Details

analyze304.0ms (4.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
49.9%	49.9%	0.2%	5
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
49.9%	49.9%	0.2%	8
74.9%	25%	0.2%	9
74.9%	25%	0.2%	10
74.9%	25%	0.2%	11
74.9%	25%	0.2%	12
87.3%	12.5%	0.2%	13
87.3%	12.5%	0.2%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.4s (19.4%)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify149.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

973×	`fma-def_binary64`
752×	`fma-neg_binary64`
239×	`cancel-sign-sub-inv_binary64`
193×	`distribute-rgt-in_binary64`
133×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	33	11
3	64	11
4	125	11
5	238	11
6	414	11
7	791	11
8	1182	11
9	1373	11
10	1483	11
11	1532	11
12	1538	11
13	1543	11
14	1543	11
15	1458	11

prune6.0ms (0.1%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.3b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	3.4b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize12.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.3b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series35.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

35.0ms

(fma.f64 (-.f64 y x) (/.f64 z t) x)

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma.f64 (-.f64 y x) (/.f64 z t) x)

simplify148.0ms (2%)

Algorithm

1×	egg-herbie

Rules

539×	`distribute-rgt-neg-out_binary64`
515×	`distribute-lft-neg-out_binary64`
375×	`distribute-rgt-in_binary64`
373×	`distribute-lft-in_binary64`
270×	`times-frac_binary64`

Counts

58 → 31

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	946
1	88	635
2	194	623
3	469	623
4	2305	623
5	4632	623
6	5238	623

prune45.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	29	2	31
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	29	4	33

Error

0.0b

Counts

33 → 4

Alt Table

Status	Error	Program
✓	2.3b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	3.4b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))
▶	3.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	28.2b	(*.f64 z (/.f64 (-.f64 y x) t))

Compiler

Compiled 480 to 136 computations (71.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	2.3b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	14.9b	(cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))

series1.0s (13.9%)

Counts

3 → 144

Calls

3 calls:

720.0ms

(*.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))

236.0ms

(cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))

42.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))

rewrite42.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

14.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))

9.0ms

(*.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))

1.0ms

(cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))

simplify521.0ms (7.2%)

Algorithm

1×	egg-herbie

Rules

938×	`fma-def_binary64`
540×	`*-commutative_binary64`
218×	`+-commutative_binary64`
210×	`associate-r_binary64`
141×	`associate-+r+_binary64`

Counts

237 → 277

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1216	19471
1	4389	19186
2	5141	19186

prune1.5s (21.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	552	2	554
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	552	6	558

Error

0.0b

Counts

558 → 6

Alt Table

Status	Error	Program
	24.7b	(.f64 (cbrt.f64 (.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x) (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	3.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))))
✓	2.3b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
▶	3.4b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))
✓	3.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	28.2b	(*.f64 z (/.f64 (-.f64 y x) t))

Compiler

Compiled 45010 to 18393 computations (59.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))
✓	0.0b	(*.f64 (-.f64 y x) z)
✓	4.1b	(/.f64 (*.f64 (-.f64 y x) z) t)

series170.0ms (2.4%)

Counts

3 → 132

Calls

3 calls:

99.0ms	(/.f64 (*.f64 (-.f64 y x) z) t)
56.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))
14.0ms	(*.f64 (-.f64 y x) z)

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 66

Calls

3 calls:

11.0ms	(/.f64 (*.f64 (-.f64 y x) z) t)
8.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))
8.0ms	(*.f64 (-.f64 y x) z)

simplify142.0ms (2%)

Algorithm

1×	egg-herbie

Rules

546×	`times-frac_binary64`
512×	`associate-/l*_binary64`
379×	`div-sub_binary64`
319×	`distribute-rgt-in_binary64`
318×	`associate-*l/_binary64`

Counts

198 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	138	2596
1	365	2080
2	1123	1980
3	4594	1980
4	5596	1980

prune177.0ms (2.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	2	1	3
Picked	1	0	1
Done	1	1	2
Total	127	5	132

