Details

analyze1.9s (17.2%)

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
0%	99.7%	0.3%	11
1.1%	98.6%	0.3%	12
1.9%	97.8%	0.3%	13
7%	92.7%	0.3%	14

Compiler

Compiled 28 to 17 computations (39.3% saved)

sample1.3s (11.7%)

Results

1.2s	8255×	body	128	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 83 to 50 computations (39.8% saved)

simplify92.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

765×	`sub-neg_binary64`
731×	`fma-neg_binary64`
652×	`neg-mul-1_binary64`
505×	`fma-def_binary64`
495×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	29
1	37	29
2	85	29
3	194	27
4	486	27
5	1003	27
6	1920	27
7	3406	27
8	4078	27
9	4431	27
10	4919	27
11	5085	27

prune3.0ms (0%)

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

29.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	29.6b	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))

Compiler

Compiled 96 to 51 computations (46.9% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.5b	(fma.f64 (+.f64 x y) z (*.f64 t a))
✓	1.7b	(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
✓	27.6b	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))

series174.0ms (1.6%)

Counts

3 → 204

Calls

3 calls:

138.0ms	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))
24.0ms	(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
12.0ms	(fma.f64 (+.f64 x y) z (*.f64 t a))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
15×	`times-frac_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out_binary64`

Counts

3 → 59

Calls

3 calls:

5.0ms	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))
0.0ms	(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
0.0ms	(fma.f64 (+.f64 x y) z (*.f64 t a))

simplify140.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

591×	`associate-/l*_binary64`
378×	`associate-/r*_binary64`
286×	`+-commutative_binary64`
241×	`associate-+r+_binary64`
237×	`associate--l+_binary64`

Counts

263 → 200

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	673	11356
1	1961	11106
2	5078	11106

prune192.0ms (1.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	188	12	200
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	189	12	201

Error

2.9b

Counts

201 → 12

Alt Table

Status	Error	Program
	47.9b	(.f64 (sqrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t)))) (/.f64 (sqrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t)))) (+.f64 (+.f64 t x) y)))
	43.6b	z
	29.6b	(.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))
	42.6b	a
	30.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t)))) (cbrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t))))) (cbrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))))
	41.4b	(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
	44.8b	(/.f64 (fma.f64 a t (*.f64 z x)) (+.f64 x (+.f64 y t)))
	50.6b	(/.f64 (*.f64 a (+.f64 y t)) (+.f64 y (+.f64 t x)))
	51.3b	(.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 y t) 3))) (+.f64 (.f64 x x) (-.f64 (.f64 (+.f64 y t) (+.f64 y t)) (*.f64 x (+.f64 y t)))))
	29.7b	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
▶	27.2b	(-.f64 (+.f64 a z) b)
	49.5b	(/.f64 (*.f64 z (+.f64 y x)) (+.f64 y (+.f64 t x)))

Compiler

Compiled 10663 to 3159 computations (70.4% saved)

localize3.0ms (0%)

prune10.0ms (0.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	11	11
Picked	1	1
Done	0	0
Total	12	12

Error

2.9b

Counts

12 → 12

Alt Table

Status	Error	Program
	47.9b	(.f64 (sqrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t)))) (/.f64 (sqrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t)))) (+.f64 (+.f64 t x) y)))
	43.6b	z
▶	29.6b	(.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))
	42.6b	a
	30.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t)))) (cbrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t))))) (cbrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))))
	41.4b	(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
	44.8b	(/.f64 (fma.f64 a t (*.f64 z x)) (+.f64 x (+.f64 y t)))
	50.6b	(/.f64 (*.f64 a (+.f64 y t)) (+.f64 y (+.f64 t x)))
	51.3b	(.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 y t) 3))) (+.f64 (.f64 x x) (-.f64 (.f64 (+.f64 y t) (+.f64 y t)) (*.f64 x (+.f64 y t)))))
	29.7b	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
✓	27.2b	(-.f64 (+.f64 a z) b)
	49.5b	(/.f64 (*.f64 z (+.f64 y x)) (+.f64 y (+.f64 t x)))

