Details

analyze3.3s (23.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
5.8%	93.9%	0.3%	11
8.4%	91.3%	0.3%	12
9.7%	90%	0.3%	13
10.7%	89%	0.3%	14

Compiler

Compiled 24 to 16 computations (33.3% saved)

sample121.0ms (0.9%)

Algorithm

1×

intervals

Results

40.0ms	256×	body	128	valid
1.0ms	10×	body	128	invalid

Compiler

Compiled 53 to 37 computations (30.2% saved)

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`fma-def_binary64`
6×	`+-commutative_binary64`
6×	`*-commutative_binary64`
4×	`associate-/l*_binary64`
4×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	29	25
2	41	21
3	51	21
4	61	21
5	65	21
6	64	21

prune8.0ms (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

11.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	15.2b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
	16.4b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))

Compiler

Compiled 126 to 78 computations (38.1% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 y z) t))
✓	4.2b	(/.f64 (*.f64 y z) t)
✓	4.9b	(/.f64 (*.f64 y b) t)
✓	10.7b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))

series560.0ms (4.1%)

Counts

4 → 120

Calls

4 calls:

471.0ms	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
30.0ms	(+.f64 x (/.f64 (*.f64 y z) t))
30.0ms	(/.f64 (*.f64 y b) t)
27.0ms	(/.f64 (*.f64 y z) t)

rewrite75.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`*-un-lft-identity_binary64`
26×	`times-frac_binary64`
22×	`distribute-lft-out_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`

Counts

4 → 112

Calls

4 calls:

29.0ms	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
18.0ms	(+.f64 x (/.f64 (*.f64 y z) t))
7.0ms	(/.f64 (*.f64 y b) t)
7.0ms	(/.f64 (*.f64 y z) t)

simplify278.0ms (2%)

Algorithm

1×	egg-herbie

Rules

897×	`times-frac_binary64`
656×	`associate-/l*_binary64`
274×	`fma-def_binary64`
148×	`+-commutative_binary64`
118×	`distribute-rgt-in_binary64`

Counts

232 → 201

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	521	10152
1	1626	9540
2	5047	9540

prune609.0ms (4.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	190	11	201
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	191	12	203

Error

0.3b

Counts

203 → 12

Alt Table

Status	Error	Program
	29.2b	(.f64 (/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (-.f64 (pow.f64 (+.f64 1 a) 2) (.f64 (/.f64 (.f64 y b) t) (/.f64 (.f64 y b) t)))) (-.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
	28.0b	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
	41.4b	(.f64 (sqrt.f64 (+.f64 x (/.f64 (.f64 y z) t))) (/.f64 (sqrt.f64 (+.f64 x (/.f64 (.f64 y z) t))) (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	35.1b	(-.f64 (fma.f64 (/.f64 y t) (/.f64 z (+.f64 1 (/.f64 (.f64 y b) t))) (/.f64 x (+.f64 1 (/.f64 (.f64 y b) t)))) (fma.f64 (/.f64 a t) (/.f64 (.f64 y z) (pow.f64 (+.f64 1 (/.f64 (.f64 y b) t)) 2)) (/.f64 (.f64 a x) (pow.f64 (+.f64 1 (/.f64 (.f64 y b) t)) 2))))
	16.0b	(fma.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) (/.f64 z t) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
▶	13.8b	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	15.2b	(.f64 (+.f64 x (/.f64 (.f64 y z) t)) (/.f64 1 (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))))
	17.0b	(/.f64 (+.f64 x (/.f64 y (/.f64 t z))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
	16.4b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	42.4b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (/.f64 (.f64 a (.f64 z t)) (.f64 y (*.f64 b b)))))
	42.6b	(-.f64 (+.f64 (/.f64 z b) (/.f64 (.f64 t x) (.f64 y b))) (+.f64 (/.f64 (.f64 t z) (.f64 y (pow.f64 b 2))) (/.f64 (.f64 a (.f64 t z)) (*.f64 y (pow.f64 b 2)))))
	43.6b	(/.f64 z b)

Compiler

Compiled 10393 to 4485 computations (56.8% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.6b	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
✓	4.6b	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
	4.9b	(/.f64 (*.f64 y b) t)
✓	10.4b	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))

series566.0ms (4.1%)

Counts

3 → 152

Calls

3 calls:

267.0ms	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))
257.0ms	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
41.0ms	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)

rewrite72.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64`
19×	`add-cbrt-cube_binary64`
19×	`add-exp-log_binary64`
17×	`add-sqr-sqrt_binary64`
16×	`times-frac_binary64`

