Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample924.0ms (28.1%)

Symmetry

(sort lo hi x)

Results

859.0ms

8256×

body

128

valid

Compiler

Compiled 44 to 28 computations (36.4% saved)

simplify19.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

308×	`fma-neg_binary64`
219×	`fma-def_binary64`
205×	`rules-42_binary64`
196×	`rules-40_binary64`
175×	`rules-41_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	37	10
2	94	10
3	271	10
4	667	10
5	8	10

prune2.0ms (0.1%)

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

64.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	64.0b	(/.f64 (-.f64 x lo) (-.f64 hi lo))

Compiler

Compiled 30 to 18 computations (40% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	62.0b	(/.f64 (-.f64 x lo) (-.f64 hi lo))

series22.0ms (0.7%)

Counts

1 → 36

Calls

1 calls:

22.0ms

(/.f64 (-.f64 x lo) (-.f64 hi lo))

rewrite51.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

818×	`log1p-expm1-u_binary64`
818×	`expm1-log1p-u_binary64`
551×	`prod-diff_binary64`
80×	`add-sqr-sqrt_binary64`
73×	`add-cbrt-cube_binary64`

Counts

1 → 30

Calls

1 calls:

50.0ms

(/.f64 (-.f64 x lo) (-.f64 hi lo))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	170	10
2	2311	10
3	6252	10
0	0	0
1	0	0

simplify73.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

847×	`rules-40_binary64`
847×	`rules-41_binary64`
847×	`rules-42_binary64`
847×	`rules-43_binary64`
292×	`rules-7-rev_binary64`

Counts

66 → 61

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	78	1095
1	565	1041
2	2889	1041
3	4995	1041
4	5646	1041

prune26.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	58	3	61
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	3	62

Error

51.5b

Counts

62 → 3

Alt Table

Status	Error	Program
	52.0b	1
▶	51.6b	(/.f64 x (-.f64 hi lo))
	52.0b	(*.f64 -1 (/.f64 lo (-.f64 hi lo)))

Compiler

Compiled 1228 to 495 computations (59.7% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 hi lo))

series17.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

17.0ms

(/.f64 x (-.f64 hi lo))

rewrite43.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

648×	`log1p-expm1-u_binary64`
648×	`expm1-log1p-u_binary64`
328×	`prod-diff_binary64`
119×	`log1p-udef_binary64`
66×	`add-sqr-sqrt_binary64`

Counts

1 → 30

Calls

1 calls:

42.0ms

(/.f64 x (-.f64 hi lo))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	142	7
2	1866	7
3	5013	7
0	0	0
1	0	0

simplify37.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

656×	`fma-def_binary64`
601×	`fma-neg_binary64`
524×	`rules-13_binary64`
326×	`rules-40_binary64`
326×	`rules-41_binary64`

Counts

54 → 44

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	43	609
1	291	543
2	1264	501
3	5372	501

prune29.0ms (0.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	34	10	44
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	35	12	47

Error

51.5b

Counts

47 → 12

Alt Table

Status	Error	Program
	51.6b	(expm1.f64 (log1p.f64 (/.f64 x (-.f64 hi lo))))
	51.6b	(*.f64 x (/.f64 1 (-.f64 hi lo)))
	51.6b	(cbrt.f64 (pow.f64 (/.f64 x (-.f64 hi lo)) 3))
	51.6b	(log.f64 (+.f64 1 (expm1.f64 (/.f64 x (-.f64 hi lo)))))
	51.6b	(log.f64 (exp.f64 (/.f64 x (-.f64 hi lo))))
	51.6b	(pow.f64 (sqrt.f64 (/.f64 x (-.f64 hi lo))) 2)
	51.6b	(pow.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) 3)
	51.6b	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 hi lo)))
▶	51.6b	(*.f64 -1 (/.f64 x lo))
	51.6b	(*.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) (pow.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) 2))
	52.0b	1
	52.0b	(*.f64 -1 (/.f64 lo (-.f64 hi lo)))

Compiler

Compiled 782 to 383 computations (51% saved)

localize3.0ms (0.1%)

prune10.0ms (0.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	11	11
Picked	1	1
Done	0	0
Total	12	12

Error

51.5b

Counts

12 → 12

Alt Table

Status	Error	Program
	51.6b	(expm1.f64 (log1p.f64 (/.f64 x (-.f64 hi lo))))
	51.6b	(*.f64 x (/.f64 1 (-.f64 hi lo)))
	51.6b	(cbrt.f64 (pow.f64 (/.f64 x (-.f64 hi lo)) 3))
	51.6b	(log.f64 (+.f64 1 (expm1.f64 (/.f64 x (-.f64 hi lo)))))
	51.6b	(log.f64 (exp.f64 (/.f64 x (-.f64 hi lo))))
	51.6b	(pow.f64 (sqrt.f64 (/.f64 x (-.f64 hi lo))) 2)
	51.6b	(pow.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) 3)
	51.6b	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 hi lo)))
✓	51.6b	(*.f64 -1 (/.f64 x lo))
▶	51.6b	(*.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) (pow.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) 2))
	52.0b	1
	52.0b	(*.f64 -1 (/.f64 lo (-.f64 hi lo)))