Compiler

Compiled 597 to 298 computations (50.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x (+.f64 y t)))
	0.5b	(fma.f64 (+.f64 x y) z (*.f64 t a))
	1.7b	(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
✓	27.6b	(.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))

series153.0ms (1.4%)

Counts

2 → 108

Calls

2 calls:

129.0ms	(.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))
23.0ms	(/.f64 1 (+.f64 x (+.f64 y t)))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
29×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
21×	`distribute-lft-out_binary64`

Counts

2 → 89

Calls

2 calls:

10.0ms	(.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))
5.0ms	(/.f64 1 (+.f64 x (+.f64 y t)))

simplify135.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

671×	`associate-/l*_binary64`
456×	`associate-/r*_binary64`
306×	`+-commutative_binary64`
245×	`associate-+r+_binary64`
176×	`fma-def_binary64`

Counts

197 → 229

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	745	11101
1	2289	10838
2	5016	10838

prune231.0ms (2.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	302	2	304
Fresh	2	8	10
Picked	0	1	1
Done	0	1	1
Total	304	12	316

Error

2.9b

Counts

316 → 12

Alt Table

Status	Error	Program
	47.9b	(.f64 (sqrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t)))) (/.f64 (sqrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t)))) (+.f64 (+.f64 t x) y)))
	43.6b	z
✓	29.6b	(.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))
	42.6b	a
	29.7b	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
	44.9b	(.f64 (fma.f64 a t (.f64 z x)) (/.f64 1 (+.f64 x (+.f64 y t))))
	50.6b	(/.f64 (*.f64 a (+.f64 y t)) (+.f64 y (+.f64 t x)))
	51.3b	(.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 y t) 3))) (+.f64 (.f64 x x) (-.f64 (.f64 (+.f64 y t) (+.f64 y t)) (*.f64 x (+.f64 y t)))))
✓	27.2b	(-.f64 (+.f64 a z) b)
	41.4b	(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
	49.5b	(/.f64 (*.f64 z (+.f64 y x)) (+.f64 y (+.f64 t x)))
▶	29.6b	(-.f64 (+.f64 (/.f64 (.f64 z y) (+.f64 (+.f64 t x) y)) (+.f64 (/.f64 (.f64 z x) (+.f64 (+.f64 t x) y)) (+.f64 (/.f64 (.f64 a t) (+.f64 (+.f64 t x) y)) (/.f64 (.f64 a y) (+.f64 (+.f64 t x) y))))) (/.f64 (*.f64 y b) (+.f64 (+.f64 t x) y)))

Compiler

Compiled 14316 to 4562 computations (68.1% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	9.6b	(/.f64 (*.f64 a t) (+.f64 (+.f64 t x) y))
✓	10.0b	(/.f64 (*.f64 z x) (+.f64 (+.f64 t x) y))
✓	10.5b	(/.f64 (*.f64 y b) (+.f64 (+.f64 t x) y))
✓	11.1b	(/.f64 (*.f64 a y) (+.f64 (+.f64 t x) y))

series192.0ms (1.8%)

Counts

4 → 192

Calls

4 calls:

49.0ms	(/.f64 (*.f64 y b) (+.f64 (+.f64 t x) y))
49.0ms	(/.f64 (*.f64 a y) (+.f64 (+.f64 t x) y))
47.0ms	(/.f64 (*.f64 a t) (+.f64 (+.f64 t x) y))
47.0ms	(/.f64 (*.f64 z x) (+.f64 (+.f64 t x) y))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64`
24×	`distribute-lft-out_binary64`
24×	`add-cbrt-cube_binary64`
24×	`add-exp-log_binary64`
20×	`associate-/r*_binary64`

Counts

4 → 116

Calls

4 calls:

6.0ms	(/.f64 (*.f64 a y) (+.f64 (+.f64 t x) y))
6.0ms	(/.f64 (*.f64 a t) (+.f64 (+.f64 t x) y))
5.0ms	(/.f64 (*.f64 y b) (+.f64 (+.f64 t x) y))
5.0ms	(/.f64 (*.f64 z x) (+.f64 (+.f64 t x) y))

simplify149.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

941×	`associate-/l*_binary64`
271×	`associate-/r/_binary64`
234×	`sub-neg_binary64`
230×	`associate-/l/_binary64`
207×	`+-commutative_binary64`

