Details

analyze101.0ms (0.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
46.8%	53.1%	0.1%	6
70.2%	29.7%	0.1%	7
76.5%	23.4%	0.1%	8
83.5%	16.4%	0.1%	9
87%	12.9%	0.1%	10
91.1%	8.8%	0.1%	11
93.2%	6.7%	0.1%	12
95.4%	4.5%	0.1%	13
96.5%	3.4%	0.1%	14

Compiler

Compiled 20 to 10 computations (50% saved)

sample928.0ms (6.8%)

Symmetry

(sort x y)

Results

811.0ms

8256×

body

128

valid

Compiler

Compiled 59 to 29 computations (50.8% saved)

simplify137.0ms (1%)

Algorithm

1×	egg-herbie

Rules

985×	`associate-/l*_binary64`
659×	`distribute-lft-out_binary64`
601×	`*-commutative_binary64`
469×	`distribute-rgt-out_binary64`
356×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	39	25
2	135	23
3	474	23
4	1536	23
5	2122	23
6	2589	23
7	2567	23
8	2620	23
9	2677	23
10	2770	23
11	3956	23
12	4088	23
13	4454	23
14	4983	23
15	4968	23
16	4961	23

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

20.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	20.0b	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
▶	20.0b	(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

Compiler

Compiled 109 to 47 computations (56.9% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))
✓	0.0b	(pow.f64 (+.f64 x y) 3)
✓	19.8b	(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

series94.0ms (0.7%)

Counts

3 → 72

Calls

3 calls:

73.0ms	(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
13.0ms	(fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))
8.0ms	(pow.f64 (+.f64 x y) 3)

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`

Counts

3 → 62

Calls

3 calls:

3.0ms	(pow.f64 (+.f64 x y) 3)
3.0ms	(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
0.0ms	(fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))

simplify155.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

326×	`fma-def_binary64`
301×	`times-frac_binary64`
297×	`associate-+r+_binary64`
257×	`associate-/l*_binary64`
223×	`+-commutative_binary64`

Counts

134 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	347	4819
1	1047	4272
2	4702	4260
3	4981	4260
4	4996	4260
5	4981	4260

prune167.0ms (1.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	156	6	162
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	158	6	164

Error

4.2b

Counts

164 → 6

Alt Table

Status	Error	Program
▶	20.0b	(/.f64 (*.f64 y x) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
	41.2b	(/.f64 x (pow.f64 y 2))
	40.2b	(/.f64 y (pow.f64 x 2))
	32.8b	(*.f64 (/.f64 x (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))))
	31.2b	(*.f64 (/.f64 x (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (/.f64 y (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
	22.2b	(/.f64 (.f64 (/.f64 x (.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2))) (cbrt.f64 (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2))))) y) (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))

Compiler

Compiled 5923 to 3134 computations (47.1% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))
	0.0b	(pow.f64 (+.f64 x y) 3)
✓	19.8b	(/.f64 (*.f64 y x) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

series71.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

71.0ms

(/.f64 (*.f64 y x) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
3×	`associate-/r*_binary64`
3×	`*-un-lft-identity_binary64`
3×	`times-frac_binary64`

Counts

1 → 23

Calls

1 calls:

3.0ms

(/.f64 (*.f64 y x) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

simplify92.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

301×	`times-frac_binary64`
256×	`associate-/l*_binary64`
215×	`sub-neg_binary64`
214×	`associate-+r+_binary64`
204×	`cancel-sign-sub-inv_binary64`

Counts

47 → 72

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	275	3123
1	832	2816
2	3905	2801
3	4960	2801
4	4978	2801

prune157.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	162	6	168

Error

4.2b

Counts

168 → 6

Alt Table

Status	Error	Program
✓	20.0b	(/.f64 (*.f64 y x) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
	41.2b	(/.f64 x (pow.f64 y 2))
	40.2b	(/.f64 y (pow.f64 x 2))
	32.8b	(*.f64 (/.f64 x (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))))
	31.2b	(*.f64 (/.f64 x (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (/.f64 y (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
▶	22.2b	(/.f64 (.f64 (/.f64 x (.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2))) (cbrt.f64 (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2))))) y) (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))

Compiler

Compiled 5915 to 3069 computations (48.1% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	13.5b	(+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2))
✓	13.7b	(/.f64 x (*.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2))) (cbrt.f64 (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2)))))
✓	33.4b	(cbrt.f64 (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2)))
✓	33.4b	(cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

series3.1s (22.8%)

Counts

4 → 96

Calls

4 calls:

2.9s	(/.f64 x (*.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2))) (cbrt.f64 (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2)))))
87.0ms	(cbrt.f64 (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2)))
83.0ms	(cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
15.0ms	(+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2))

rewrite58.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
14×	`fma-def_binary64`
14×	`cbrt-div_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`

