Details

analyze1.2s (25.9%)

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
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
22.4%	77.4%	0.2%	13
23.5%	76.3%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (24.7%)

Results

1.0s	8256×	body	128	valid
93.0ms	742×	body	128	invalid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify121.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1627×	`fma-def_binary64`
927×	`div-sub_binary64`
619×	`times-frac_binary64`
541×	`fma-neg_binary64`
386×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	21	14
2	40	14
3	78	14
4	161	14
5	302	14
6	659	14
7	1591	14
8	3045	14
9	3070	14
10	3380	14
11	3469	14
12	3480	14
13	4892	14
14	5124	14

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

2.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.1b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

Compiler

Compiled 56 to 29 computations (48.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	1.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

series48.0ms (1%)

Counts

2 → 96

Calls

2 calls:

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

rewrite11.0ms (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:

7.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
0.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

simplify115.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

690×	`cancel-sign-sub-inv_binary64`
647×	`times-frac_binary64`
542×	`fma-neg_binary64`
354×	`sub-neg_binary64`
188×	`neg-mul-1_binary64`

Counts

160 → 138

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	267	4118
1	740	4035
2	2434	3427
3	4231	3410
4	4964	3410

prune107.0ms (2.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	133	5	138
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	133	6	139

Error

Counts

139 → 6

Alt Table

Status	Error	Program
	2.6b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	10.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
	3.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)))
	22.6b	(+.f64 (+.f64 x y) (*.f64 (/.f64 y t) (-.f64 a z)))
▶	2.1b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)
✓	2.1b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

Compiler

Compiled 3437 to 1150 computations (66.5% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 a t) (-.f64 z t))
✓	0.2b	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t)))
✓	1.9b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

series70.0ms (1.5%)

Counts

3 → 132

Calls

3 calls:

35.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)
17.0ms	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t)))
17.0ms	(/.f64 (-.f64 a t) (-.f64 z t))

rewrite39.0ms (0.8%)

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:

8.0ms	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t)))
8.0ms	(/.f64 (-.f64 a t) (-.f64 z t))
0.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

simplify182.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

927×	`cancel-sign-sub-inv_binary64`
524×	`sub-neg_binary64`
249×	`associate--l+_binary64`
234×	`+-commutative_binary64`
217×	`fma-neg_binary64`

Counts

346 → 337

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	391	8735
1	1041	8263
2	3678	8083
3	5565	8083

prune225.0ms (4.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	337	0	337
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	337	6	343

Error

Counts

343 → 6

Alt Table

Status	Error	Program
▶	2.6b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	10.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
	3.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)))
	22.6b	(+.f64 (+.f64 x y) (*.f64 (/.f64 y t) (-.f64 a z)))
✓	2.1b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)
✓	2.1b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

Compiler

Compiled 8714 to 2788 computations (68% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 a t))
✓	8.3b	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))

series43.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

29.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
14.0ms	(/.f64 y (-.f64 a t))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64`
52×	`*-un-lft-identity_binary64`
36×	`add-cube-cbrt_binary64`
31×	`times-frac_binary64`
21×	`associate-l_binary64`

Counts

2 → 113

Calls

2 calls:

11.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
3.0ms	(/.f64 y (-.f64 a t))

simplify150.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

766×	`cancel-sign-sub-inv_binary64`
366×	`fma-neg_binary64`
238×	`sub-neg_binary64`
178×	`times-frac_binary64`
174×	`associate-/l*_binary64`

Counts

185 → 203

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	340	4235
1	810	4049
2	3050	3971
3	4777	3970
4	4973	3970
5	4980	3970

prune147.0ms (3.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	201	2	203
Fresh	3	0	3
Picked	0	1	1
Done	0	2	2
Total	204	5	209

Error

Counts

209 → 5

Alt Table

Status	Error	Program
✓	2.6b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
✓	2.1b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)
	10.3b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
✓	2.1b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
▶	2.6b	(+.f64 x (.f64 (.f64 y (/.f64 1 (-.f64 a t))) (-.f64 z t)))

Compiler

Compiled 5116 to 1475 computations (71.2% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 a t))
✓	0.2b	(*.f64 y (/.f64 1 (-.f64 a t)))
✓	8.3b	(.f64 (.f64 y (/.f64 1 (-.f64 a t))) (-.f64 z t))

series58.0ms (1.2%)

Counts

3 → 108

Calls

3 calls:

33.0ms	(.f64 (.f64 y (/.f64 1 (-.f64 a t))) (-.f64 z t))
16.0ms	(*.f64 y (/.f64 1 (-.f64 a t)))
8.0ms	(/.f64 1 (-.f64 a t))

rewrite33.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`add-sqr-sqrt_binary64`
55×	`*-un-lft-identity_binary64`
38×	`add-cube-cbrt_binary64`
32×	`times-frac_binary64`
31×	`add-exp-log_binary64`

Counts

3 → 149

Calls

3 calls:

10.0ms	(.f64 (.f64 y (/.f64 1 (-.f64 a t))) (-.f64 z t))
8.0ms	(*.f64 y (/.f64 1 (-.f64 a t)))
4.0ms	(/.f64 1 (-.f64 a t))

simplify119.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

809×	`cancel-sign-sub-inv_binary64`
324×	`associate-l_binary64`
278×	`associate-r_binary64`
259×	`fma-neg_binary64`
243×	`sub-neg_binary64`

Counts

257 → 257

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	358	5020
1	855	4726
2	3386	4648
3	4985	4648

prune166.0ms (3.5%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	257	0	257
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	257	5	262

Error

Counts

262 → 5

Alt Table

Status	Error	Program
✓	2.6b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
✓	2.1b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)
	10.3b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
✓	2.1b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
✓	2.6b	(+.f64 x (.f64 (.f64 y (/.f64 1 (-.f64 a t))) (-.f64 z t)))

Compiler

Compiled 6348 to 2472 computations (61.1% saved)

regimes559.0ms (11.8%)

Accuracy

Total 0.5b remaining (97.3%)

Threshold costs 0.5b (97.3%)

Counts

56 → 3

Compiler

Compiled 7852 to 4706 computations (40.1% saved)

bsearch11.0ms (0.2%)

Steps

Iters	Range		Point
2	4.322915473226912e-91	7.571944416430077e-90	3.7040622508066614e-90
2	-3042702039633579000.0	-537276393096478000.0	-8.5196827904596e+17

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`*-commutative_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	65
1	31	65
2	42	65
3	53	65
4	59	65
5	62	65
6	63	65
7	63	65

end73.0ms (1.5%)

Compiler: Compiled 182 to 94 computations (48.4% saved)

Details

analyze1.2s (25.9%)

sample1.2s (24.7%)

simplify121.0ms (2.6%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series48.0ms (1%)

rewrite11.0ms (0.2%)

simplify115.0ms (2.4%)

prune107.0ms (2.3%)

localize8.0ms (0.2%)

series70.0ms (1.5%)

rewrite39.0ms (0.8%)

simplify182.0ms (3.8%)

prune225.0ms (4.8%)

localize8.0ms (0.2%)

series43.0ms (0.9%)

rewrite23.0ms (0.5%)

simplify150.0ms (3.2%)

prune147.0ms (3.1%)

localize11.0ms (0.2%)

series58.0ms (1.2%)

rewrite33.0ms (0.7%)

simplify119.0ms (2.5%)

prune166.0ms (3.5%)

regimes559.0ms (11.8%)

bsearch11.0ms (0.2%)

simplify4.0ms (0.1%)

end73.0ms (1.5%)

Profiling