Compiler

Compiled 246 to 168 computations (31.7% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 x (-.f64 hi lo))
✓	0.3b	(*.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) (pow.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) 2))
✓	0.5b	(cbrt.f64 (/.f64 x (-.f64 hi lo)))
✓	0.5b	(pow.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) 2)

series663.0ms (20.2%)

Counts

3 → 108

Calls

3 calls:

342.0ms	(pow.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) 2)
289.0ms	(cbrt.f64 (/.f64 x (-.f64 hi lo)))
31.0ms	(*.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) (pow.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) 2))

rewrite71.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

859×	`log1p-expm1-u_binary64`
859×	`expm1-log1p-u_binary64`
400×	`prod-diff_binary64`
141×	`egg-rr`
92×	`add-sqr-sqrt_binary64`

Counts

3 → 141

Calls

3 calls:

67.0ms	(*.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) (pow.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) 2))
67.0ms	(cbrt.f64 (/.f64 x (-.f64 hi lo)))
67.0ms	(pow.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	214	26
2	2508	26
3	6267	26
0	0	0
1	0	0

simplify96.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

591×	`fma-neg_binary64`
560×	`rules-20_binary64`
541×	`rules-21_binary64`
541×	`rules-41_binary64`
541×	`rules-43_binary64`

Counts

249 → 259

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	334	4197
1	2294	4197
2	4938	4197

prune278.0ms (8.5%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	421	12	433
Fresh	7	3	10
Picked	1	0	1
Done	0	1	1
Total	429	16	445

Error

51.5b

Counts

445 → 16

Alt Table

Status	Error	Program
	51.6b	(.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) (pow.f64 (cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) 2) (cbrt.f64 (/.f64 x (-.f64 hi lo))))) 2))
	51.6b	(*.f64 x (/.f64 1 (-.f64 hi lo)))
	51.6b	(/.f64 (/.f64 x (pow.f64 (cbrt.f64 (-.f64 hi lo)) 2)) (cbrt.f64 (-.f64 hi lo)))
	51.6b	(.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) (pow.f64 (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) 4))) (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 x (-.f64 hi lo)) 2/3)))) 2))
	51.6b	(+.f64 (fma.f64 (cbrt.f64 (pow.f64 (/.f64 x (-.f64 hi lo)) 2/3)) (.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) 4))) (neg.f64 (.f64 0 (cbrt.f64 (/.f64 x (-.f64 hi lo)))))) (fma.f64 0 (cbrt.f64 (/.f64 x (-.f64 hi lo))) (*.f64 0 (cbrt.f64 (/.f64 x (-.f64 hi lo))))))
	51.6b	(.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) (pow.f64 (.f64 (cbrt.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo)))) (cbrt.f64 (pow.f64 (/.f64 x (-.f64 hi lo)) 2/3))) 2))
	51.6b	(*.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) (pow.f64 (log.f64 (exp.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))))) 2))
	51.6b	(*.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) (pow.f64 (pow.f64 (exp.f64 1/3) (+.f64 (neg.f64 (log.f64 (-.f64 hi lo))) (log.f64 x))) 2))
	51.6b	(*.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo)))) 3) 2))
	51.6b	(*.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) (pow.f64 (-.f64 (exp.f64 (log1p.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))))) 1) 2))
	51.6b	(.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) (/.f64 (pow.f64 (/.f64 x (-.f64 hi lo)) 2) (+.f64 (pow.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) 4) (+.f64 0 (.f64 (pow.f64 (/.f64 x (-.f64 hi lo)) 2/3) 0)))))
	51.6b	(*.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) (pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (-.f64 hi lo))) 2))
✓	51.6b	(*.f64 -1 (/.f64 x lo))
	52.0b	1
	52.0b	(*.f64 -1 (/.f64 lo (-.f64 hi lo)))
	51.6b	(*.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))) (pow.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (/.f64 x (-.f64 hi lo))))) 2))

Compiler

Compiled 13741 to 6612 computations (51.9% saved)

regimes328.0ms (10%)

Accuracy

Total 0.1b remaining (0.2%)

Threshold costs 0.1b (0.2%)

Counts

86 → 1

Compiler

Compiled 7398 to 4048 computations (45.3% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	6	7

end578.0ms (17.6%)

Compiler: Compiled 385 to 218 computations (43.4% saved)

Details

analyze2.0ms (0.1%)

sample924.0ms (28.1%)

simplify19.0ms (0.6%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series22.0ms (0.7%)

rewrite51.0ms (1.5%)

simplify73.0ms (2.2%)

prune26.0ms (0.8%)

localize3.0ms (0.1%)

series17.0ms (0.5%)

rewrite43.0ms (1.3%)

simplify37.0ms (1.1%)

prune29.0ms (0.9%)

localize3.0ms (0.1%)

prune10.0ms (0.3%)

localize7.0ms (0.2%)

series663.0ms (20.2%)

rewrite71.0ms (2.2%)

simplify96.0ms (2.9%)

prune278.0ms (8.5%)

regimes328.0ms (10%)

simplify1.0ms (0%)

end578.0ms (17.6%)

Profiling