Details

analyze1.3s (26.6%)

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 (25.9%)

Results

1.1s	8256×	body	128	valid
105.0ms	771×	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

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

1.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
▶	1.3b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))

Compiler

Compiled 88 to 49 computations (44.3% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	1.6b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

series52.0ms (1.1%)

Counts

2 → 84

Calls

2 calls:

32.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))
20.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
70×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-r_binary64`
26×	`add-cube-cbrt_binary64`

Counts

2 → 106

Calls

2 calls:

9.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))
6.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

simplify130.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

737×	`cancel-sign-sub-inv_binary64`
386×	`sub-neg_binary64`
263×	`fma-neg_binary64`
194×	`associate-/l*_binary64`
184×	`div-sub_binary64`

Counts

190 → 184

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	290	4483
1	807	4312
2	3067	4264
3	4766	4260
4	5066	4260

prune129.0ms (2.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	180	4	184
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	181	5	186

Error

Counts

186 → 5

Alt Table

Status	Error	Program
▶	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	33.2b	(+.f64 x (.f64 (.f64 y (/.f64 1 (sqrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 a t)))))
	1.4b	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))))
	31.9b	(+.f64 x (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (/.f64 (-.f64 z t) (-.f64 a t)))))
	11.1b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 4764 to 1507 computations (68.4% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	1.2b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

series37.0ms (0.8%)

Counts

1 → 60

Calls

1 calls:

37.0ms

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

simplify89.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

562×	`fma-def_binary64`
506×	`times-frac_binary64`
476×	`cancel-sign-sub-inv_binary64`
453×	`associate-/l*_binary64`
373×	`fma-neg_binary64`

Counts

70 → 54

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	2025
1	375	1996
2	1299	1448
3	4541	1448
4	4981	1448
5	4975	1448

prune111.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	137	5	142

Error

Counts

142 → 5

Alt Table

Status	Error	Program
▶	1.4b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	33.2b	(+.f64 x (.f64 (.f64 y (/.f64 1 (sqrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 a t)))))
	25.8b	(+.f64 (+.f64 x y) (*.f64 (/.f64 y t) (-.f64 a z)))
	11.1b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 3392 to 1099 computations (67.6% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 a t))
✓	0.2b	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
✓	1.2b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)

series65.0ms (1.4%)

Counts

3 → 120

Calls

3 calls:

36.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
19.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
10.0ms	(/.f64 1 (-.f64 a t))

rewrite21.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

3 → 105

Calls

3 calls:

9.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
4.0ms	(/.f64 1 (-.f64 a t))
0.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)

simplify135.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

700×	`cancel-sign-sub-inv_binary64`
675×	`times-frac_binary64`
380×	`fma-neg_binary64`
354×	`sub-neg_binary64`
192×	`+-commutative_binary64`

Counts

225 → 227

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	298	4903
1	792	4646
2	2764	4604
3	4923	4603
4	5113	4603

prune148.0ms (3.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	227	0	227
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	227	5	232

Error

Counts

232 → 5

Alt Table

Status	Error	Program
✓	1.4b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	33.2b	(+.f64 x (.f64 (.f64 y (/.f64 1 (sqrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 a t)))))
	25.8b	(+.f64 (+.f64 x y) (*.f64 (/.f64 y t) (-.f64 a z)))
▶	11.1b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 5290 to 1958 computations (63% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 z t) y)
✓	11.6b	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))

series39.0ms (0.8%)

Counts

2 → 60

Calls

2 calls:

33.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))
6.0ms	(*.f64 (-.f64 z t) y)

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 55

Calls

2 calls:

6.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))
4.0ms	(*.f64 (-.f64 z t) y)

simplify90.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

611×	`fma-def_binary64`
550×	`cancel-sign-sub-inv_binary64`
360×	`div-sub_binary64`
329×	`fma-neg_binary64`
296×	`distribute-rgt-in_binary64`

Counts

115 → 124

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	199	2430
1	555	2202
2	2168	1959
3	4400	1957
4	5131	1957

prune91.0ms (1.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	124	5	129

Error

Counts

129 → 5

Alt Table

Status	Error	Program
✓	1.4b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	33.2b	(+.f64 x (.f64 (.f64 y (/.f64 1 (sqrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 a t)))))
	25.8b	(+.f64 (+.f64 x y) (*.f64 (/.f64 y t) (-.f64 a z)))
✓	11.1b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 2792 to 893 computations (68% saved)

regimes798.0ms (16.9%)

Accuracy

Total 0.4b remaining (93.5%)

Threshold costs 0.4b (93.5%)

Counts

85 → 3

Compiler

Compiled 12345 to 7491 computations (39.3% saved)

bsearch27.0ms (0.6%)

Steps

Iters	Range		Point
6	0.003111371390951811	11.91278277155073	0.009889904661523138
4	-2.7435961110591997e-40	-7.836757707528564e-42	-3.694153495670011e-41

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	58
1	29	58
2	35	58
3	37	58
4	38	58
5	38	58

end80.0ms (1.7%)

Compiler: Compiled 178 to 94 computations (47.2% saved)

Details

analyze1.3s (26.6%)

sample1.2s (25.9%)

simplify121.0ms (2.6%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series52.0ms (1.1%)

rewrite25.0ms (0.5%)

simplify130.0ms (2.8%)

prune129.0ms (2.7%)

localize8.0ms (0.2%)

series37.0ms (0.8%)

rewrite1.0ms (0%)

simplify89.0ms (1.9%)

prune111.0ms (2.4%)

localize8.0ms (0.2%)

series65.0ms (1.4%)

rewrite21.0ms (0.5%)

simplify135.0ms (2.9%)

prune148.0ms (3.1%)

localize7.0ms (0.2%)

series39.0ms (0.8%)

rewrite13.0ms (0.3%)

simplify90.0ms (1.9%)

prune91.0ms (1.9%)

regimes798.0ms (16.9%)

bsearch27.0ms (0.6%)

simplify3.0ms (0.1%)

end80.0ms (1.7%)

Profiling