Details

analyze861.0ms (8.4%)

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample3.7s (35.7%)

Results

1.1s	5336×	body	128	valid
977.0ms	1137×	body	2048	valid
530.0ms	788×	body	1024	valid
425.0ms	418×	body	4096	valid
216.0ms	1026×	body	128	invalid
204.0ms	401×	body	512	valid
67.0ms	176×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify432.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

2009×	`fma-neg_binary64`
1508×	`div-sub_binary64`
1334×	`associate-/l*_binary64`
1156×	`fma-def_binary64`
685×	`associate-/l/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	34	22
2	64	22
3	132	22
4	198	22
5	325	22
6	552	22
7	918	22
8	1352	22
9	1554	22
10	2359	22
11	3158	22
12	2565	22
13	2653	22
14	3219	22
15	3361	22
16	3461	22
17	3985	22
18	4171	22
19	4439	22
20	4659	22
21	4701	22
22	4757	22
23	4941	22
24	4941	22
25	3365	22
26	3059	22
27	2983	22
28	2985	22
29	2997	22
30	2997	22
31	2997	22
32	2997	22
33	2736	22

prune7.0ms (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

35.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	35.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
▶	35.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
✓	1.7b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
✓	1.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
✓	22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series249.0ms (2.4%)

Counts

4 → 96

Calls

4 calls:

98.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
78.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
60.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
12.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`fma-def_binary64`
10×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64`

Counts

4 → 90

Calls

4 calls:

19.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
8.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
3.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
3.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify133.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

697×	`fma-neg_binary64`
327×	`cancel-sign-sub-inv_binary64`
226×	`distribute-rgt-neg-in_binary64`
150×	`distribute-rgt-neg-out_binary64`
146×	`associate-r_binary64`

Counts

186 → 207

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	4202
1	693	3825
2	2488	3724
3	4652	3704
4	4985	3704

prune262.0ms (2.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	197	10	207
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	199	10	209

Error

4.5b

Counts

209 → 10

Alt Table

Status	Error	Program
	36.6b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
	40.6b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a))
	35.3b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
	47.6b	(/.f64 (neg.f64 b) a)
	41.6b	(-.f64 (neg.f64 (/.f64 c b)) (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))
	35.7b	(neg.f64 (/.f64 c b))
	35.8b	(/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (/.f64 (.f64 2 a) (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))))
	47.1b	(/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) 3)) (.f64 (.f64 2 a) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))))
	55.6b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
▶	35.2b	(/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (neg.f64 b)) (.f64 2 a))

Compiler

Compiled 5745 to 3210 computations (44.1% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (neg.f64 b)) (.f64 2 a))
✓	1.7b	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) (neg.f64 b))
	1.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
	22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series152.0ms (1.5%)

Counts

2 → 40

Calls

2 calls:

92.0ms	(/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (neg.f64 b)) (.f64 2 a))
60.0ms	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) (neg.f64 b))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
6×	`distribute-lft-out_binary64`
6×	`add-log-exp_binary64`

Counts

2 → 55

Calls

2 calls:

13.0ms	(/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (neg.f64 b)) (.f64 2 a))
8.0ms	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) (neg.f64 b))

simplify167.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

590×	`fma-def_binary64`
446×	`fma-neg_binary64`
283×	`distribute-rgt-in_binary64`
218×	`distribute-lft-in_binary64`
160×	`cancel-sign-sub-inv_binary64`

Counts

95 → 123

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	183	2627
1	543	2426
2	1895	2313
3	4692	2313
4	4999	2313
5	4992	2313
6	4918	2313

prune200.0ms (1.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	206	10	216

Error

4.5b

Counts

216 → 10

Alt Table

Status	Error	Program
	36.6b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
	40.6b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a))
▶	35.3b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
	47.6b	(/.f64 (neg.f64 b) a)
	41.6b	(-.f64 (neg.f64 (/.f64 c b)) (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))
	35.7b	(neg.f64 (/.f64 c b))
	35.8b	(/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (/.f64 (.f64 2 a) (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))))
	47.1b	(/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) 3)) (.f64 (.f64 2 a) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))))
	55.6b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
✓	35.2b	(/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (neg.f64 b)) (.f64 2 a))

Compiler

Compiled 5731 to 3223 computations (43.8% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
	1.7b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
	1.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
	22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series172.0ms (1.7%)

Counts

1 → 20

Calls

1 calls:

172.0ms

(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))

rewrite42.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`times-frac_binary64`
37×	`*-un-lft-identity_binary64`
22×	`add-exp-log_binary64`
21×	`add-sqr-sqrt_binary64`
21×	`add-cube-cbrt_binary64`

Counts

1 → 74

Calls

1 calls:

24.0ms

(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))

simplify166.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

665×	`associate-/l*_binary64`
599×	`div-sub_binary64`
346×	`fma-def_binary64`
296×	`fma-neg_binary64`
265×	`associate-/r/_binary64`