Counts

308 → 367

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	788	11096
1	2326	10768
2	5125	10768

prune315.0ms (2.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	363	4	367
Fresh	5	4	9
Picked	1	0	1
Done	0	2	2
Total	369	10	379

Error

1.4b

Counts

379 → 10

Alt Table

Status	Error	Program
	51.3b	(.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 y t) 3))) (+.f64 (.f64 x x) (-.f64 (.f64 (+.f64 y t) (+.f64 y t)) (*.f64 x (+.f64 y t)))))
	28.0b	(-.f64 (+.f64 (/.f64 (.f64 z y) (+.f64 (+.f64 t x) y)) (+.f64 (/.f64 (.f64 z x) (+.f64 (+.f64 t x) y)) (+.f64 (/.f64 (.f64 a t) (+.f64 (+.f64 t x) y)) (/.f64 (.f64 a y) (+.f64 (+.f64 t x) y))))) (*.f64 y (/.f64 b (+.f64 y (+.f64 t x)))))
✓	29.6b	(.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))
	42.6b	a
	43.6b	z
	24.3b	(-.f64 (+.f64 (/.f64 (.f64 z y) (+.f64 (+.f64 t x) y)) (+.f64 (.f64 z (/.f64 x (+.f64 y (+.f64 t x)))) (+.f64 (/.f64 (.f64 a t) (+.f64 (+.f64 t x) y)) (/.f64 (.f64 a y) (+.f64 (+.f64 t x) y))))) (/.f64 (*.f64 y b) (+.f64 (+.f64 t x) y)))
	27.8b	(-.f64 (+.f64 (/.f64 (.f64 z y) (+.f64 (+.f64 t x) y)) (+.f64 (/.f64 (.f64 z x) (+.f64 (+.f64 t x) y)) (+.f64 (/.f64 (.f64 a t) (+.f64 (+.f64 t x) y)) (/.f64 (.f64 a y) (+.f64 (+.f64 t x) y))))) (/.f64 y (/.f64 (+.f64 (+.f64 t x) y) b)))
✓	27.2b	(-.f64 (+.f64 a z) b)
	41.4b	(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
	27.2b	(-.f64 (+.f64 (/.f64 (.f64 z y) (+.f64 (+.f64 t x) y)) (+.f64 (/.f64 (.f64 z x) (+.f64 (+.f64 t x) y)) (+.f64 (/.f64 (.f64 a t) (+.f64 (+.f64 t x) y)) (/.f64 a (/.f64 (+.f64 (+.f64 t x) y) y))))) (/.f64 (.f64 y b) (+.f64 (+.f64 t x) y)))

Compiler

Compiled 25672 to 5154 computations (79.9% saved)

regimes5.7s (52.3%)

Accuracy

Total 6.4b remaining (81.1%)

Threshold costs 0b (0%)

Counts

186 → 3

Compiler

Compiled 42894 to 22273 computations (48.1% saved)

bsearch9.0ms (0.1%)

Compiler: Compiled 27 to 16 computations (40.7% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

18×	`+-commutative_binary64`
11×	`*-commutative_binary64`
7×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	154
1	67	154
2	83	154
3	91	154
4	95	154
5	95	154

end145.0ms (1.3%)

Compiler: Compiled 554 to 237 computations (57.2% saved)

Details

analyze1.9s (17.2%)

sample1.3s (11.7%)

simplify92.0ms (0.8%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series174.0ms (1.6%)

rewrite9.0ms (0.1%)

simplify140.0ms (1.3%)

prune192.0ms (1.8%)

localize3.0ms (0%)

prune10.0ms (0.1%)

localize15.0ms (0.1%)

series153.0ms (1.4%)

rewrite21.0ms (0.2%)

simplify135.0ms (1.2%)

prune231.0ms (2.1%)

localize18.0ms (0.2%)

series192.0ms (1.8%)

rewrite28.0ms (0.3%)

simplify149.0ms (1.4%)

prune315.0ms (2.9%)

regimes5.7s (52.3%)

bsearch9.0ms (0.1%)

simplify6.0ms (0.1%)

end145.0ms (1.3%)

Profiling