Counts

3 → 88

Calls

3 calls:

27.0ms	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))
16.0ms	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
16.0ms	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)

simplify294.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

938×	`times-frac_binary64`
627×	`associate-/l*_binary64`
490×	`associate-/r*_binary64`
153×	`fma-def_binary64`
91×	`*-commutative_binary64`

Counts

240 → 187

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	395	10369
1	1285	9529
2	5042	9529

prune907.0ms (6.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	238	5	243
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	245	10	255

Error

0.0b

Counts

255 → 10

Alt Table

Status	Error	Program
▶	10.4b	(+.f64 (/.f64 (.f64 y z) (fma.f64 y b (fma.f64 a t t))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	17.0b	(/.f64 (+.f64 x (/.f64 y (/.f64 t z))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
	27.9b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	16.4b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	13.9b	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (/.f64 (.f64 y b) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))))))
	42.4b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (/.f64 (.f64 a (.f64 z t)) (.f64 y (*.f64 b b)))))
	16.5b	(+.f64 (/.f64 y (/.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) (/.f64 z t))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	13.0b	(+.f64 (/.f64 y (/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	15.2b	(.f64 (+.f64 x (/.f64 (.f64 y z) t)) (/.f64 1 (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))))
	42.6b	(-.f64 (+.f64 (/.f64 z b) (/.f64 (.f64 t x) (.f64 y b))) (+.f64 (/.f64 (.f64 t z) (.f64 y (pow.f64 b 2))) (/.f64 (.f64 a (.f64 t z)) (*.f64 y (pow.f64 b 2)))))

Compiler

Compiled 11154 to 4425 computations (60.3% saved)

localize96.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(fma.f64 y b (fma.f64 a t t))
	2.6b	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
	4.9b	(/.f64 (*.f64 y b) t)
✓	10.4b	(/.f64 (*.f64 y z) (fma.f64 y b (fma.f64 a t t)))

series282.0ms (2%)

Counts

2 → 108

Calls

2 calls:

258.0ms	(/.f64 (*.f64 y z) (fma.f64 y b (fma.f64 a t t)))
24.0ms	(fma.f64 y b (fma.f64 a t t))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 33

Calls

2 calls:

7.0ms	(/.f64 (*.f64 y z) (fma.f64 y b (fma.f64 a t t)))
1.0ms	(fma.f64 y b (fma.f64 a t t))

simplify192.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

484×	`times-frac_binary64`
480×	`cancel-sign-sub-inv_binary64`
335×	`associate-/l*_binary64`
238×	`associate-/r*_binary64`
211×	`fma-neg_binary64`

Counts

141 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	232	4826
1	717	4480
2	3716	4438
3	5080	4438

prune636.0ms (4.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	201	2	203
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	204	9	213

Error

0.0b

Counts

213 → 9

Alt Table

Status	Error	Program
	10.5b	(+.f64 (/.f64 (.f64 y z) (fma.f64 y b (fma.f64 a t t))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (/.f64 (.f64 y b) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))))))
▶	10.5b	(+.f64 (.f64 y (/.f64 z (fma.f64 y b (fma.f64 t a t)))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	17.0b	(/.f64 (+.f64 x (/.f64 y (/.f64 t z))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
	27.9b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	16.4b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	16.5b	(+.f64 (/.f64 y (/.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) (/.f64 z t))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	15.2b	(.f64 (+.f64 x (/.f64 (.f64 y z) t)) (/.f64 1 (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))))
	42.4b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (/.f64 (.f64 a (.f64 z t)) (.f64 y (*.f64 b b)))))
	42.6b	(-.f64 (+.f64 (/.f64 z b) (/.f64 (.f64 t x) (.f64 y b))) (+.f64 (/.f64 (.f64 t z) (.f64 y (pow.f64 b 2))) (/.f64 (.f64 a (.f64 t z)) (*.f64 y (pow.f64 b 2)))))

Compiler

Compiled 8761 to 3125 computations (64.3% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	2.6b	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
	4.9b	(/.f64 (*.f64 y b) t)
✓	5.3b	(/.f64 z (fma.f64 y b (fma.f64 t a t)))
✓	7.6b	(*.f64 y (/.f64 z (fma.f64 y b (fma.f64 t a t))))

series490.0ms (3.5%)

Counts

2 → 120

Calls

2 calls:

