Details

analyze1.0ms (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)

sample2.0s (70.4%)

Results

1.8s

8256×

body

256

valid

Compiler

Compiled 74 to 61 computations (17.6% saved)

simplify165.0ms (5.7%)

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

prune3.0ms (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)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 t (.f64 t 1/25000000000000000000000000000000))
✓	0.4b	(*.f64 t 1/25000000000000000000000000000000)

series4.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

2.0ms	(.f64 t (.f64 t 1/25000000000000000000000000000000))
2.0ms	(*.f64 t 1/25000000000000000000000000000000)

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`

Counts

2 → 40

Calls

2 calls:

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

simplify79.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

970×	`fma-def_binary64`
331×	`associate-l_binary64`
261×	`associate-*r/_binary64`
229×	`associate-*l/_binary64`
217×	`*-commutative_binary64`

Counts

64 → 62

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	478
1	112	430
2	327	421
3	594	419
4	851	419
5	1427	419
6	3364	419
7	4801	419
8	4930	419

prune43.0ms (1.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	55	7	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	7	63

Error

Counts

63 → 7

Alt Table

Status	Error	Program
	0.6b	(cbrt.f64 (*.f64 1/15625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 6)))
	0.4b	(*.f64 1/25000000000000000000000000000000 (pow.f64 t 2))
▶	0.4b	(.f64 t (.f64 (*.f64 t 1/5000000000000000) (sqrt.f64 1/25000000000000000000000000000000)))
	0.6b	(.f64 t (.f64 (sqrt.f64 (.f64 t 1/25000000000000000000000000000000)) (sqrt.f64 (.f64 t 1/25000000000000000000000000000000))))
	0.7b	(.f64 (sqrt.f64 t) (.f64 (sqrt.f64 t) (*.f64 t 1/25000000000000000000000000000000)))
	0.6b	(.f64 t (cbrt.f64 (.f64 (.f64 (.f64 t 1/25000000000000000000000000000000) (.f64 t 1/25000000000000000000000000000000)) (.f64 t 1/25000000000000000000000000000000))))
	0.5b	(cbrt.f64 (.f64 (.f64 (.f64 t t) t) (.f64 (.f64 (.f64 t 1/25000000000000000000000000000000) (.f64 t 1/25000000000000000000000000000000)) (.f64 t 1/25000000000000000000000000000000))))

Compiler

Compiled 739 to 483 computations (34.6% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 t 1/5000000000000000)
✓	0.2b	(.f64 (.f64 t 1/5000000000000000) (sqrt.f64 1/25000000000000000000000000000000))
✓	0.3b	(.f64 t (.f64 (*.f64 t 1/5000000000000000) (sqrt.f64 1/25000000000000000000000000000000)))

series6.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

3.0ms

(*.f64 t (*.f64 (*.f64 t 1/5000000000000000) (sqrt.f64 1/25000000000000000000000000000000)))

2.0ms

(*.f64 (*.f64 t 1/5000000000000000) (sqrt.f64 1/25000000000000000000000000000000))

1.0ms

(*.f64 t 1/5000000000000000)

rewrite18.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-cbrt-cube_binary64`
19×	`add-exp-log_binary64`
19×	`pow1_binary64`
10×	`associate-r_binary64`
10×	`add-sqr-sqrt_binary64`

Counts

3 → 66

Calls

3 calls:

7.0ms

(*.f64 (*.f64 t 1/5000000000000000) (sqrt.f64 1/25000000000000000000000000000000))

6.0ms

(*.f64 t (*.f64 (*.f64 t 1/5000000000000000) (sqrt.f64 1/25000000000000000000000000000000)))

3.0ms

(*.f64 t 1/5000000000000000)

simplify78.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

649×	`unswap-sqr_binary64`
623×	`fma-def_binary64`
280×	`*-commutative_binary64`
272×	`associate-*r/_binary64`
234×	`associate-*l/_binary64`

Counts

102 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	751
1	174	652
2	571	640
3	854	638
4	1191	638
5	1833	638
6	4792	638
7	4941	638

prune53.0ms (1.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	91	4	95

Error

Counts

95 → 4

Alt Table

Status	Error	Program
▶	0.4b	(.f64 t (expm1.f64 (log1p.f64 (.f64 1/25000000000000000000000000000000 t))))
	0.4b	(*.f64 1/25000000000000000000000000000000 (pow.f64 t 2))
	0.5b	(.f64 t (.f64 t (*.f64 1/5000000000000000 (sqrt.f64 1/25000000000000000000000000000000))))
	0.5b	(cbrt.f64 (.f64 (.f64 (.f64 t t) t) (.f64 (.f64 (.f64 t 1/25000000000000000000000000000000) (.f64 t 1/25000000000000000000000000000000)) (.f64 t 1/25000000000000000000000000000000))))

