Details

analyze1.6s (11.4%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	93.6%	6.4%	7
0%	93.6%	6.4%	8
0%	91.3%	8.7%	9
0%	86.6%	13.4%	10
0%	85.8%	14.2%	11
0%	83.1%	16.9%	12
0%	80.6%	19.4%	13
0%	79.4%	20.6%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample3.1s (22.6%)

Results

926.0ms	5397×	body	128	valid
703.0ms	1172×	body	2048	valid
452.0ms	722×	body	1024	valid
328.0ms	381×	body	8192	exit
283.0ms	403×	body	4096	valid
138.0ms	903×	body	128	invalid
133.0ms	374×	body	512	valid
51.0ms	188×	body	256	valid

Compiler

Compiled 41 to 29 computations (29.3% saved)

simplify260.0ms (1.9%)

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

34.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	34.7b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	34.8b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize11.0ms (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))
✓	0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	2.0b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series197.0ms (1.4%)

Counts

4 → 96

Calls

4 calls:

84.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
56.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
45.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite28.0ms (0.2%)

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:

9.0ms	(/.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	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify127.0ms (0.9%)

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

prune462.0ms (3.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	198	9	207
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	200	9	209

Error

5.3b

Counts

209 → 9

Alt Table

Status	Error	Program
	42.6b	(/.f64 (neg.f64 b) a)
	38.9b	(neg.f64 (/.f64 c b))
	41.8b	(/.f64 (+.f64 (neg.f64 b) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
	39.1b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
	48.3b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
	35.2b	(/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (.f64 2 a) (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
	57.9b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
▶	34.9b	(/.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a))
	42.6b	(-.f64 (/.f64 c b) (/.f64 b a))

Compiler

Compiled 5741 to 3347 computations (41.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b) b)))
✓	0.3b	(cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))
✓	0.7b	(-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)
✓	14.3b	(sqrt.f64 (.f64 c (.f64 a -4)))

series2.4s (17.1%)

Counts

4 → 36

Calls

4 calls:

1.6s	(.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b) b)))
572.0ms	(cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))
170.0ms	(-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)
27.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
33×	`cbrt-prod_binary64`
21×	`add-cube-cbrt_binary64`
17×	`pow1_binary64`

Counts

4 → 119

Calls

4 calls:

10.0ms	(.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b) b)))
3.0ms	(-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)
3.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))
2.0ms	(cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))

simplify164.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

813×	`fma-def_binary64`
369×	`cancel-sign-sub-inv_binary64`
246×	`fma-neg_binary64`
235×	`associate-r_binary64`
195×	`unswap-sqr_binary64`

Counts

155 → 241

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	331	6487
1	775	5780
2	2761	5241
3	4871	5241
4	4950	5241

prune608.0ms (4.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	513	0	513
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	513	9	522

Error

5.3b

Counts

522 → 9

Alt Table

Status	Error	Program
	42.6b	(/.f64 (neg.f64 b) a)
	38.9b	(neg.f64 (/.f64 c b))
	41.8b	(/.f64 (+.f64 (neg.f64 b) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
	39.1b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
	48.3b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
▶	35.2b	(/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (.f64 2 a) (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
	57.9b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
✓	34.9b	(/.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a))
	42.6b	(-.f64 (/.f64 c b) (/.f64 b a))

Compiler

Compiled 28984 to 19411 computations (33% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (.f64 2 a) (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
	0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
	2.0b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
	22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series89.0ms (0.6%)

Counts

1 → 20

Calls

1 calls:

89.0ms

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

rewrite62.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

184×	`times-frac_binary64`
154×	`*-un-lft-identity_binary64`
120×	`sqrt-prod_binary64`
58×	`add-sqr-sqrt_binary64`
58×	`add-cube-cbrt_binary64`

Counts

1 → 155

Calls

1 calls:

21.0ms

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

simplify202.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

697×	`associate-/r*_binary64`
493×	`associate-/r/_binary64`
486×	`associate-/l/_binary64`
276×	`fma-def_binary64`
113×	`associate-/l*_binary64`

Counts

175 → 181

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	245	12220
1	613	10163
2	1982	9278
3	5053	9278

prune439.0ms (3.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	461	0	461
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	461	9	470

Error

5.3b

Counts

470 → 9

Alt Table

Status	Error	Program
	42.6b	(/.f64 (neg.f64 b) a)
▶	38.9b	(neg.f64 (/.f64 c b))
	41.8b	(/.f64 (+.f64 (neg.f64 b) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
	39.1b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
	48.3b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
✓	35.2b	(/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (.f64 2 a) (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
	57.9b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
✓	34.9b	(/.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a))
	42.6b	(-.f64 (/.f64 c b) (/.f64 b a))

Compiler

Compiled 21409 to 12477 computations (41.7% saved)

localize4.0ms (0%)

prune8.0ms (0.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	6	6
Picked	1	1
Done	2	2
Total	9	9

Error

5.3b

Counts

9 → 9

Alt Table

Status	Error	Program
	42.6b	(/.f64 (neg.f64 b) a)
✓	38.9b	(neg.f64 (/.f64 c b))
	41.8b	(/.f64 (+.f64 (neg.f64 b) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
	39.1b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
	48.3b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
✓	35.2b	(/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (.f64 2 a) (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
	57.9b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
✓	34.9b	(/.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a))
	42.6b	(-.f64 (/.f64 c b) (/.f64 b a))

Compiler

Compiled 228 to 148 computations (35.1% saved)

regimes3.8s (27.4%)

Accuracy

Total 5.2b remaining (48.2%)

Threshold costs 0b (0%)

Counts

221 → 3

Compiler

Compiled 25330 to 17564 computations (30.7% saved)

bsearch81.0ms (0.6%)

Steps

Iters	Range		Point
9	9.764945508846091e-116	4.0351767613776376e-107	2.7432365902385795e-107
5	-1.5025545493462965e+51	-3.921873444536741e+50	-1.4766992338866856e+51

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
9×	`+-commutative_binary64`
8×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	50
1	47	48
2	70	48
3	82	48
4	88	48
5	89	48
6	87	48

end154.0ms (1.1%)

Compiler: Compiled 298 to 194 computations (34.9% saved)

Details

analyze1.6s (11.4%)

sample3.1s (22.6%)

simplify260.0ms (1.9%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series197.0ms (1.4%)

rewrite28.0ms (0.2%)

simplify127.0ms (0.9%)

prune462.0ms (3.4%)

localize13.0ms (0.1%)

series2.4s (17.1%)

rewrite30.0ms (0.2%)

simplify164.0ms (1.2%)

prune608.0ms (4.4%)

localize14.0ms (0.1%)

series89.0ms (0.6%)

rewrite62.0ms (0.5%)

simplify202.0ms (1.5%)

prune439.0ms (3.2%)

localize4.0ms (0%)

prune8.0ms (0.1%)

regimes3.8s (27.4%)

bsearch81.0ms (0.6%)

simplify4.0ms (0%)

end154.0ms (1.1%)

Profiling