Details

analyze1.3s (21.9%)

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
3.5%	96.2%	0.2%	10
9.2%	90.6%	0.2%	11
13.7%	86%	0.2%	12
22.1%	77.7%	0.2%	13
23%	76.7%	0.2%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.5s (24%)

Results

898.0ms	6948×	body	128	valid
150.0ms	503×	body	512	valid
139.0ms	374×	body	1024	valid
97.0ms	757×	body	128	invalid
78.0ms	360×	body	256	valid
35.0ms	71×	body	2048	valid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify127.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1303×	`div-sub_binary64`
658×	`fma-def_binary64`
640×	`sub-neg_binary64`
569×	`unsub-neg_binary64`
393×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	23	19
2	58	19
3	143	17
4	344	17
5	967	17
6	2282	17
7	3646	17
8	3700	17
9	4097	17
10	4253	17
11	4543	17
12	4719	17
13	5478	17

prune3.0ms (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

10.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	11.6b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
	16.3b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 100 to 56 computations (44% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) (-.f64 a t))
✓	3.1b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

series52.0ms (0.8%)

Counts

2 → 96

Calls

2 calls:

35.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
17.0ms	(/.f64 (-.f64 t z) (-.f64 a t))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

2 → 64

Calls

2 calls:

6.0ms	(/.f64 (-.f64 t z) (-.f64 a t))
0.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

simplify126.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

671×	`times-frac_binary64`
644×	`fma-neg_binary64`
523×	`cancel-sign-sub-inv_binary64`
397×	`sub-neg_binary64`
195×	`div-sub_binary64`

Counts

160 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	273	4255
1	740	4157
2	2480	3550
3	4430	3531
4	5167	3531

prune115.0ms (1.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	129	8	137
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	131	8	139

Error

0.0b

Counts

139 → 8

Alt Table

Status	Error	Program
	11.6b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z))) (+.f64 x y))
	38.8b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
	20.8b	(fma.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 t z) (-.f64 a t)) 3)) (+.f64 x y))
	33.0b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	22.5b	(-.f64 (+.f64 y x) (/.f64 (*.f64 y z) a))
▶	11.6b	(+.f64 y (+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))))
	11.8b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (cbrt.f64 (-.f64 t z)) (-.f64 a t))) (+.f64 x y))
	25.0b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))

Compiler

Compiled 3668 to 1250 computations (65.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 t z) (-.f64 a t))
✓	0.0b	(+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t))))
✓	2.1b	(+.f64 y (+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))))
✓	2.3b	(*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))

series108.0ms (1.8%)

Counts

3 → 168

Calls

3 calls:

41.0ms	(+.f64 y (+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))))
39.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t))))
27.0ms	(*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
31×	`associate-r_binary64`
26×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`

Counts

3 → 87

Calls

3 calls:

13.0ms	(*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))
4.0ms	(+.f64 y (+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))))
2.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t))))

simplify197.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

617×	`sub-neg_binary64`
455×	`fma-neg_binary64`
281×	`associate--r+_binary64`
235×	`associate--l+_binary64`
214×	`+-commutative_binary64`

Counts

255 → 225

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	343	6826
1	972	6577
2	3775	5912
3	4796	5912
4	4993	5912
5	4969	5912

prune241.0ms (4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	303	3	306
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	305	9	314

Error

0.0b

Counts

314 → 9

Alt Table

Status	Error	Program
▶	11.6b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z))) (+.f64 x y))
	38.8b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
	15.5b	(+.f64 y (+.f64 x (neg.f64 (/.f64 (*.f64 y z) (-.f64 a t)))))
	47.3b	(cbrt.f64 (pow.f64 (+.f64 y (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x)) 3))
	20.8b	(fma.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 t z) (-.f64 a t)) 3)) (+.f64 x y))
	33.0b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	16.3b	(+.f64 y (+.f64 x (.f64 (.f64 y (-.f64 t z)) (/.f64 1 (-.f64 a t)))))
✓	11.6b	(+.f64 y (+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))))
	25.0b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))

Compiler

Compiled 8652 to 2640 computations (69.5% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 a t) (-.f64 t z))
✓	0.3b	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z)))
✓	3.1b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z))) (+.f64 x y))

series65.0ms (1.1%)

Counts

3 → 132

Calls

3 calls:

33.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z))) (+.f64 x y))
16.0ms	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z)))
15.0ms	(/.f64 (-.f64 a t) (-.f64 t z))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
195×	`*-un-lft-identity_binary64`
195×	`add-sqr-sqrt_binary64`
91×	`add-cube-cbrt_binary64`
52×	`distribute-lft-out--_binary64`

Counts

3 → 214

Calls

3 calls:

9.0ms	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z)))
6.0ms	(/.f64 (-.f64 a t) (-.f64 t z))
0.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z))) (+.f64 x y))

simplify180.0ms (3%)

Algorithm

1×	egg-herbie

Rules

672×	`cancel-sign-sub-inv_binary64`
565×	`sub-neg_binary64`
292×	`fma-neg_binary64`
225×	`+-commutative_binary64`
218×	`associate--r+_binary64`

