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)

sample2.3s (65.1%)

Results

2.1s

8256×

body

256

valid

Compiler

Compiled 74 to 61 computations (17.6% saved)

simplify163.0ms (4.6%)

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

prune4.0ms (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
✓	0.2b	(.f64 t (.f64 t 1/25000000000000000000000000000000))
✓	0.3b	(*.f64 t 1/25000000000000000000000000000000)

series5.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

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

rewrite9.0ms (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:

5.0ms	(.f64 t (.f64 t 1/25000000000000000000000000000000))
3.0ms	(*.f64 t 1/25000000000000000000000000000000)

simplify76.0ms (2.1%)

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

prune42.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	56	6	62
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	56	7	63

Error

Counts

63 → 7

Alt Table

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

Compiler

Compiled 739 to 479 computations (35.2% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 t 1/5000000000000000)
✓	0.2b	(.f64 t (.f64 (*.f64 t 1/5000000000000000) (sqrt.f64 1/25000000000000000000000000000000)))
✓	0.3b	(.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 (0.5%)

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

5.0ms

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

3.0ms

(*.f64 t 1/5000000000000000)

simplify80.0ms (2.3%)

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 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	751
1	175	652
2	571	640
3	854	638
4	1191	638
5	1833	638
6	4792	638
7	4941	638

prune65.0ms (1.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	92	4	96

Error

Counts

96 → 4

Alt Table

Status	Error	Program
	0.6b	(.f64 (sqrt.f64 (.f64 t (.f64 t 1/25000000000000000000000000000000))) (sqrt.f64 (.f64 t (*.f64 t 1/25000000000000000000000000000000))))
	0.6b	(.f64 t (.f64 t (*.f64 1/5000000000000000 (sqrt.f64 1/25000000000000000000000000000000))))
▶	0.5b	(.f64 t (cbrt.f64 (.f64 (.f64 (.f64 t t) t) (.f64 (.f64 1/25000000000000000000000000000000 1/25000000000000000000000000000000) 1/25000000000000000000000000000000))))
✓	0.4b	(.f64 t (.f64 t 1/25000000000000000000000000000000))

Compiler

Compiled 1176 to 874 computations (25.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (.f64 (.f64 (.f64 t t) t) (.f64 (*.f64 1/25000000000000000000000000000000 1/25000000000000000000000000000000) 1/25000000000000000000000000000000)))
✓	0.6b	(.f64 (.f64 (.f64 t t) t) (.f64 (*.f64 1/25000000000000000000000000000000 1/25000000000000000000000000000000) 1/25000000000000000000000000000000))
✓	1.0b	(*.f64 1/25000000000000000000000000000000 1/25000000000000000000000000000000)
✓	1.0b	(.f64 (.f64 1/25000000000000000000000000000000 1/25000000000000000000000000000000) 1/25000000000000000000000000000000)

series18.0ms (0.5%)

Counts

4 → 24

Calls

4 calls:

15.0ms	(cbrt.f64 (.f64 (.f64 (.f64 t t) t) (.f64 (*.f64 1/25000000000000000000000000000000 1/25000000000000000000000000000000) 1/25000000000000000000000000000000)))
3.0ms	(.f64 (.f64 (.f64 t t) t) (.f64 (*.f64 1/25000000000000000000000000000000 1/25000000000000000000000000000000) 1/25000000000000000000000000000000))
0.0ms	(.f64 (.f64 1/25000000000000000000000000000000 1/25000000000000000000000000000000) 1/25000000000000000000000000000000)
0.0ms	(*.f64 1/25000000000000000000000000000000 1/25000000000000000000000000000000)

rewrite51.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

154×	`pow1_binary64`
57×	`pow-prod-down_binary64`
50×	`add-cbrt-cube_binary64`
47×	`add-exp-log_binary64`
47×	`pow-plus_binary64`

Counts

4 → 134

Calls

4 calls:

18.0ms	(.f64 (.f64 (.f64 t t) t) (.f64 (*.f64 1/25000000000000000000000000000000 1/25000000000000000000000000000000) 1/25000000000000000000000000000000))
15.0ms	(cbrt.f64 (.f64 (.f64 (.f64 t t) t) (.f64 (*.f64 1/25000000000000000000000000000000 1/25000000000000000000000000000000) 1/25000000000000000000000000000000)))
5.0ms	(.f64 (.f64 1/25000000000000000000000000000000 1/25000000000000000000000000000000) 1/25000000000000000000000000000000)
3.0ms	(*.f64 1/25000000000000000000000000000000 1/25000000000000000000000000000000)

simplify127.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

698×	`fma-def_binary64`
673×	`unswap-sqr_binary64`
589×	`associate-l_binary64`
392×	`associate-r_binary64`
249×	`associate-+l+_binary64`

