Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 27 to 22 computations (18.5% saved)

sample3.2s (62.4%)

Results

3.0s

8256×

body

256

valid

Compiler

Compiled 74 to 61 computations (17.6% saved)

simplify192.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

955×	`fma-def_binary64`
760×	`unsub-neg_binary64`
633×	`distribute-neg-in_binary64`
628×	`distribute-rgt-neg-in_binary64`
564×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	35	19
2	98	17
3	302	15
4	923	7
5	2332	7
6	3226	7
7	3864	7
8	4544	7
9	4793	7
10	4822	7
11	4798	7
12	4830	7
13	4680	7
14	4874	7
15	4821	7

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.4b	(.f64 t (.f64 t 1/25000000000000000000000000000000))

Compiler

Compiled 37 to 28 computations (24.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 t (.f64 t 1/25000000000000000000000000000000))
✓	0.4b	(*.f64 t 1/25000000000000000000000000000000)

series7.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(.f64 t (.f64 t 1/25000000000000000000000000000000))
3.0ms	(*.f64 t 1/25000000000000000000000000000000)

rewrite97.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

760×	`log1p-udef_binary64`
414×	`log1p-expm1-u_binary64`
414×	`expm1-log1p-u_binary64`
352×	`pow1_binary64`
308×	`unpow-prod-down_binary64`

Counts

2 → 40

Calls

2 calls:

96.0ms	(.f64 t (.f64 t 1/25000000000000000000000000000000))
96.0ms	(*.f64 t 1/25000000000000000000000000000000)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	102	11
2	1113	11
3	4782	11
4	5985	11
0	0	0
1	0	0

simplify184.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
573×	`fabs-mul_binary64`
560×	`cube-prod_binary64`
536×	`pow-sqr_binary64`
454×	`associate-l_binary64`

Counts

64 → 43

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	132
1	14	132
2	22	132
3	41	132
4	88	132
5	221	132
6	693	132
7	1098	132
8	1100	132
9	1248	132
10	1418	132
11	1600	132
12	1825	132
13	2110	132
14	2529	132
15	3094	132
16	3780	132
17	3998	132
18	4242	132
19	4324	132
20	4357	132
21	4378	132
22	4947	132

prune48.0ms (0.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	37	6	43
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	37	7	44

Error

0.0b

Counts

44 → 7

Alt Table

Status	Error	Program
	0.8b	(cbrt.f64 (pow.f64 (*.f64 t 1/5000000000000000) 6))
	0.5b	(sqrt.f64 (pow.f64 (*.f64 t 1/5000000000000000) 4))
✓	0.4b	(.f64 t (.f64 t 1/25000000000000000000000000000000))
	0.6b	(.f64 t (cbrt.f64 (.f64 (pow.f64 t 3) 1/15625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)))
▶	0.3b	(.f64 t (sqrt.f64 (.f64 (*.f64 t t) 1/625000000000000000000000000000000000000000000000000000000000000)))
	0.7b	(.f64 t (pow.f64 (.f64 (sqrt.f64 t) 1/5000000000000000) 2))
	1.8b	(.f64 t (pow.f64 (cbrt.f64 (.f64 t 1/25000000000000000000000000000000)) 3))

Compiler

Compiled 476 to 356 computations (25.2% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (.f64 (.f64 t t) 1/625000000000000000000000000000000000000000000000000000000000000))
✓	0.2b	(.f64 t (sqrt.f64 (.f64 (*.f64 t t) 1/625000000000000000000000000000000000000000000000000000000000000)))
✓	0.3b	(.f64 (.f64 t t) 1/625000000000000000000000000000000000000000000000000000000000000)

series11.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

4.0ms

(*.f64 (*.f64 t t) 1/625000000000000000000000000000000000000000000000000000000000000)

4.0ms

(*.f64 t (sqrt.f64 (*.f64 (*.f64 t t) 1/625000000000000000000000000000000000000000000000000000000000000)))

3.0ms

(sqrt.f64 (*.f64 (*.f64 t t) 1/625000000000000000000000000000000000000000000000000000000000000))

rewrite103.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

567×	`log1p-expm1-u_binary64`
567×	`expm1-log1p-u_binary64`
562×	`unpow-prod-down_binary64`
332×	`log-prod_binary64`
165×	`pow2_binary64`

