Details

analyze316.0ms (2.4%)

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
25%	74.9%	0.1%	4
37.4%	62.4%	0.1%	5
37.4%	62.4%	0.1%	6
37.4%	56.2%	6.4%	7
45.2%	48.4%	6.4%	8
49.1%	42.1%	8.7%	9
51.5%	35.1%	13.4%	10
58.1%	27.7%	14.2%	11
60.8%	22.6%	16.5%	12
62.3%	18.7%	19%	13
66.2%	14.4%	19.4%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.0s (14.8%)

Infinites

8.6% of outputs are infinite.

Results

728.0ms	5548×	body	128	valid
412.0ms	1051×	body	2048	valid
351.0ms	720×	body	1024	valid
174.0ms	376×	body	4096	valid
97.0ms	400×	body	512	valid
66.0ms	647×	body	128	invalid
28.0ms	161×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify258.0ms (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

29.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	29.8b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	29.8b	(.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)

localize12.0ms (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))
✓	0.9b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series183.0ms (1.4%)

Counts

4 → 96

Calls

4 calls:

80.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
51.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
41.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite29.0ms (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:

10.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
8.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
3.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify121.0ms (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

prune504.0ms (3.8%)

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

3.2b

Counts

209 → 10

Alt Table

Status	Error	Program
	30.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) 2) (/.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) a))
	38.4b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
	40.3b	(neg.f64 (/.f64 c b))
	29.9b	(.f64 (/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) 2) (/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) a))
▶	29.8b	(/.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))) 2) a)
	44.4b	(/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) 3)) (.f64 (.f64 2 a) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (.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))))))))
	37.0b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a))
	41.4b	(-.f64 (/.f64 c b) (/.f64 b a))
	41.4b	(/.f64 (neg.f64 b) a)
	29.8b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))

Compiler

Compiled 5811 to 3393 computations (41.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))) 2) a)
	0.9b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
	1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
	23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series92.0ms (0.7%)

Counts

1 → 20

Calls

1 calls:

92.0ms

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

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

117×	`times-frac_binary64`
105×	`*-un-lft-identity_binary64`
57×	`add-sqr-sqrt_binary64`
57×	`add-cube-cbrt_binary64`
24×	`distribute-lft-out_binary64`

Counts

1 → 97

Calls

1 calls:

11.0ms

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

simplify123.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

761×	`div-sub_binary64`
548×	`times-frac_binary64`
476×	`associate-/r*_binary64`
438×	`associate-/l*_binary64`
368×	`associate-/l/_binary64`

Counts

117 → 156

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	223	4616
1	550	4206
2	1502	4048
3	4594	4048
4	6385	4048

prune298.0ms (2.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	295	1	296
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	297	9	306

Error

3.2b

Counts

306 → 9

Alt Table

Status	Error	Program
	40.3b	(neg.f64 (/.f64 c b))
	38.4b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
✓	29.8b	(/.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))) 2) a)
	29.9b	(/.f64 (sqrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) 2)) (/.f64 a (sqrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) 2))))
	44.4b	(/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) 3)) (.f64 (.f64 2 a) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (.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))))))))
	37.0b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a))
	41.4b	(-.f64 (/.f64 c b) (/.f64 b a))
	41.4b	(/.f64 (neg.f64 b) a)
▶	29.8b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))

Compiler

Compiled 8888 to 5272 computations (40.7% saved)

localize14.0ms (0.1%)

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 (.f64 4 a) c))))))
	0.9b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
	1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
	23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series95.0ms (0.7%)

Counts

1 → 20

Calls

1 calls:

95.0ms

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

rewrite20.0ms (0.1%)

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 (0.8%)

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

prune240.0ms (1.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	256	1	257
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	257	9	266