Counts

94 → 117

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	164	3247
1	434	2847
2	1512	2670
3	4587	2670
4	6171	2670

prune247.0ms (2.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	254	3	257
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	258	9	267

Error

4.4b

Counts

267 → 9

Alt Table

Status	Error	Program
	35.8b	(/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (/.f64 (.f64 2 a) (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))))
	36.6b	(/.f64 1 (/.f64 (.f64 2 a) (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b)))))
	55.6b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
	35.7b	(.f64 (.f64 (.f64 4 (.f64 c a)) (/.f64 1/2 a)) (/.f64 1 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))))
▶	29.5b	(/.f64 (.f64 (.f64 4 (.f64 c a)) (/.f64 1/2 a)) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))
	40.6b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a))
	47.6b	(/.f64 (neg.f64 b) a)
	35.7b	(neg.f64 (/.f64 c b))
✓	35.2b	(/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (neg.f64 b)) (.f64 2 a))

Compiler

Compiled 7792 to 4557 computations (41.5% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
	1.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
✓	13.0b	(.f64 (.f64 4 (*.f64 c a)) (/.f64 1/2 a))
	22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series120.0ms (1.2%)

Counts

2 → 44

Calls

2 calls:

108.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
11.0ms	(.f64 (.f64 4 (*.f64 c a)) (/.f64 1/2 a))

rewrite77.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`prod-diff_binary64`
56×	`*-un-lft-identity_binary64`
56×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
34×	`sqrt-prod_binary64`

Counts

2 → 135

Calls

2 calls:

20.0ms	(.f64 (.f64 4 (*.f64 c a)) (/.f64 1/2 a))
19.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))

simplify275.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

574×	`fma-neg_binary64`
539×	`fma-def_binary64`
322×	`associate-l_binary64`
270×	`associate-r_binary64`
156×	`exp-prod_binary64`

Counts

179 → 176

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	262	6296
1	639	4141
2	2508	3117
3	4448	3115
4	4873	3115

prune258.0ms (2.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	257	2	259
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	260	8	268

Error

4.4b

Counts

268 → 8

Alt Table

Status	Error	Program
	27.1b	(/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))
	36.6b	(/.f64 1 (/.f64 (.f64 2 a) (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b)))))
	40.2b	(/.f64 (.f64 (.f64 4 (.f64 c a)) (/.f64 1/2 a)) (/.f64 (.f64 4 (.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b) b)))
	40.6b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a))
	47.6b	(/.f64 (neg.f64 b) a)
	35.7b	(neg.f64 (/.f64 c b))
	35.7b	(.f64 (.f64 (.f64 4 (.f64 c a)) (/.f64 1/2 a)) (/.f64 1 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))))
✓	35.2b	(/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (neg.f64 b)) (.f64 2 a))

Compiler

Compiled 10778 to 5634 computations (47.7% saved)

regimes2.4s (23.2%)

Accuracy

Total 1.6b remaining (23.6%)

Threshold costs 0b (0%)

Counts

216 → 4

Compiler

Compiled 20448 to 14305 computations (30% saved)

bsearch121.0ms (1.2%)

Steps

Iters	Range	Point
6	4.245300539973689e+84	2.9179576036075558e+85	2.3431308109665615e+85
11	-1.7242544591762952e-294	9.40127380898348e-302	-1.9357207753357807e-308
5	-3.8345071439982345e+37	-1.0151334156400121e+37	-3.7715774085615172e+37

Iters

Range

Point

4.245300539973689e+84

2.9179576036075558e+85

2.3431308109665615e+85

-1.7242544591762952e-294

9.40127380898348e-302

-1.9357207753357807e-308

-3.8345071439982345e+37

-1.0151334156400121e+37

-3.7715774085615172e+37

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64`
13×	`+-commutative_binary64`
11×	`sub-neg_binary64`
9×	`neg-sub0_binary64`
9×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	90
1	59	90
2	83	90
3	103	90
4	112	90
5	116	90
6	117	90
7	115	90

end128.0ms (1.2%)

Compiler: Compiled 281 to 192 computations (31.7% saved)

Details

analyze861.0ms (8.4%)

sample3.7s (35.7%)

simplify432.0ms (4.2%)

prune7.0ms (0.1%)

localize22.0ms (0.2%)

series249.0ms (2.4%)

rewrite38.0ms (0.4%)

simplify133.0ms (1.3%)

prune262.0ms (2.5%)

localize18.0ms (0.2%)

series152.0ms (1.5%)

rewrite24.0ms (0.2%)

simplify167.0ms (1.6%)

prune200.0ms (1.9%)

localize24.0ms (0.2%)

series172.0ms (1.7%)

rewrite42.0ms (0.4%)

simplify166.0ms (1.6%)

prune247.0ms (2.4%)

localize29.0ms (0.3%)

series120.0ms (1.2%)

rewrite77.0ms (0.7%)

simplify275.0ms (2.7%)

prune258.0ms (2.5%)

regimes2.4s (23.2%)

bsearch121.0ms (1.2%)

simplify6.0ms (0.1%)

end128.0ms (1.2%)

Profiling