Details

analyze898.0ms (11.9%)

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)

sample57.0ms (0.8%)

Algorithm

1×

intervals

Results

16.0ms	160×	body	128	valid
12.0ms	39×	body	2048	valid
6.0ms	24×	body	1024	valid
5.0ms	12×	body	4096	valid
2.0ms	12×	body	512	valid
1.0ms	22×	body	128	nan
1.0ms	9×	body	256	valid
1.0ms	12×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify332.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

1319×	`div-sub_binary64`
932×	`unsub-neg_binary64`
843×	`associate-/l*_binary64`
678×	`distribute-rgt-in_binary64`
643×	`distribute-lft-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	37	26
2	93	26
3	213	24
4	320	24
5	522	24
6	913	24
7	995	24
8	1154	24
9	1806	24
10	2663	24
11	2356	24
12	2303	24
13	2372	24
14	2398	24
15	2585	24
16	3881	24
17	3563	24
18	3397	24
19	3505	24
20	3509	24
21	3623	24
22	3691	24
23	3691	24
24	2163	24
25	2363	24
26	2081	24
27	2083	24
28	2083	24
29	2083	24
30	1834	24

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

34.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	34.1b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))

Compiler

Compiled 59 to 41 computations (30.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.6b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
22.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite171.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

33.8b

Rules

22×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
9×	`sqrt-prod_binary64`
9×	`add-cube-cbrt_binary64`

Counts

4 → 82

Calls

4 calls:

10.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
9.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
3.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
3.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2131 to 1059 computations (50.3% saved)

series148.0ms (2%)

Error

5.3b

Counts

4 → 54

Calls

4 calls:

38.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
33.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
32.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
24.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2205 to 1594 computations (27.7% saved)

simplify140.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

653×	`div-sub_binary64`
242×	`distribute-rgt-in_binary64`
237×	`cancel-sign-sub-inv_binary64`
204×	`distribute-rgt-neg-in_binary64`
187×	`exp-prod_binary64`

Counts

136 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	234	3475
1	655	3076
2	2122	3050
3	4482	3050
4	5475	3050

prune63.0ms (0.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	116	10	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	10	127

Error

5.2b

Counts

127 → 10

Alt Table

Status	Error	Program
	34.1b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (+.f64 (.f64 b b) (.f64 c (.f64 a -4))))) (.f64 2 a))
	43.7b	(-.f64 (neg.f64 (/.f64 c b)) (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))
	48.2b	(/.f64 (neg.f64 b) a)
	47.7b	(/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 (.f64 a 2) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b)))
	53.0b	(/.f64 (-.f64 (neg.f64 b) (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 c a)) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 c a) (+.f64 (.f64 4 (.f64 c a)) (.f64 b b)))))))) (*.f64 2 a))
	49.2b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))) (.f64 a 2)) 3))
	38.4b	(neg.f64 (/.f64 c b))
	43.1b	(/.f64 (neg.f64 c) (*.f64 a (/.f64 b a)))
▶	31.8b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))) b)) (.f64 2 a))
	57.8b	0

Compiler

Compiled 1984 to 1073 computations (45.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b)
4.1b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))) b)) (.f64 2 a))
9.4b	(/.f64 (.f64 4 (.f64 c a)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b))
22.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))

rewrite132.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

5.2b

Rules

45×	`add-cbrt-cube_binary64`
45×	`add-exp-log_binary64`
33×	`add-sqr-sqrt_binary64`
30×	`times-frac_binary64`
22×	`*-un-lft-identity_binary64`

Counts

4 → 115

Calls

4 calls:

13.0ms	(/.f64 (.f64 4 (.f64 c a)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b))
13.0ms	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))) b)) (.f64 2 a))
7.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b)
3.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))

Compiler

Compiled 3995 to 2050 computations (48.7% saved)

series193.0ms (2.5%)

Error

5.2b

Counts

4 → 57

Calls

4 calls:

56.0ms	(/.f64 (.f64 4 (.f64 c a)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b))
42.0ms	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))) b)) (.f64 2 a))
41.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b)
40.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))