Counts

3 → 91

Calls

3 calls:

100.0ms

(sqrt.f64 (*.f64 (*.f64 t t) 1/625000000000000000000000000000000000000000000000000000000000000))

100.0ms

(*.f64 t (sqrt.f64 (*.f64 (*.f64 t t) 1/625000000000000000000000000000000000000000000000000000000000000)))

100.0ms

(*.f64 (*.f64 t t) 1/625000000000000000000000000000000000000000000000000000000000000)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	28
1	143	18
2	1532	18
3	5714	18
0	0	0
1	0	0

simplify186.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

1104×	`sqr-pow_binary64`
661×	`fabs-mul_binary64`
628×	`pow-sqr_binary64`
611×	`cube-prod_binary64`
310×	`cube-mult_binary64`

Counts

127 → 99

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	216
1	22	216
2	36	216
3	71	216
4	162	216
5	435	216
6	530	216
7	767	216
8	792	216
9	902	216
10	1020	216
11	1187	216
12	1351	216
13	1579	216
14	1913	216
15	2308	216
16	2866	216
17	3550	216
18	3775	216
19	4040	216
20	4132	216
21	4166	216
22	4187	216
23	4870	216

prune95.0ms (1.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	101	5	106

Error

Counts

106 → 5

Alt Table

Status	Error	Program
	0.8b	(cbrt.f64 (pow.f64 (*.f64 t 1/5000000000000000) 6))
	0.5b	(sqrt.f64 (pow.f64 (*.f64 t 1/5000000000000000) 4))
✓	0.4b	(.f64 t (.f64 t 1/25000000000000000000000000000000))
✓	0.3b	(.f64 t (sqrt.f64 (.f64 (*.f64 t t) 1/625000000000000000000000000000000000000000000000000000000000000)))
▶	0.2b	(sqrt.f64 (*.f64 (pow.f64 t 4) 1/625000000000000000000000000000000000000000000000000000000000000))

Compiler

Compiled 1109 to 772 computations (30.4% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (*.f64 (pow.f64 t 4) 1/625000000000000000000000000000000000000000000000000000000000000))
✓	0.3b	(*.f64 (pow.f64 t 4) 1/625000000000000000000000000000000000000000000000000000000000000)

series11.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(*.f64 (pow.f64 t 4) 1/625000000000000000000000000000000000000000000000000000000000000)
5.0ms	(sqrt.f64 (*.f64 (pow.f64 t 4) 1/625000000000000000000000000000000000000000000000000000000000000))

rewrite81.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

539×	`log1p-expm1-u_binary64`
539×	`expm1-log1p-u_binary64`
447×	`unpow-prod-down_binary64`
275×	`log-prod_binary64`
160×	`pow2_binary64`

Counts

2 → 70

Calls

2 calls:

78.0ms	(sqrt.f64 (*.f64 (pow.f64 t 4) 1/625000000000000000000000000000000000000000000000000000000000000))
78.0ms	(*.f64 (pow.f64 t 4) 1/625000000000000000000000000000000000000000000000000000000000000)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	147	14
2	1446	14
3	5160	14
0	0	0
1	0	0

simplify171.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

1078×	`sqr-pow_binary64`
520×	`pow-sqr_binary64`
443×	`cube-prod_binary64`
411×	`associate-l_binary64`
377×	`fabs-mul_binary64`

Counts

94 → 72

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	168
1	19	168
2	38	168
3	84	168
4	213	168
5	645	168
6	959	168
7	981	168
8	1135	168
9	1320	168
10	1560	168
11	1824	168
12	2152	168
13	2538	168
14	3070	168
15	3715	168
16	3899	168
17	4087	168
18	4149	168
19	4169	168
20	4178	168
21	4652	168

prune68.0ms (1.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	1	1	2
Picked	0	1	1
Done	1	1	2
Total	73	4	77

