Details

analyze1.4s (20%)

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
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.3%	0.2%	12
12.2%	87.5%	0.2%	13
21.9%	77.7%	0.4%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample31.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	216×	body	128	valid
2.0ms	16×	body	512	valid
2.0ms	11×	body	1024	valid
2.0ms	39×	body	128	invalid
1.0ms	10×	body	256	valid
1.0ms	3×	body	2048	valid

Compiler

Compiled 42 to 28 computations (33.3% saved)

simplify89.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

930×	`fma-def_binary64`
859×	`div-sub_binary64`
817×	`unsub-neg_binary64`
555×	`neg-mul-1_binary64`
380×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	24	17
2	52	17
3	155	17
4	477	17
5	1268	17
6	3213	17
7	4154	17
8	4434	17
9	4965	17
10	4951	17

prune4.0ms (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

14.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	14.4b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
▶	14.4b	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

Compiler

Compiled 100 to 54 computations (46% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t x) (-.f64 a z))
✓	2.6b	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
✓	5.1b	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))

series211.0ms (3.1%)

Counts

3 → 168

Calls

3 calls:

95.0ms	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
66.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))
49.0ms	(/.f64 (-.f64 t x) (-.f64 a z))

rewrite56.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`add-sqr-sqrt_binary64`
74×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-r_binary64`
28×	`add-cube-cbrt_binary64`

Counts

3 → 128

Calls

3 calls:

18.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))
13.0ms	(/.f64 (-.f64 t x) (-.f64 a z))
3.0ms	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

simplify375.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

382×	`fma-neg_binary64`
293×	`associate--l+_binary64`
285×	`associate-/l*_binary64`
274×	`associate--r+_binary64`
253×	`times-frac_binary64`

Counts

296 → 252

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	529	11325
1	1595	11220
2	4875	11220
3	5221	11220

prune396.0ms (5.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	242	10	252
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	243	11	254

Error

0.7b

Counts

254 → 11

Alt Table

Status	Error	Program
	24.3b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
	14.4b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
	38.2b	(+.f64 x (.f64 (.f64 (-.f64 y z) (sqrt.f64 (-.f64 t x))) (/.f64 (sqrt.f64 (-.f64 t x)) (-.f64 a z))))
	37.2b	(+.f64 x (.f64 (sqrt.f64 (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) (sqrt.f64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))))
	15.0b	(+.f64 x (.f64 (-.f64 y z) (.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))))
	29.5b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	35.1b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
	35.9b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	37.4b	(+.f64 x (*.f64 (/.f64 (-.f64 y z) (sqrt.f64 (-.f64 a z))) (/.f64 (-.f64 t x) (sqrt.f64 (-.f64 a z)))))
▶	14.4b	(+.f64 x (.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))))
	14.7b	(+.f64 x (*.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x)))))

Compiler

Compiled 9341 to 2813 computations (69.9% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 a z))
✓	0.3b	(*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))
✓	4.3b	(+.f64 x (.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))))
✓	5.1b	(.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))))

series396.0ms (5.8%)

Counts

4 → 192

Calls

4 calls:

188.0ms	(+.f64 x (.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))))
129.0ms	(.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))))
61.0ms	(*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))
17.0ms	(/.f64 1 (-.f64 a z))

rewrite88.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
45×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
32×	`add-exp-log_binary64`
26×	`add-cube-cbrt_binary64`

Counts

4 → 157

Calls

4 calls:

26.0ms	(.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))))
24.0ms	(*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))
8.0ms	(/.f64 1 (-.f64 a z))
7.0ms	(+.f64 x (.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))))

simplify365.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

405×	`fma-neg_binary64`
293×	`associate--l+_binary64`
274×	`associate-l_binary64`
264×	`associate-r_binary64`
259×	`associate-/l*_binary64`

Counts

349 → 341

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	561	12130
1	1667	11821
2	4831	11818
3	5194	11818

prune267.0ms (3.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	340	1	341
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	341	11	352

Error

0.7b

Counts

352 → 11

Alt Table

Status	Error	Program
	24.3b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
▶	14.4b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
	34.8b	(expm1.f64 (log1p.f64 (+.f64 x (.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))))))
	35.9b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	38.2b	(+.f64 x (.f64 (.f64 (-.f64 y z) (sqrt.f64 (-.f64 t x))) (/.f64 (sqrt.f64 (-.f64 t x)) (-.f64 a z))))
	37.2b	(+.f64 x (.f64 (sqrt.f64 (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) (sqrt.f64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))))
	15.0b	(+.f64 x (.f64 (-.f64 y z) (.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))))
	29.5b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	35.1b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
	37.4b	(+.f64 x (*.f64 (/.f64 (-.f64 y z) (sqrt.f64 (-.f64 a z))) (/.f64 (-.f64 t x) (sqrt.f64 (-.f64 a z)))))
	14.7b	(+.f64 x (*.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x)))))

Compiler

Compiled 11628 to 4078 computations (64.9% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 t x) (-.f64 a z))
✓	14.4b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

series85.0ms (1.3%)