Compiler

Compiled 3275 to 2222 computations (32.2% saved)

simplify218.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

369×	`associate-/l*_binary64`
337×	`times-frac_binary64`
243×	`associate-/r*_binary64`
241×	`associate-/l/_binary64`
239×	`div-sub_binary64`

Counts

172 → 133

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	308	6064
1	870	4976
2	3610	4835
3	4644	4835
4	4966	4835
5	4924	4835

prune49.0ms (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	136	7	143

Error

5.2b

Counts

143 → 7

Alt Table

Status	Error	Program
▶	28.7b	(.f64 2 (.f64 1 (/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b))))
	34.1b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (+.f64 (.f64 b b) (.f64 c (.f64 a -4))))) (.f64 2 a))
	48.2b	(/.f64 (neg.f64 b) a)
	49.2b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))) (.f64 a 2)) 3))
	38.4b	(neg.f64 (/.f64 c b))
	43.1b	(/.f64 (neg.f64 c) (*.f64 a (/.f64 b a)))
✓	31.8b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))) b)) (.f64 2 a))

Compiler

Compiled 2064 to 1103 computations (46.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b)
22.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))

rewrite86.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

5.2b

Rules

38×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`

Counts

4 → 85

Calls

4 calls:

7.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b))
6.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b)
3.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))
3.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))

Compiler

Compiled 2295 to 1236 computations (46.1% saved)

series175.0ms (2.3%)

Error

5.2b

Counts

4 → 63

Calls

4 calls:

50.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b)
38.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b))
37.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))
35.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))

Compiler

Compiled 2838 to 2090 computations (26.4% saved)

simplify143.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

829×	`times-frac_binary64`
461×	`associate-/l*_binary64`
386×	`associate-/r*_binary64`
163×	`cancel-sign-sub-inv_binary64`
134×	`distribute-rgt-neg-in_binary64`

Counts

148 → 94

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	256	3748
1	572	3531
2	1564	3471
3	4924	3471
4	4944	3471

prune35.0ms (0.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	93	8	101

Error

5.2b

Counts

101 → 8

Alt Table

Status	Error	Program
✓	28.7b	(.f64 2 (.f64 1 (/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b))))
▶	34.1b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (+.f64 (.f64 b b) (.f64 c (.f64 a -4))))) (.f64 2 a))
	48.2b	(/.f64 (neg.f64 b) a)
	39.2b	(.f64 2 (/.f64 c (-.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b)))
	49.2b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))) (.f64 a 2)) 3))
	38.4b	(neg.f64 (/.f64 c b))
	43.1b	(/.f64 (neg.f64 c) (*.f64 a (/.f64 b a)))
✓	31.8b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))) b)) (.f64 2 a))

Compiler

Compiled 1023 to 601 computations (41.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (+.f64 (.f64 b b) (.f64 c (.f64 a -4))))) (.f64 2 a))
0.8b	(+.f64 (.f64 b b) (.f64 c (*.f64 a -4)))
1.6b	(-.f64 (neg.f64 b) (sqrt.f64 (+.f64 (.f64 b b) (.f64 c (*.f64 a -4)))))
22.5b	(sqrt.f64 (+.f64 (.f64 b b) (.f64 c (*.f64 a -4))))

rewrite84.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

5.2b

Rules

22×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
9×	`sqrt-prod_binary64`
9×	`add-cube-cbrt_binary64`

Counts

4 → 81

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (+.f64 (.f64 b b) (.f64 c (.f64 a -4))))) (.f64 2 a))
7.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (+.f64 (.f64 b b) (.f64 c (*.f64 a -4)))))
6.0ms	(+.f64 (.f64 b b) (.f64 c (*.f64 a -4)))
3.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 c (*.f64 a -4))))

Compiler

Compiled 2112 to 1177 computations (44.3% saved)

series134.0ms (1.8%)

Error

5.2b

Counts

4 → 54

Calls

4 calls:

38.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (+.f64 (.f64 b b) (.f64 c (.f64 a -4))))) (.f64 2 a))
34.0ms	(+.f64 (.f64 b b) (.f64 c (*.f64 a -4)))
30.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (+.f64 (.f64 b b) (.f64 c (*.f64 a -4)))))
23.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 c (*.f64 a -4))))

