Details

analyze644.0ms (8.6%)

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)

sample2.7s (36.1%)

Results

1.1s	5408×	body	128	valid
634.0ms	1171×	body	2048	valid
318.0ms	737×	body	1024	valid
257.0ms	390×	body	4096	valid
158.0ms	1157×	body	128	invalid
130.0ms	373×	body	512	valid
42.0ms	177×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify259.0ms (3.5%)

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 → 2

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%)

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

32.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	33.0b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
▶	32.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize10.0ms (0.1%)

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 (.f64 4 a) c)))) (.f64 2 a))
✓	0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	1.1b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	22.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series204.0ms (2.7%)

Counts

4 → 96

Calls

4 calls:

86.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
53.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
43.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
21.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite29.0ms (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:

10.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
7.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
3.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify124.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

701×	`fma-neg_binary64`
334×	`cancel-sign-sub-inv_binary64`
215×	`distribute-rgt-neg-in_binary64`
159×	`associate-r_binary64`
150×	`distribute-rgt-neg-out_binary64`

Counts

186 → 207

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	4208
1	695	3858
2	2512	3724
3	4694	3704
4	5031	3704

prune153.0ms (2.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	197	10	207
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	198	11	209

Error

6.0b

Counts

209 → 11

Alt Table

Status	Error	Program
	57.0b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
	38.9b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a))
	38.9b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
	39.7b	(neg.f64 (/.f64 c b))
	33.0b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	34.1b	(/.f64 (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (*.f64 a -2))
	36.1b	(/.f64 (+.f64 (neg.f64 b) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (.f64 2 a))
	35.9b	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a))
▶	33.0b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	45.4b	(/.f64 (neg.f64 b) a)
	44.3b	(-.f64 (neg.f64 (/.f64 c b)) (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))

Compiler

Compiled 5667 to 3323 computations (41.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
✓	1.1b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	22.1b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series182.0ms (2.4%)

Counts

3 → 60

Calls

3 calls:

84.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
53.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
45.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64`
27×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
17×	`sqrt-prod_binary64`

Counts

3 → 99

Calls

3 calls:

10.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
4.0ms	(-.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)))

simplify123.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

505×	`fma-neg_binary64`
316×	`distribute-rgt-in_binary64`
279×	`distribute-lft-in_binary64`
261×	`cancel-sign-sub-inv_binary64`
151×	`associate-r_binary64`

Counts

159 → 207

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	258	4859
1	662	3980
2	2479	3807
3	4859	3807
4	4966	3807

prune142.0ms (1.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	203	4	207
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	209	9	218

Error

6.0b

Counts

218 → 9

Alt Table

Status	Error	Program
	57.0b	(*.f64 (-.f64 b b) (/.f64 1/2 a))
▶	33.0b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	45.4b	(/.f64 (neg.f64 b) a)
	38.9b	(.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))) b) (/.f64 1/2 a))
	38.9b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
	39.7b	(neg.f64 (/.f64 c b))
	34.1b	(/.f64 (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (*.f64 a -2))
	34.6b	(/.f64 (.f64 (+.f64 (.f64 a (.f64 c -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	35.9b	(.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))) (/.f64 1/2 a))

Compiler

Compiled 5828 to 3402 computations (41.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
	1.1b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
	22.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series85.0ms (1.1%)

Counts

1 → 20

Calls

1 calls:

85.0ms

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

rewrite20.0ms (0.3%)

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:

11.0ms

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

simplify101.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

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

Counts

94 → 117

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	164	3247
1	439	2847
2	1517	2670
3	4595	2670
4	6178	2670

prune178.0ms (2.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	257	0	257
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	257	9	266

