compiler

Compiled 3336 to 2402 computations (28% saved)

simplify140.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

664×	`fma-neg_binary64`
320×	`associate-l_binary64`
311×	`associate-r_binary64`
234×	`associate-/l*_binary64`
221×	`times-frac_binary64`

Counts

242 → 179

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	265	5614
1	727	5029
2	3877	4979
3	4956	4979

prune113.0ms (1.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	174	5	179
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	179	6	185

Error

Counts

185 → 6

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 (/.f64 (.f64 -2 (.f64 c a)) a) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
	2.1b	(.f64 (-.f64 (.f64 -2 (+.f64 (.f64 (/.f64 c b) a) (/.f64 (.f64 (.f64 c c) (.f64 a a)) (pow.f64 b 3)))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)))) (/.f64 1/2 a))
	0.4b	(/.f64 (.f64 -2 (.f64 c a)) (.f64 a (+.f64 b (sqrt.f64 (fma.f64 (.f64 c a) -4 (*.f64 b b))))))
	1.5b	(neg.f64 (fma.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)) (+.f64 (/.f64 c b) (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))
	0.4b	(.f64 (/.f64 c (/.f64 (+.f64 b (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b)))) (.f64 a -4))) (/.f64 1/2 a))
	1.7b	(.f64 (/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (-.f64 (.f64 2 (-.f64 b (+.f64 (.f64 (/.f64 c b) a) (/.f64 (.f64 (.f64 c c) (.f64 a a)) (pow.f64 b 3))))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))) (/.f64 1/2 a))

Compiler

Compiled 3611 to 2043 computations (43.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(fma.f64 a (.f64 c -4) (.f64 b b))
0.1b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
0.1b	(/.f64 (/.f64 (.f64 -2 (.f64 c a)) a) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
0.1b	(/.f64 (.f64 -2 (.f64 c a)) a)

rewrite204.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

38×	`add-cube-cbrt_binary64`
26×	`add-exp-log_binary64`
20×	`add-cbrt-cube_binary64`
16×	`pow1_binary64`
16×	`add-sqr-sqrt_binary64`

Counts

4 → 168

Calls

4 calls:

16.0ms	(/.f64 (.f64 -2 (.f64 c a)) a)
14.0ms	(/.f64 (/.f64 (.f64 -2 (.f64 c a)) a) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
13.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
10.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

Compiler

Compiled 4234 to 2186 computations (48.4% saved)

series128.0ms (1.9%)

Error

Counts

4 → 60

Calls

4 calls:

48.0ms	(/.f64 (/.f64 (.f64 -2 (.f64 c a)) a) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
30.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
27.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))
8.0ms	(/.f64 (.f64 -2 (.f64 c a)) a)

Compiler

Compiled 2369 to 1590 computations (32.9% saved)

simplify144.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

738×	`fma-def_binary64`
420×	`fma-neg_binary64`
230×	`associate-r_binary64`
207×	`associate-l_binary64`
188×	`times-frac_binary64`

Counts

228 → 154

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	231	4279
1	627	3961
2	3000	3605
3	4960	3605
4	4941	3605

prune105.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	151	3	154
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	154	6	160

Error

Counts

160 → 6

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 (/.f64 (.f64 -2 (.f64 c a)) a) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
	2.1b	(.f64 (-.f64 (.f64 -2 (+.f64 (.f64 (/.f64 c b) a) (/.f64 (.f64 (.f64 c c) (.f64 a a)) (pow.f64 b 3)))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)))) (/.f64 1/2 a))
	2.6b	(/.f64 (/.f64 (.f64 -2 (.f64 c a)) a) (.f64 2 (-.f64 b (.f64 (/.f64 c b) a))))
▶	0.4b	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))) (.f64 -2 (.f64 c 1))))
	1.5b	(-.f64 (.f64 -2 (/.f64 (.f64 (pow.f64 c 3) (.f64 a a)) (pow.f64 b 5))) (fma.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7)) (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))
	0.4b	(.f64 (/.f64 c (/.f64 (+.f64 b (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b)))) (.f64 a -4))) (/.f64 1/2 a))