Error

Counts

77 → 4

Alt Table

Status	Error	Program
▶	0.5b	(sqrt.f64 (pow.f64 (*.f64 t 1/5000000000000000) 4))
✓	0.4b	(.f64 t (.f64 t 1/25000000000000000000000000000000))
	0.6b	(.f64 (.f64 t t) (pow.f64 1/625000000000000000000000000000000000000000000000000000000000000 1/2))
✓	0.2b	(sqrt.f64 (*.f64 (pow.f64 t 4) 1/625000000000000000000000000000000000000000000000000000000000000))

Compiler

Compiled 817 to 591 computations (27.7% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (pow.f64 (*.f64 t 1/5000000000000000) 4))
✓	0.2b	(*.f64 t 1/5000000000000000)
✓	0.8b	(pow.f64 (*.f64 t 1/5000000000000000) 4)

series14.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

5.0ms	(pow.f64 (*.f64 t 1/5000000000000000) 4)
5.0ms	(sqrt.f64 (pow.f64 (*.f64 t 1/5000000000000000) 4))
3.0ms	(*.f64 t 1/5000000000000000)

rewrite92.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

544×	`log1p-expm1-u_binary64`
544×	`expm1-log1p-u_binary64`
522×	`unpow-prod-down_binary64`
277×	`log-prod_binary64`
161×	`pow2_binary64`

Counts

3 → 142

Calls

3 calls:

88.0ms	(sqrt.f64 (pow.f64 (*.f64 t 1/5000000000000000) 4))
88.0ms	(*.f64 t 1/5000000000000000)
88.0ms	(pow.f64 (*.f64 t 1/5000000000000000) 4)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	148	18
2	1457	18
3	5294	18
0	0	0
1	0	0

simplify196.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

1078×	`sqr-pow_binary64`
520×	`pow-sqr_binary64`
443×	`cube-prod_binary64`
426×	`associate-l_binary64`
390×	`*-commutative_binary64`

Counts

178 → 145

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	216
1	22	216
2	41	216
3	91	216
4	228	216
5	682	216
6	996	216
7	1018	216
8	1172	216
9	1357	216
10	1597	216
11	1861	216
12	2189	216
13	2575	216
14	3107	216
15	3752	216
16	3936	216
17	4124	216
18	4186	216
19	4206	216
20	4215	216
21	4689	216

prune137.0ms (2.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	145	4	149

Error

Counts

149 → 4

Alt Table

Status	Error	Program
✓	0.5b	(sqrt.f64 (pow.f64 (*.f64 t 1/5000000000000000) 4))
✓	0.4b	(.f64 t (.f64 t 1/25000000000000000000000000000000))
	0.6b	(.f64 (.f64 t t) (pow.f64 1/625000000000000000000000000000000000000000000000000000000000000 1/2))
✓	0.2b	(sqrt.f64 (*.f64 (pow.f64 t 4) 1/625000000000000000000000000000000000000000000000000000000000000))

Compiler

Compiled 1735 to 1386 computations (20.1% saved)

regimes108.0ms (2.1%)

Accuracy

Total 0.2b remaining (94.3%)

Threshold costs 0.2b (94.3%)

Counts

20 → 1

Compiler

Compiled 624 to 494 computations (20.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	9	10
2	9	10

end102.0ms (2%)

Compiler: Compiled 44 to 36 computations (18.2% saved)

Details

analyze2.0ms (0%)

sample3.2s (62.4%)

simplify192.0ms (3.7%)

prune6.0ms (0.1%)

localize5.0ms (0.1%)

series7.0ms (0.1%)

rewrite97.0ms (1.9%)

simplify184.0ms (3.6%)

prune48.0ms (0.9%)

localize9.0ms (0.2%)

series11.0ms (0.2%)

rewrite103.0ms (2%)

simplify186.0ms (3.6%)

prune95.0ms (1.8%)

localize7.0ms (0.1%)

series11.0ms (0.2%)

rewrite81.0ms (1.6%)

simplify171.0ms (3.3%)

prune68.0ms (1.3%)

localize8.0ms (0.1%)

series14.0ms (0.3%)

rewrite92.0ms (1.8%)

simplify196.0ms (3.8%)

prune137.0ms (2.7%)

regimes108.0ms (2.1%)

simplify3.0ms (0.1%)

end102.0ms (2%)

Profiling