Error

6.0b

Counts

266 → 9

Alt Table

Status	Error	Program
	57.0b	(*.f64 (-.f64 b b) (/.f64 1/2 a))
✓	33.0b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	45.4b	(/.f64 (neg.f64 b) a)
	38.9b	(.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))) b) (/.f64 1/2 a))
	38.9b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
	39.7b	(neg.f64 (/.f64 c b))
▶	34.1b	(/.f64 (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (*.f64 a -2))
	34.6b	(/.f64 (.f64 (+.f64 (.f64 a (.f64 c -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	35.9b	(.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))) (/.f64 1/2 a))

Compiler

Compiled 7734 to 4740 computations (38.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)
✓	0.1b	(/.f64 (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (*.f64 a -2))
✓	0.4b	(-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))
✓	13.9b	(sqrt.f64 (.f64 c (.f64 a -4)))

series572.0ms (7.7%)

Counts

4 → 38

Calls

4 calls:

274.0ms	(/.f64 (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (*.f64 a -2))
168.0ms	(-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))
109.0ms	(hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)
20.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
10×	`pow1_binary64`
9×	`prod-diff_binary64`

Counts

4 → 84

Calls

4 calls:

6.0ms	(/.f64 (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (*.f64 a -2))
3.0ms	(-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))
3.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))
0.0ms	(hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)

simplify123.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

675×	`fma-def_binary64`
343×	`fma-neg_binary64`
293×	`cancel-sign-sub-inv_binary64`
146×	`distribute-rgt-in_binary64`
144×	`distribute-rgt-neg-in_binary64`

Counts

122 → 199

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	245	3472
1	632	3007
2	2126	2816
3	4438	2808
4	4951	2808
5	4898	2808

prune135.0ms (1.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	198	1	199
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	200	8	208

Error

2.6b

Counts

208 → 8

Alt Table

Status	Error	Program
	57.0b	(*.f64 (-.f64 b b) (/.f64 1/2 a))
✓	33.0b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	38.9b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
	39.7b	(neg.f64 (/.f64 c b))
✓	34.1b	(/.f64 (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (*.f64 a -2))
	47.9b	(/.f64 (-.f64 b (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -4))) b)) (*.f64 a -2))
	34.6b	(/.f64 (.f64 (+.f64 (.f64 a (.f64 c -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	45.4b	(/.f64 (neg.f64 b) a)

Compiler

Compiled 5540 to 3598 computations (35.1% saved)

regimes1.4s (18.4%)

Accuracy

Total 6.4b remaining (69%)

Threshold costs 0b (0%)

Counts

124 → 4

Compiler

Compiled 10396 to 7370 computations (29.1% saved)

bsearch109.0ms (1.5%)

Steps

Iters	Range		Point
7	798027922064775.8	26176556420618184.0	25822214016469920.0
8	3.4683611661046985e-102	1.357450429999656e-98	3.5099172996677927e-102
6	-1.0610538078350422e+130	-6.974551193561284e+128	-3.5922101775304284e+129

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary64`
9×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	92
1	63	92
2	81	92
3	91	92
4	98	92
5	100	92
6	98	92

end116.0ms (1.6%)

Compiler: Compiled 261 to 179 computations (31.4% saved)

Details

analyze644.0ms (8.6%)

sample2.7s (36.1%)

simplify259.0ms (3.5%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series204.0ms (2.7%)

rewrite29.0ms (0.4%)

simplify124.0ms (1.7%)

prune153.0ms (2.1%)

localize9.0ms (0.1%)

series182.0ms (2.4%)

rewrite22.0ms (0.3%)

simplify123.0ms (1.7%)

prune142.0ms (1.9%)

localize11.0ms (0.2%)

series85.0ms (1.1%)

rewrite20.0ms (0.3%)

simplify101.0ms (1.4%)

prune178.0ms (2.4%)

localize9.0ms (0.1%)

series572.0ms (7.7%)

rewrite18.0ms (0.2%)

simplify123.0ms (1.6%)

prune135.0ms (1.8%)

regimes1.4s (18.4%)

bsearch109.0ms (1.5%)

simplify5.0ms (0.1%)

end116.0ms (1.6%)

Profiling