Error

Counts

132 → 5

Alt Table

Status	Error	Program
✓	2.3b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	2.5b	(+.f64 x (/.f64 (.f64 (/.f64 (-.f64 y x) (.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t)))
▶	2.3b	(+.f64 x (/.f64 (-.f64 y x) (/.f64 t z)))
	3.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) z) (/.f64 1 t)))
	28.2b	(*.f64 z (/.f64 (-.f64 y x) t))

Compiler

Compiled 1933 to 553 computations (71.4% saved)

localize13.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (-.f64 y x) (/.f64 t z)))
✓	6.3b	(/.f64 (-.f64 y x) (/.f64 t z))

series85.0ms (1.2%)

Counts

2 → 96

Calls

2 calls:

45.0ms	(+.f64 x (/.f64 (-.f64 y x) (/.f64 t z)))
40.0ms	(/.f64 (-.f64 y x) (/.f64 t z))

rewrite74.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

119×	`times-frac_binary64`
89×	`*-un-lft-identity_binary64`
87×	`add-sqr-sqrt_binary64`
59×	`add-cube-cbrt_binary64`
14×	`distribute-lft-out--_binary64`

Counts

2 → 121

Calls

2 calls:

35.0ms	(+.f64 x (/.f64 (-.f64 y x) (/.f64 t z)))
15.0ms	(/.f64 (-.f64 y x) (/.f64 t z))

simplify216.0ms (3%)

Algorithm

1×	egg-herbie

Rules

507×	`associate-/r/_binary64`
407×	`div-sub_binary64`
361×	`associate-/l*_binary64`
352×	`associate-/l/_binary64`
304×	`times-frac_binary64`

Counts

217 → 185

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	4031
1	657	3505
2	1847	3496
3	4543	3496
4	5374	3496

prune184.0ms (2.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	183	2	185
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	185	5	190

Error

Counts

190 → 5

Alt Table

Status	Error	Program
✓	2.3b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	2.3b	(+.f64 x (/.f64 (-.f64 y x) (/.f64 t z)))
	3.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) z) (/.f64 1 t)))
	3.5b	(+.f64 x (*.f64 (/.f64 1 t) (/.f64 (-.f64 y x) (/.f64 1 z))))
	4.4b	(fma.f64 z (/.f64 (-.f64 y x) t) x)

Compiler

Compiled 3376 to 792 computations (76.5% saved)

regimes715.0ms (9.9%)

Accuracy

Total 0.8b remaining (98.8%)

Threshold costs 0.8b (98.8%)

Counts

56 → 3

Compiler

Compiled 5846 to 2918 computations (50.1% saved)

bsearch16.0ms (0.2%)

Steps

Iters	Range		Point
2	4939916.485193775	7718897202.572241	1226576968.5346966
1	-1.421952898420934e-34	-1.3277355352381629e-34	-1.3748442168295486e-34

Compiler

Compiled 5 to 4 computations (20% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	56
1	29	56
2	34	56
3	36	56
4	37	56
5	37	56

end147.0ms (2%)

Compiler: Compiled 153 to 86 computations (43.8% saved)

Details

analyze304.0ms (4.2%)

sample1.4s (19.4%)

simplify149.0ms (2.1%)

prune6.0ms (0.1%)

localize12.0ms (0.2%)

series35.0ms (0.5%)

rewrite2.0ms (0%)

simplify148.0ms (2%)

prune45.0ms (0.6%)

localize12.0ms (0.2%)

series1.0s (13.9%)

rewrite42.0ms (0.6%)

simplify521.0ms (7.2%)

prune1.5s (21.4%)

localize8.0ms (0.1%)

series170.0ms (2.4%)

rewrite33.0ms (0.5%)

simplify142.0ms (2%)

prune177.0ms (2.5%)

localize13.0ms (0.2%)

series85.0ms (1.2%)

rewrite74.0ms (1%)

simplify216.0ms (3%)

prune184.0ms (2.6%)

regimes715.0ms (9.9%)

bsearch16.0ms (0.2%)

simplify7.0ms (0.1%)

end147.0ms (2%)

Profiling