Counts

158 → 137

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	109	1065
1	173	896
2	457	881
3	1513	851
4	2096	843
5	3538	843
6	4419	843
7	4993	843
8	4923	843

prune88.0ms (2.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	137	4	141

Error

Counts

141 → 4

Alt Table

Status	Error	Program
✓	0.4b	(.f64 t (.f64 t 1/25000000000000000000000000000000))
▶	0.6b	(.f64 t (.f64 (cbrt.f64 1/15625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) t))
	0.6b	(.f64 (sqrt.f64 (.f64 t (.f64 t 1/25000000000000000000000000000000))) (sqrt.f64 (.f64 t (*.f64 t 1/25000000000000000000000000000000))))
✓	0.5b	(.f64 t (cbrt.f64 (.f64 (.f64 (.f64 t t) t) (.f64 (.f64 1/25000000000000000000000000000000 1/25000000000000000000000000000000) 1/25000000000000000000000000000000))))

Compiler

Compiled 2395 to 1559 computations (34.9% saved)

localize4.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 t (.f64 (cbrt.f64 1/15625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) t))
✓	0.3b	(*.f64 (cbrt.f64 1/15625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) t)
✓	1.0b	(cbrt.f64 1/15625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)

series14.0ms (0.4%)

Counts

3 → 12

Calls

3 calls:

7.0ms

(*.f64 (cbrt.f64 1/15625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) t)

7.0ms

(*.f64 t (*.f64 (cbrt.f64 1/15625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) t))

0.0ms

(cbrt.f64 1/15625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`
9×	`associate-l_binary64`
8×	`*-un-lft-identity_binary64`

Counts

3 → 57

Calls

3 calls:

4.0ms

(*.f64 t (*.f64 (cbrt.f64 1/15625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) t))

4.0ms

(*.f64 (cbrt.f64 1/15625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) t)

1.0ms

(cbrt.f64 1/15625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)

simplify91.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

702×	`fma-def_binary64`
272×	`associate-l_binary64`
238×	`associate-*r/_binary64`
236×	`*-commutative_binary64`
227×	`associate-/l*_binary64`

Counts

69 → 75

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	686
1	119	603
2	298	584
3	564	582
4	837	582
5	1456	582
6	3433	582
7	4967	582
8	4969	582

prune52.0ms (1.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	75	4	79

Error

Counts

79 → 4

Alt Table

Status	Error	Program
✓	0.4b	(.f64 t (.f64 t 1/25000000000000000000000000000000))
✓	0.6b	(.f64 t (.f64 (cbrt.f64 1/15625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) t))
	0.6b	(.f64 (sqrt.f64 t) (.f64 (cbrt.f64 1/15625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (pow.f64 t 3/2)))
✓	0.5b	(.f64 t (cbrt.f64 (.f64 (.f64 (.f64 t t) t) (.f64 (.f64 1/25000000000000000000000000000000 1/25000000000000000000000000000000) 1/25000000000000000000000000000000))))

Compiler

Compiled 832 to 591 computations (29% saved)

regimes239.0ms (6.7%)

Accuracy

Total 0.4b remaining (95.8%)

Threshold costs 0.4b (95.8%)

Counts

88 → 1

Compiler

Compiled 2974 to 2241 computations (24.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	7	7
2	7	7

end57.0ms (1.6%)

Compiler: Compiled 50 to 36 computations (28% saved)

Details

analyze1.0ms (0%)

sample2.3s (65.1%)

simplify163.0ms (4.6%)

prune4.0ms (0.1%)

localize3.0ms (0.1%)

series5.0ms (0.1%)

rewrite9.0ms (0.3%)

simplify76.0ms (2.1%)

prune42.0ms (1.2%)

localize6.0ms (0.2%)

series6.0ms (0.2%)

rewrite18.0ms (0.5%)

simplify80.0ms (2.3%)

prune65.0ms (1.8%)

localize8.0ms (0.2%)

series18.0ms (0.5%)

rewrite51.0ms (1.4%)

simplify127.0ms (3.6%)

prune88.0ms (2.5%)

localize4.0ms (0.1%)

series14.0ms (0.4%)

rewrite10.0ms (0.3%)

simplify91.0ms (2.5%)

prune52.0ms (1.5%)

regimes239.0ms (6.7%)

simplify2.0ms (0%)

end57.0ms (1.6%)

Profiling