Counts

4 → 92

Calls

4 calls:

27.0ms	(/.f64 x (*.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2))) (cbrt.f64 (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2)))))
12.0ms	(+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2))
11.0ms	(cbrt.f64 (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2)))
1.0ms	(cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

simplify234.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

503×	`*-commutative_binary64`
308×	`+-commutative_binary64`
286×	`unswap-sqr_binary64`
278×	`fma-def_binary64`
268×	`associate-+r+_binary64`

Counts

188 → 198

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1202	15867
1	3919	15519
2	4929	15519

prune547.0ms (4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	260	1	261
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	261	6	267

Error

4.2b

Counts

267 → 6

Alt Table

Status	Error	Program
▶	22.2b	(/.f64 (.f64 (/.f64 x (.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2))) (*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 2)))))) y) (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
	31.2b	(*.f64 (/.f64 x (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (/.f64 y (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
✓	20.0b	(/.f64 (*.f64 y x) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
	41.2b	(/.f64 x (pow.f64 y 2))
	40.2b	(/.f64 y (pow.f64 x 2))
	32.8b	(*.f64 (/.f64 x (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))))

Compiler

Compiled 25839 to 16224 computations (37.2% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	13.7b	(/.f64 x (.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2))) (.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 2))))))
✓	23.2b	(cbrt.f64 (+.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 2)))
	33.4b	(cbrt.f64 (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2)))
	33.4b	(cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

series5.5s (40.5%)

Counts

2 → 48

Calls

2 calls:

5.4s

(/.f64 x (*.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2))) (*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 2))))))

70.0ms

(cbrt.f64 (+.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 2)))

rewrite52.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`cbrt-div_binary64`
28×	`frac-times_binary64`
28×	`flip-+_binary64`
28×	`flip3-+_binary64`
26×	`associate-/r/_binary64`

Counts

2 → 71

Calls

2 calls:

28.0ms

(/.f64 x (*.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2))) (*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 2))))))

7.0ms

(cbrt.f64 (+.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 2)))

simplify227.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

445×	`*-commutative_binary64`
405×	`times-frac_binary64`
296×	`+-commutative_binary64`
274×	`fma-def_binary64`
248×	`associate-+r+_binary64`

Counts

119 → 188

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1343	15061
1	4317	14771
2	5080	14771

prune683.0ms (5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	260	2	262
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	261	7	268

Error

4.2b

Counts

268 → 7

Alt Table

Status	Error	Program
✓	20.0b	(/.f64 (*.f64 y x) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
	41.2b	(/.f64 x (pow.f64 y 2))
	40.2b	(/.f64 y (pow.f64 x 2))
	10.8b	(/.f64 (.f64 (/.f64 x (.f64 (.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 2)))) (.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 2)))))) y) (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
	32.8b	(*.f64 (/.f64 x (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))))
	31.2b	(*.f64 (/.f64 x (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (/.f64 y (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
	22.2b	(/.f64 (.f64 (/.f64 x (.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2))) (*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 2)))))) y) (pow.f64 (cbrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) 1))

Compiler

Compiled 32249 to 18943 computations (41.3% saved)

regimes815.0ms (6%)

Accuracy

Total 2.0b remaining (29.1%)

Threshold costs 0b (0%)

Counts

135 → 3

Compiler

Compiled 13946 to 7448 computations (46.6% saved)

bsearch85.0ms (0.6%)

Steps

Iters	Range		Point
8	-8.921777513528145e-161	-9.757783414731248e-164	-9.891408611722913e-164
7	-1.438875869995299e+100	-6.017776958423828e+97	-2.9269061851776803e+98

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	126
1	46	126
2	45	126

end309.0ms (2.3%)

Compiler: Compiled 535 to 265 computations (50.5% saved)

Details

analyze101.0ms (0.7%)

sample928.0ms (6.8%)

simplify137.0ms (1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series94.0ms (0.7%)

rewrite10.0ms (0.1%)

simplify155.0ms (1.1%)

prune167.0ms (1.2%)

localize7.0ms (0.1%)

series71.0ms (0.5%)

rewrite4.0ms (0%)

simplify92.0ms (0.7%)

prune157.0ms (1.2%)

localize16.0ms (0.1%)

series3.1s (22.8%)

rewrite58.0ms (0.4%)

simplify234.0ms (1.7%)

prune547.0ms (4%)

localize24.0ms (0.2%)

series5.5s (40.5%)

rewrite52.0ms (0.4%)

simplify227.0ms (1.7%)

prune683.0ms (5%)

regimes815.0ms (6%)

bsearch85.0ms (0.6%)

simplify3.0ms (0%)

end309.0ms (2.3%)

Profiling