Details

analyze9.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 19 to 15 computations (21.1% saved)

sample3.1s (63.7%)

Results

3.0s

8256×

body

128

valid

Compiler

Compiled 38 to 30 computations (21.1% saved)

preprocess22.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	17	25
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	17	25

Stop Event

1×

saturated

Counts

1 → 1

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 x (+.f64 99229/100000 (*.f64 x 4481/100000))))) x)

Compiler

Compiled 54 to 42 computations (22.2% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x (+.f64 99229/100000 (.f64 x 4481/100000)))
✓	0.4b	(*.f64 x 4481/100000)
✓	0.4b	(*.f64 x 27061/100000)
✓	17.7b	(/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 x (+.f64 99229/100000 (*.f64 x 4481/100000)))))

series8.0ms (0.2%)

Counts

4 → 48

Calls

12 calls:

1.0ms	(/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 x (+.f64 99229/100000 (*.f64 x 4481/100000)))))	x	inf
1.0ms	(/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 x (+.f64 99229/100000 (*.f64 x 4481/100000)))))	x	-inf
1.0ms	(.f64 x (+.f64 99229/100000 (.f64 x 4481/100000)))	x	-inf
1.0ms	(/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 x (+.f64 99229/100000 (*.f64 x 4481/100000)))))	x	0
1.0ms	(.f64 x (+.f64 99229/100000 (.f64 x 4481/100000)))	x	inf

rewrite50.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

321×	`log-prod_binary64`
251×	`expm1-udef_binary64`
251×	`log1p-udef_binary64`
247×	`pow1/3_binary64`
229×	`pow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	40
1	278	40
2	2826	40

Stop Event

1×	node limit

Counts

4 → 69

simplify314.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

1717×	`sqr-pow_binary64`
842×	`pow-sqr_binary64`
57×	`cube-prod_binary64`
57×	`cube-mult_binary64`
57×	`unpow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	442
1	68	442
2	81	442
3	95	442
4	115	442
5	136	442
6	160	442
7	185	442
8	214	442
9	244	442
10	278	442
11	313	442
12	352	442
13	392	442
14	436	442
15	481	442
16	530	442
17	580	442
18	634	442
19	689	442
20	748	442
21	808	442
22	872	442
23	937	442
24	1006	442
25	1076	442
26	1150	442
27	1225	442
28	1304	442
29	1384	442
30	1468	442
31	1553	442
32	1642	442
33	1732	442
34	1826	442
35	1921	442
36	2020	442
37	2120	442
38	2146	442
39	2148	442
40	2148	442
41	2247	442
42	2351	442
43	2458	442
44	2569	442
45	2681	442
46	2797	442
47	2914	442
48	3035	442
49	3157	442
50	3283	442
51	3410	442
52	3541	442
53	3673	442
54	3809	442
55	3946	442
56	3979	442
57	3981	442
58	3981	442
59	4117	442
60	4258	442
61	4402	442
62	4550	442
63	4699	442
64	4852	442

Stop Event

1×	node limit

Counts

117 → 89

prune102.0ms (2.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	2	90

Error

Counts

90 → 2

Alt Table

Status	Error	Program
	0.5b	(-.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 x (+.f64 99229/100000 (*.f64 x 4481/100000)))))) 3) x)
▶	0.1b	(-.f64 (/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 99229/100000 (.f64 x 4481/100000))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 99229/100000 (*.f64 x 4481/100000)))))))) x)

Status

Error

Program

0.5b

(-.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 230753/100000 (*.f64 x 27061/100000)) (+.f64 1 (*.f64 x (+.f64 99229/100000 (*.f64 x 4481/100000)))))) 3) x)

▶

0.1b

(-.f64 (/.f64 (+.f64 230753/100000 (*.f64 x 27061/100000)) (+.f64 1 (+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 99229/100000 (*.f64 x 4481/100000))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 99229/100000 (*.f64 x 4481/100000)))))))) x)