Counts

346 → 344

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	398	8897
1	1039	8416
2	3680	8214
3	5459	8214

prune261.0ms (4.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	344	0	344
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	344	9	353

Error

0.0b

Counts

353 → 9

Alt Table

Status	Error	Program
✓	11.6b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z))) (+.f64 x y))
	38.8b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
▶	15.5b	(+.f64 y (+.f64 x (neg.f64 (/.f64 (*.f64 y z) (-.f64 a t)))))
	47.3b	(cbrt.f64 (pow.f64 (+.f64 y (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x)) 3))
	20.8b	(fma.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 t z) (-.f64 a t)) 3)) (+.f64 x y))
	33.0b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	16.3b	(+.f64 y (+.f64 x (.f64 (.f64 y (-.f64 t z)) (/.f64 1 (-.f64 a t)))))
✓	11.6b	(+.f64 y (+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))))
	25.0b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))

Compiler

Compiled 9523 to 2926 computations (69.3% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (neg.f64 (/.f64 (*.f64 y z) (-.f64 a t))))
✓	5.9b	(/.f64 (*.f64 y z) (-.f64 a t))

series46.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

23.0ms	(/.f64 (*.f64 y z) (-.f64 a t))
23.0ms	(+.f64 x (neg.f64 (/.f64 (*.f64 y z) (-.f64 a t))))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
6×	`add-log-exp_binary64`

Counts

2 → 50

Calls

2 calls:

7.0ms	(+.f64 x (neg.f64 (/.f64 (*.f64 y z) (-.f64 a t))))
5.0ms	(/.f64 (*.f64 y z) (-.f64 a t))

simplify88.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

818×	`times-frac_binary64`
547×	`fma-def_binary64`
340×	`fma-neg_binary64`
261×	`associate-/l/_binary64`
219×	`cancel-sign-sub-inv_binary64`

Counts

134 → 104

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	171	2569
1	476	2475
2	1671	2201
3	4861	2201
4	5097	2201

prune81.0ms (1.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	2	4	6
Picked	0	1	1
Done	1	1	2
Total	106	7	113

Error

0.0b

Counts

113 → 7

Alt Table

Status	Error	Program
✓	15.5b	(+.f64 y (+.f64 x (neg.f64 (/.f64 (*.f64 y z) (-.f64 a t)))))
	47.3b	(cbrt.f64 (pow.f64 (+.f64 y (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x)) 3))
	12.2b	(+.f64 y (+.f64 x (neg.f64 (/.f64 y (/.f64 (-.f64 a t) z)))))
	38.8b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
✓	11.6b	(+.f64 y (+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))))
	33.0b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	25.0b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))

Compiler

Compiled 2379 to 854 computations (64.1% saved)

regimes1.3s (21.8%)

Accuracy

Total 8.2b remaining (99.4%)

Threshold costs 0b (0%)

Counts

93 → 4

Compiler

Compiled 9900 to 6156 computations (37.8% saved)

bsearch3.0ms (0%)

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

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

23×	`+-commutative_binary64`
18×	`*-commutative_binary64`
17×	`sub-neg_binary64`
13×	`neg-sub0_binary64`
13×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	157
1	71	157
2	93	157
3	119	157
4	142	157
5	164	157
6	171	157
7	172	157
8	168	157

end139.0ms (2.3%)

Compiler: Compiled 358 to 164 computations (54.2% saved)

Iter	Nodes	Cost
0	41	157
1	71	157
2	93	157
3	119	157
4	142	157
5	164	157
6	171	157
7	172	157
8	168	157

Iter	Nodes	Cost
0	41	157
1	71	157
2	93	157
3	119	157
4	142	157
5	164	157
6	171	157
7	172	157
8	168	157

Details

analyze1.3s (21.9%)

sample1.5s (24%)

simplify127.0ms (2.1%)

prune3.0ms (0.1%)

localize8.0ms (0.1%)

series52.0ms (0.8%)

rewrite10.0ms (0.2%)

simplify126.0ms (2.1%)

prune115.0ms (1.9%)

localize10.0ms (0.2%)

series108.0ms (1.8%)

rewrite25.0ms (0.4%)

simplify197.0ms (3.2%)

prune241.0ms (4%)

localize9.0ms (0.2%)

series65.0ms (1.1%)

rewrite38.0ms (0.6%)

simplify180.0ms (3%)

prune261.0ms (4.3%)

localize9.0ms (0.1%)

series46.0ms (0.8%)

rewrite15.0ms (0.2%)

simplify88.0ms (1.4%)

prune81.0ms (1.3%)

regimes1.3s (21.8%)

bsearch3.0ms (0%)

simplify11.0ms (0.2%)

end139.0ms (2.3%)

Profiling

Iter	Nodes	Cost
0	41	157
1	71	157
2	93	157
3	119	157
4	142	157
5	164	157
6	171	157
7	172	157
8	168	157