Counts

1 → 60

Calls

1 calls:

85.0ms

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

rewrite1.0ms (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:

0.0ms

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

simplify83.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

987×	`times-frac_binary64`
354×	`cancel-sign-sub-inv_binary64`
331×	`sub-neg_binary64`
320×	`associate-+r+_binary64`
233×	`distribute-neg-in_binary64`

Counts

70 → 69

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	226	3787
1	697	3752
2	2756	3716
3	5100	3716

prune111.0ms (1.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	137	3	140
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	141	10	151

Error

0.7b

Counts

151 → 10

Alt Table

Status	Error	Program
▶	14.4b	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)
	38.2b	(+.f64 x (.f64 (.f64 (-.f64 y z) (sqrt.f64 (-.f64 t x))) (/.f64 (sqrt.f64 (-.f64 t x)) (-.f64 a z))))
	15.0b	(fma.f64 (-.f64 y z) (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))) x)
	35.9b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	14.6b	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x))) x)
	37.2b	(+.f64 x (.f64 (sqrt.f64 (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) (sqrt.f64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))))
	29.5b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	35.1b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
	24.3b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
	37.4b	(+.f64 x (*.f64 (/.f64 (-.f64 y z) (sqrt.f64 (-.f64 a z))) (/.f64 (-.f64 t x) (sqrt.f64 (-.f64 a z)))))

Compiler

Compiled 4983 to 1559 computations (68.7% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (-.f64 a z))
	0.3b	(*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))
✓	14.3b	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)

series63.0ms (0.9%)

Counts

1 → 60

Calls

1 calls:

63.0ms

(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)

rewrite1.0ms (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:

0.0ms

(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)

simplify79.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

987×	`times-frac_binary64`
354×	`cancel-sign-sub-inv_binary64`
331×	`sub-neg_binary64`
320×	`associate-+r+_binary64`
233×	`distribute-neg-in_binary64`

Counts

70 → 69

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	227	3832
1	701	3758
2	2768	3716
3	5107	3716

prune170.0ms (2.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	221	1	222
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	221	11	232

Error

0.7b

Counts

232 → 11

Alt Table

Status	Error	Program
	34.8b	(expm1.f64 (log1p.f64 (fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)))
	38.2b	(+.f64 x (.f64 (.f64 (-.f64 y z) (sqrt.f64 (-.f64 t x))) (/.f64 (sqrt.f64 (-.f64 t x)) (-.f64 a z))))
✓	14.4b	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)
	15.0b	(fma.f64 (-.f64 y z) (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))) x)
	35.9b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	14.6b	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x))) x)
	37.2b	(+.f64 x (.f64 (sqrt.f64 (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) (sqrt.f64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))))
	29.5b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	35.1b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
	24.3b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
	37.4b	(+.f64 x (*.f64 (/.f64 (-.f64 y z) (sqrt.f64 (-.f64 a z))) (/.f64 (-.f64 t x) (sqrt.f64 (-.f64 a z)))))

Compiler

Compiled 6598 to 2281 computations (65.4% saved)

regimes1.3s (19.3%)

Accuracy

Total 5.0b remaining (85.5%)

Threshold costs 0b (0%)

Counts

129 → 3

Compiler

Compiled 18066 to 10368 computations (42.6% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 18 to 11 computations (38.9% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

20×	`+-commutative_binary64`
18×	`*-commutative_binary64`
14×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	177
1	65	177
2	80	177
3	96	177
4	118	177
5	130	177
6	138	177
7	141	177
8	141	177

end1.0ms (0%)

Compiler: Compiled 121 to 42 computations (65.3% saved)

sample1.2s (17.5%)

Algorithm

1×

intervals

Results

361.0ms	6742×	body	128	valid
78.0ms	370×	body	1024	valid
66.0ms	472×	body	512	valid
62.0ms	1239×	body	128	invalid
35.0ms	360×	body	256	valid
19.0ms	56×	body	2048	valid

Compiler

Compiled 400 to 201 computations (49.8% saved)

Details

analyze1.4s (20%)

sample31.0ms (0.5%)

simplify89.0ms (1.3%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

series211.0ms (3.1%)

rewrite56.0ms (0.8%)

simplify375.0ms (5.5%)

prune396.0ms (5.8%)

localize25.0ms (0.4%)

series396.0ms (5.8%)

rewrite88.0ms (1.3%)

simplify365.0ms (5.4%)

prune267.0ms (3.9%)

localize9.0ms (0.1%)

series85.0ms (1.3%)

rewrite1.0ms (0%)

simplify83.0ms (1.2%)

prune111.0ms (1.6%)

localize9.0ms (0.1%)

series63.0ms (0.9%)

rewrite1.0ms (0%)

simplify79.0ms (1.2%)

prune170.0ms (2.5%)

regimes1.3s (19.3%)

bsearch5.0ms (0.1%)

simplify11.0ms (0.2%)

end1.0ms (0%)

sample1.2s (17.5%)

Profiling