Compiler

Compiled 1162 to 864 computations (25.6% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 t (expm1.f64 (log1p.f64 (.f64 1/25000000000000000000000000000000 t))))
✓	0.4b	(*.f64 1/25000000000000000000000000000000 t)

series4.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

3.0ms	(.f64 t (expm1.f64 (log1p.f64 (.f64 1/25000000000000000000000000000000 t))))
2.0ms	(*.f64 1/25000000000000000000000000000000 t)

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`
6×	`associate-l_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 40

Calls

2 calls:

3.0ms	(*.f64 1/25000000000000000000000000000000 t)
3.0ms	(.f64 t (expm1.f64 (log1p.f64 (.f64 1/25000000000000000000000000000000 t))))

simplify65.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
399×	`associate-*r/_binary64`
385×	`associate-*l/_binary64`
287×	`log-div_binary64`
277×	`associate-l_binary64`

Counts

52 → 58

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	64	437
1	111	401
2	294	401
3	578	399
4	841	393
5	1385	393
6	3935	393
7	4900	393

prune32.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	58	4	62

Error

Counts

62 → 4

Alt Table

Status	Error	Program
✓	0.4b	(.f64 t (expm1.f64 (log1p.f64 (.f64 1/25000000000000000000000000000000 t))))
▶	0.4b	(*.f64 1/25000000000000000000000000000000 (pow.f64 t 2))
	0.5b	(.f64 t (.f64 t (*.f64 1/5000000000000000 (sqrt.f64 1/25000000000000000000000000000000))))
	0.5b	(cbrt.f64 (.f64 (.f64 (.f64 t t) t) (.f64 (.f64 (.f64 t 1/25000000000000000000000000000000) (.f64 t 1/25000000000000000000000000000000)) (.f64 t 1/25000000000000000000000000000000))))

Compiler

Compiled 755 to 538 computations (28.7% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 1/25000000000000000000000000000000 (pow.f64 t 2))

series3.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

3.0ms

(*.f64 1/25000000000000000000000000000000 (pow.f64 t 2))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
6×	`add-exp-log_binary64`
4×	`unswap-sqr_binary64`
4×	`unpow-prod-down_binary64`

Counts

1 → 29

Calls

1 calls:

4.0ms

(*.f64 1/25000000000000000000000000000000 (pow.f64 t 2))

simplify79.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

964×	`fma-def_binary64`
644×	`unswap-sqr_binary64`
397×	`log-prod_binary64`
394×	`sqr-pow_binary64`
337×	`*-commutative_binary64`

Counts

29 → 45

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	303
1	98	231
2	199	221
3	637	215
4	1073	215
5	2846	215
6	3959	215
7	4849	215
8	4882	215

prune24.0ms (0.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	44	1	45
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	45	4	49

Error

Counts

49 → 4

Alt Table

Status	Error	Program
✓	0.4b	(.f64 t (expm1.f64 (log1p.f64 (.f64 1/25000000000000000000000000000000 t))))
✓	0.4b	(*.f64 1/25000000000000000000000000000000 (pow.f64 t 2))
	0.5b	(.f64 (.f64 (sqrt.f64 1/25000000000000000000000000000000) t) (*.f64 (sqrt.f64 1/25000000000000000000000000000000) t))
	0.5b	(.f64 t (.f64 t (*.f64 1/5000000000000000 (sqrt.f64 1/25000000000000000000000000000000))))

Compiler

Compiled 490 to 374 computations (23.7% saved)

regimes99.0ms (3.5%)

Accuracy

Total 0.4b remaining (98%)

Threshold costs 0.4b (98%)

Counts

39 → 1

Compiler

Compiled 1373 to 1022 computations (25.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	11	10
2	10	10

end55.0ms (1.9%)

Compiler: Compiled 49 to 38 computations (22.4% saved)

Details

analyze1.0ms (0%)

sample2.0s (70.4%)

simplify165.0ms (5.7%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series4.0ms (0.1%)

rewrite8.0ms (0.3%)

simplify79.0ms (2.7%)

prune43.0ms (1.5%)

localize8.0ms (0.3%)

series6.0ms (0.2%)

rewrite18.0ms (0.6%)

simplify78.0ms (2.7%)

prune53.0ms (1.8%)

localize5.0ms (0.2%)

series4.0ms (0.2%)

rewrite7.0ms (0.2%)

simplify65.0ms (2.3%)

prune32.0ms (1.1%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite5.0ms (0.2%)

simplify79.0ms (2.7%)

prune24.0ms (0.8%)

regimes99.0ms (3.5%)

simplify2.0ms (0.1%)

end55.0ms (1.9%)

Profiling