Compiler

Compiled 2795 to 1610 computations (42.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(fma.f64 c (.f64 a -4) (.f64 b b))
0.1b	(+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))
0.1b	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))) (.f64 -2 (.f64 c 1)))
0.3b	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))) (.f64 -2 (.f64 c 1))))

rewrite198.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

38×	`add-cube-cbrt_binary64`
26×	`add-exp-log_binary64`
20×	`add-cbrt-cube_binary64`
16×	`pow1_binary64`
16×	`add-sqr-sqrt_binary64`

Counts

4 → 173

Calls

4 calls:

16.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))) (.f64 -2 (.f64 c 1)))
15.0ms	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))) (.f64 -2 (.f64 c 1))))
14.0ms	(+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))
10.0ms	(fma.f64 c (.f64 a -4) (.f64 b b))

Compiler

Compiled 4309 to 2740 computations (36.4% saved)

series166.0ms (2.5%)

Error

Counts

4 → 72

Calls

4 calls:

48.0ms	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))) (.f64 -2 (.f64 c 1))))
38.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))) (.f64 -2 (.f64 c 1)))
32.0ms	(+.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 2758 to 2053 computations (25.6% saved)

simplify157.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

554×	`fma-neg_binary64`
428×	`cancel-sign-sub-inv_binary64`
211×	`associate-r_binary64`
196×	`associate-l_binary64`
180×	`unswap-sqr_binary64`

Counts

245 → 155

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	248	4817
1	665	4328
2	2837	4269
3	4863	4269
4	4954	4269

prune96.0ms (1.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	155	6	161

Error

Counts

161 → 6

Alt Table

Status	Error	Program
	0.2b	(/.f64 (/.f64 (.f64 -2 (.f64 c a)) a) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
	2.1b	(.f64 (-.f64 (.f64 -2 (+.f64 (.f64 (/.f64 c b) a) (/.f64 (.f64 (.f64 c c) (.f64 a a)) (pow.f64 b 3)))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)))) (/.f64 1/2 a))
	2.6b	(/.f64 (/.f64 (.f64 -2 (.f64 c a)) a) (.f64 2 (-.f64 b (.f64 (/.f64 c b) a))))
	0.4b	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))) (.f64 -2 (.f64 c 1))))
	1.5b	(-.f64 (.f64 -2 (/.f64 (.f64 (pow.f64 c 3) (.f64 a a)) (pow.f64 b 5))) (fma.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7)) (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))
	0.4b	(.f64 (/.f64 c (/.f64 (+.f64 b (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b)))) (.f64 a -4))) (/.f64 1/2 a))

Compiler

Compiled 2386 to 1455 computations (39% saved)

regimes1.7s (26%)

Accuracy

Total 0.1b remaining (81.2%)

Threshold costs 0.1b (81.2%)

Compiler

Compiled 39872 to 26634 computations (33.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	22
1	21	22
2	20	22

end1.0ms (0%)

Compiler: Compiled 18 to 12 computations (33.3% saved)

sample1.8s (26.6%)

Algorithm

1×

intervals

Results

485.0ms	3772×	body	256	valid
295.0ms	1511×	body	512	valid
277.0ms	8773×	pre	128	true
183.0ms	2717×	body	128	valid
51.0ms	773×	body	128	nan

Compiler

Compiled 224 to 155 computations (30.8% saved)

Details

analyze419.0ms (6.3%)

sample55.0ms (0.8%)

simplify274.0ms (4.1%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

rewrite184.0ms (2.8%)

series156.0ms (2.3%)

simplify119.0ms (1.8%)

prune60.0ms (0.9%)

localize15.0ms (0.2%)

rewrite213.0ms (3.2%)

series183.0ms (2.7%)

simplify140.0ms (2.1%)

prune113.0ms (1.7%)

localize12.0ms (0.2%)

rewrite204.0ms (3.1%)

series128.0ms (1.9%)

simplify144.0ms (2.2%)

prune105.0ms (1.6%)

localize12.0ms (0.2%)

rewrite198.0ms (3%)

series166.0ms (2.5%)

simplify157.0ms (2.3%)

prune96.0ms (1.4%)

regimes1.7s (26%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.8s (26.6%)

Profiling