Compiler

Compiled 2205 to 1594 computations (27.7% saved)

simplify114.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

952×	`times-frac_binary64`
333×	`cancel-sign-sub-inv_binary64`
248×	`div-sub_binary64`
165×	`sub-neg_binary64`
151×	`associate-r_binary64`

Counts

135 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	231	3467
1	672	3062
2	2357	2990
3	5094	2990

prune42.0ms (0.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	125	7	132

Error

5.2b

Counts

132 → 7

Alt Table

Status	Error	Program
✓	28.7b	(.f64 2 (.f64 1 (/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))) b))))
✓	34.1b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (+.f64 (.f64 b b) (.f64 c (.f64 a -4))))) (.f64 2 a))
	48.2b	(/.f64 (neg.f64 b) a)
	34.6b	(/.f64 (.f64 (cbrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (+.f64 (.f64 b b) (.f64 c (.f64 a -4)))))) (cbrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (+.f64 (.f64 b b) (.f64 c (.f64 a -4))))))) (/.f64 2 (/.f64 (cbrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))))) a)))
	38.4b	(neg.f64 (/.f64 c b))
	43.1b	(/.f64 (neg.f64 c) (*.f64 a (/.f64 b a)))
✓	31.8b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))) b)) (.f64 2 a))

Compiler

Compiled 1694 to 898 computations (47% saved)

regimes1.4s (18.2%)

Accuracy

Total 1.0b remaining (15.3%)

Threshold costs 1.0b (15.3%)

Compiler

Compiled 12710 to 8473 computations (33.3% saved)

bsearch121.0ms (1.6%)

Steps

Iters	Range	Point
8	2.5893053815909615e+90	4.119130104420725e+94	2.2264978507093777e+94
9	1.3850623120697785e-288	2.0531328341028702e-280	4.428128095775905e-281
7	-7.600658942055541e+136	-1.2153362895898223e+134	-9.560667674887568e+134

Iters

Range

Point

2.5893053815909615e+90

4.119130104420725e+94

2.2264978507093777e+94

1.3850623120697785e-288

2.0531328341028702e-280

4.428128095775905e-281

-7.600658942055541e+136

-1.2153362895898223e+134

-9.560667674887568e+134

Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
15×	`+-commutative_binary64`
13×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	80
1	61	80
2	81	80
3	104	80
4	116	80
5	122	80
6	124	80
7	123	80

end1.0ms (0%)

Compiler: Compiled 56 to 35 computations (37.5% saved)

sample2.8s (36.8%)

Algorithm

1×

intervals

Results

936.0ms	5196×	body	128	valid
769.0ms	1127×	body	2048	valid
174.0ms	681×	body	1024	valid
171.0ms	419×	body	4096	valid
74.0ms	390×	body	512	valid
42.0ms	651×	body	128	nan
29.0ms	408×	body	128	invalid
24.0ms	187×	body	256	valid

Compiler

Compiled 222 to 146 computations (34.2% saved)

Details

analyze898.0ms (11.9%)

sample57.0ms (0.8%)

simplify332.0ms (4.4%)

prune3.0ms (0%)

localize12.0ms (0.2%)

rewrite171.0ms (2.3%)

series148.0ms (2%)

simplify140.0ms (1.9%)

prune63.0ms (0.8%)

localize13.0ms (0.2%)

rewrite132.0ms (1.7%)

series193.0ms (2.5%)

simplify218.0ms (2.9%)

prune49.0ms (0.7%)

localize15.0ms (0.2%)

rewrite86.0ms (1.1%)

series175.0ms (2.3%)

simplify143.0ms (1.9%)

prune35.0ms (0.5%)

localize13.0ms (0.2%)

rewrite84.0ms (1.1%)

series134.0ms (1.8%)

simplify114.0ms (1.5%)

prune42.0ms (0.6%)

regimes1.4s (18.2%)

bsearch121.0ms (1.6%)

simplify7.0ms (0.1%)

end1.0ms (0%)

sample2.8s (36.8%)

Profiling