249.0ms	(/.f64 z (fma.f64 y b (fma.f64 t a t)))
239.0ms	(*.f64 y (/.f64 z (fma.f64 y b (fma.f64 t a t))))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
19×	`times-frac_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`

Counts

2 → 63

Calls

2 calls:

11.0ms	(*.f64 y (/.f64 z (fma.f64 y b (fma.f64 t a t))))
6.0ms	(/.f64 z (fma.f64 y b (fma.f64 t a t)))

simplify254.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

793×	`times-frac_binary64`
559×	`associate-/l*_binary64`
408×	`associate-/r*_binary64`
265×	`associate-r_binary64`
247×	`associate-l_binary64`

Counts

183 → 165

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	378	8731
1	1134	8284
2	5096	8284

prune486.0ms (3.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	257	2	259
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	258	10	268

Error

0.0b

Counts

268 → 10

Alt Table

Status	Error	Program
	10.5b	(+.f64 (/.f64 (.f64 y z) (fma.f64 y b (fma.f64 a t t))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (/.f64 (.f64 y b) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))))))
	17.0b	(/.f64 (+.f64 x (/.f64 y (/.f64 t z))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
	27.9b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	16.4b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	16.5b	(+.f64 (/.f64 y (/.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) (/.f64 z t))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	29.0b	(+.f64 (.f64 (sqrt.f64 (.f64 y (/.f64 z (fma.f64 y b (fma.f64 t a t))))) (sqrt.f64 (.f64 y (/.f64 z (fma.f64 y b (fma.f64 t a t)))))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	15.2b	(.f64 (+.f64 x (/.f64 (.f64 y z) t)) (/.f64 1 (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))))
	10.0b	(+.f64 (*.f64 y (/.f64 z (fma.f64 y b (fma.f64 t a t)))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 y (/.f64 t b))))))
	42.4b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (/.f64 (.f64 a (.f64 z t)) (.f64 y (*.f64 b b)))))
	42.6b	(-.f64 (+.f64 (/.f64 z b) (/.f64 (.f64 t x) (.f64 y b))) (+.f64 (/.f64 (.f64 t z) (.f64 y (pow.f64 b 2))) (/.f64 (.f64 a (.f64 t z)) (*.f64 y (pow.f64 b 2)))))

Compiler

Compiled 11887 to 4303 computations (63.8% saved)

regimes3.1s (22.7%)

Accuracy

Total 9.5b remaining (98.4%)

Threshold costs 0b (0%)

Counts

164 → 5

Compiler

Compiled 41031 to 24705 computations (39.8% saved)

bsearch101.0ms (0.7%)

Steps

Iters	Range		Point
10	2.7013164951911482e+237	1.386190197754719e+248	5.1233805809014946e+247
7	2.1706782644461752e+145	4.901944012673168e+146	1.244253742756409e+146
5	2.085482258698379e+46	5.757579194769674e+52	3.67379042608604e+52
9	-7.066530951075008e+172	-4.027980695190975e+166	-6.04812534866938e+167

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
4×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	159
1	66	159
2	65	159

end1.0ms (0%)

Compiler: Compiled 115 to 56 computations (51.3% saved)

sample1.2s (8.6%)

Algorithm

1×

intervals

Results

579.0ms	8000×	body	128	valid
18.0ms	274×	body	128	invalid

Compiler

Compiled 452 to 252 computations (44.2% saved)

Details

analyze3.3s (23.9%)

sample121.0ms (0.9%)

simplify15.0ms (0.1%)

prune8.0ms (0.1%)

localize25.0ms (0.2%)

series560.0ms (4.1%)

rewrite75.0ms (0.5%)

simplify278.0ms (2%)

prune609.0ms (4.4%)

localize27.0ms (0.2%)

series566.0ms (4.1%)

rewrite72.0ms (0.5%)

simplify294.0ms (2.1%)

prune907.0ms (6.6%)

localize96.0ms (0.7%)

series282.0ms (2%)

rewrite11.0ms (0.1%)

simplify192.0ms (1.4%)

prune636.0ms (4.6%)

localize33.0ms (0.2%)

series490.0ms (3.5%)

rewrite26.0ms (0.2%)

simplify254.0ms (1.8%)

prune486.0ms (3.5%)

regimes3.1s (22.7%)

bsearch101.0ms (0.7%)

simplify5.0ms (0%)

end1.0ms (0%)

sample1.2s (8.6%)

Profiling