Compiler

Compiled 2016 to 1586 computations (21.3% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (exp.f64 x) (+.f64 99229/100000 (*.f64 x 4481/100000)))
	0.4b	(*.f64 x 4481/100000)
	0.4b	(*.f64 x 27061/100000)
✓	2.0b	(log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 99229/100000 (*.f64 x 4481/100000)))))

series239.0ms (5%)

Counts

2 → 24

Calls

6 calls:

116.0ms	(log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 99229/100000 (*.f64 x 4481/100000)))))	x	-inf
99.0ms	(log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 99229/100000 (*.f64 x 4481/100000)))))	x	inf
21.0ms	(log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 99229/100000 (*.f64 x 4481/100000)))))	x	0
2.0ms	(pow.f64 (exp.f64 x) (+.f64 99229/100000 (*.f64 x 4481/100000)))	x	0
1.0ms	(pow.f64 (exp.f64 x) (+.f64 99229/100000 (*.f64 x 4481/100000)))	x	inf

rewrite37.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

830×	`log1p-expm1-u_binary64`
830×	`expm1-log1p-u_binary64`
101×	`add-sqr-sqrt_binary64`
97×	`add-log-exp_binary64`
95×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	199	25
2	2117	25

Stop Event

1×	node limit

Counts

2 → 33

simplify61.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1344×	`sqr-pow_binary64`
1205×	`pow-sqr_binary64`
66×	`rem-sqrt-square_binary64`
12×	`cube-mult_binary64`
12×	`unpow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	304
1	50	304
2	67	304
3	89	304
4	119	304
5	159	304
6	214	304
7	300	304
8	435	304
9	675	304
10	1086	304
11	1870	304
12	3281	304
13	3327	304
14	3329	304
15	3329	304

Stop Event

1×	node limit

Counts

57 → 46

prune183.0ms (3.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	140	2	142

Error

Counts

142 → 2

Alt Table

Status	Error	Program
▶	0.5b	(-.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 x (+.f64 99229/100000 (*.f64 x 4481/100000)))))) 3) x)
✓	0.1b	(-.f64 (/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 99229/100000 (.f64 x 4481/100000))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 99229/100000 (*.f64 x 4481/100000)))))))) x)

Status

Error

Program

▶

0.5b

(-.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 230753/100000 (*.f64 x 27061/100000)) (+.f64 1 (*.f64 x (+.f64 99229/100000 (*.f64 x 4481/100000)))))) 3) x)

✓

0.1b

(-.f64 (/.f64 (+.f64 230753/100000 (*.f64 x 27061/100000)) (+.f64 1 (+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 99229/100000 (*.f64 x 4481/100000))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 99229/100000 (*.f64 x 4481/100000)))))))) x)

Compiler

Compiled 4921 to 3755 computations (23.7% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(*.f64 x 4481/100000)
	0.4b	(*.f64 x 27061/100000)
✓	0.9b	(pow.f64 (cbrt.f64 (/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 x (+.f64 99229/100000 (*.f64 x 4481/100000)))))) 3)
	17.7b	(/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 x (+.f64 99229/100000 (*.f64 x 4481/100000)))))

series18.0ms (0.4%)

Counts

1 → 4

Calls

3 calls:

10.0ms

(pow.f64 (cbrt.f64 (/.f64 (+.f64 230753/100000 (*.f64 x 27061/100000)) (+.f64 1 (*.f64 x (+.f64 99229/100000 (*.f64 x 4481/100000)))))) 3)

4.0ms

(pow.f64 (cbrt.f64 (/.f64 (+.f64 230753/100000 (*.f64 x 27061/100000)) (+.f64 1 (*.f64 x (+.f64 99229/100000 (*.f64 x 4481/100000)))))) 3)