Error

3.2b

Counts

266 → 9

Alt Table

Status	Error	Program
	37.6b	(.f64 (.f64 (.f64 4 (.f64 c a)) (/.f64 1/2 a)) (/.f64 1 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))
	41.4b	(-.f64 (/.f64 c b) (/.f64 b a))
	40.3b	(neg.f64 (/.f64 c b))
	38.4b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
✓	29.8b	(/.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))) 2) a)
▶	29.9b	(/.f64 (sqrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) 2)) (/.f64 a (sqrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) 2))))
	37.0b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a))
	41.4b	(/.f64 (neg.f64 b) a)
✓	29.8b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))

Compiler

Compiled 7760 to 4754 computations (38.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (sqrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) 2)) (/.f64 a (sqrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) 2))))
	0.9b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
	1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
	23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series132.0ms (1%)

Counts

1 → 20

Calls

1 calls:

132.0ms

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

rewrite1.0s (7.6%)

Algorithm

1×	rewrite-expression-head

Rules

5195×	`times-frac_binary64`
3632×	`*-un-lft-identity_binary64`
2679×	`sqrt-prod_binary64`
1940×	`add-sqr-sqrt_binary64`
1940×	`add-cube-cbrt_binary64`

Counts

1 → 1673

Calls

1 calls:

55.0ms

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

simplify2.2s (16.4%)

Algorithm

1×	egg-herbie

Rules

1062×	`associate-/r/_binary64`
765×	`associate-/l*_binary64`
268×	`associate-l_binary64`
130×	`times-frac_binary64`
112×	`associate-/r*_binary64`

Counts

1693 → 1484

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1407	162744
1	2922	144157
2	4989	144157

prune2.2s (16.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	1763	1	1764
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	1764	9	1773

Error

3.2b

Counts

1773 → 9

Alt Table

Status	Error	Program
	37.6b	(.f64 (.f64 (.f64 4 (.f64 c a)) (/.f64 1/2 a)) (/.f64 1 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))
	41.4b	(-.f64 (/.f64 c b) (/.f64 b a))
	41.7b	(.f64 -2 (/.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) b) a))
✓	29.8b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	40.3b	(neg.f64 (/.f64 c b))
	38.4b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
✓	29.8b	(/.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))) 2) a)
✓	29.9b	(/.f64 (sqrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) 2)) (/.f64 a (sqrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) 2))))
	37.0b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a))

Compiler

Compiled 116033 to 70137 computations (39.6% saved)

regimes3.1s (23.6%)

Accuracy

Total 4.6b remaining (47.4%)

Threshold costs 0b (0%)

Counts

275 → 3

Compiler

Compiled 29502 to 20646 computations (30% saved)

bsearch38.0ms (0.3%)

Steps

Iters	Range		Point
2	3.027844432563723e-29	3.6064234738026667e-29	3.100166812718591e-29
6	-2.859172542401454e+165	-2.407018843767758e+164	-2.47012258144473e+164

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	55
1	48	55
2	72	55
3	86	55
4	94	55
5	96	55
6	93	55

end131.0ms (1%)

Compiler: Compiled 260 to 182 computations (30% saved)

Details

analyze316.0ms (2.4%)

sample2.0s (14.8%)

simplify258.0ms (1.9%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series183.0ms (1.4%)

rewrite29.0ms (0.2%)

simplify121.0ms (0.9%)

prune504.0ms (3.8%)

localize12.0ms (0.1%)

series92.0ms (0.7%)

rewrite25.0ms (0.2%)

simplify123.0ms (0.9%)

prune298.0ms (2.2%)

localize14.0ms (0.1%)

series95.0ms (0.7%)

rewrite20.0ms (0.1%)

simplify101.0ms (0.8%)

prune240.0ms (1.8%)

localize13.0ms (0.1%)

series132.0ms (1%)

rewrite1.0s (7.6%)

simplify2.2s (16.4%)

prune2.2s (16.8%)

regimes3.1s (23.6%)

bsearch38.0ms (0.3%)

simplify4.0ms (0%)

end131.0ms (1%)

Profiling