-inf

4.0ms

(pow.f64 (cbrt.f64 (/.f64 (+.f64 230753/100000 (*.f64 x 27061/100000)) (+.f64 1 (*.f64 x (+.f64 99229/100000 (*.f64 x 4481/100000)))))) 3)

inf

rewrite52.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

363×	`log-prod_binary64`
280×	`expm1-udef_binary64`
280×	`log1p-udef_binary64`
250×	`log-pow_binary64`
160×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	22
1	337	22
2	3259	22

Stop Event

1×	node limit

Counts

1 → 19

simplify230.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

1716×	`sqr-pow_binary64`
758×	`pow-sqr_binary64`
55×	`cube-prod_binary64`
55×	`cube-mult_binary64`
55×	`unpow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	104
1	59	104
2	80	104
3	102	104
4	130	104
5	158	104
6	189	104
7	221	104
8	257	104
9	294	104
10	335	104
11	377	104
12	423	104
13	470	104
14	521	104
15	573	104
16	629	104
17	686	104
18	747	104
19	809	104
20	875	104
21	942	104
22	1013	104
23	1085	104
24	1161	104
25	1238	104
26	1319	104
27	1401	104
28	1487	104
29	1574	104
30	1665	104
31	1757	104
32	1853	104
33	1950	104
34	2051	104
35	2153	104
36	2259	104
37	2263	104
38	2265	104
39	2265	104
40	2371	104
41	2480	104
42	2592	104
43	2708	104
44	2825	104
45	2946	104
46	3068	104
47	3194	104
48	3321	104
49	3452	104
50	3584	104
51	3720	104
52	3857	104
53	3998	104
54	4140	104
55	4144	104
56	4146	104
57	4146	104
58	4291	104
59	4436	104
60	4587	104
61	4739	104
62	4895	104

Stop Event

1×	node limit

Counts

23 → 26

prune84.0ms (1.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	92	2	94

Error

Counts

94 → 2

Alt Table

Status	Error	Program
✓	0.5b	(-.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 x (+.f64 99229/100000 (*.f64 x 4481/100000)))))) 3) x)
✓	0.1b	(-.f64 (/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 99229/100000 (.f64 x 4481/100000))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 99229/100000 (*.f64 x 4481/100000)))))))) x)

Status

Error

Program

✓

0.5b

(-.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 230753/100000 (*.f64 x 27061/100000)) (+.f64 1 (*.f64 x (+.f64 99229/100000 (*.f64 x 4481/100000)))))) 3) x)

✓

0.1b

(-.f64 (/.f64 (+.f64 230753/100000 (*.f64 x 27061/100000)) (+.f64 1 (+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 99229/100000 (*.f64 x 4481/100000))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 99229/100000 (*.f64 x 4481/100000)))))))) x)

Compiler

Compiled 2341 to 1904 computations (18.7% saved)

regimes208.0ms (4.3%)

Accuracy

Total 0.1b remaining (79.6%)

Threshold costs 0.1b (79.6%)

Counts

91 → 1

Compiler

Compiled 4014 to 3238 computations (19.3% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	32
1	20	32

Stop Event

1×

saturated

end76.0ms (1.6%)

Stop Event

1×

done

Compiler

Compiled 97 to 78 computations (19.6% saved)

Details

analyze9.0ms (0.2%)

sample3.1s (63.7%)

preprocess22.0ms (0.4%)

simplify4.0ms (0.1%)

prune2.0ms (0%)

localize13.0ms (0.3%)

series8.0ms (0.2%)

rewrite50.0ms (1.1%)

simplify314.0ms (6.6%)

prune102.0ms (2.1%)

localize16.0ms (0.3%)

series239.0ms (5%)

rewrite37.0ms (0.8%)

simplify61.0ms (1.3%)

prune183.0ms (3.8%)

localize13.0ms (0.3%)

series18.0ms (0.4%)

rewrite52.0ms (1.1%)

simplify230.0ms (4.8%)

prune84.0ms (1.8%)

regimes208.0ms (4.3%)

simplify1.0ms (0%)

end76.0ms (1.6%)

Profiling