Details

analyze1.3s (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
13.2%	86.5%	0.2%	10
17%	82.8%	0.2%	11
18.2%	81.5%	0.2%	12
21.7%	78.1%	0.2%	13
32.9%	66.9%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.3s (19.7%)

Results

1.1s	8256×	body	128	valid
98.0ms	725×	body	128	invalid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify114.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1539×	`fma-neg_binary64`
1346×	`fma-def_binary64`
1046×	`div-sub_binary64`
750×	`associate-/r/_binary64`
420×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	26	16
2	49	16
3	96	16
4	183	16
5	339	16
6	657	16
7	1726	16
8	2830	16
9	2687	16
10	2951	16
11	3172	16
12	3258	16
13	4297	16
14	5213	16

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

10.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	10.7b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Compiler

Compiled 59 to 33 computations (44.1% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 y z))
✓	10.4b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

series72.0ms (1.1%)

Counts

2 → 69

Calls

2 calls:

66.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
5.0ms	(-.f64 x (*.f64 y z))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 54

Calls

2 calls:

5.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
2.0ms	(-.f64 x (*.f64 y z))

simplify120.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

807×	`fma-def_binary64`
729×	`cancel-sign-sub-inv_binary64`
205×	`sub-neg_binary64`
190×	`div-sub_binary64`
182×	`fma-neg_binary64`

Counts

123 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	205	3797
1	628	3572
2	2362	3442
3	4895	3442
4	5108	3442

prune100.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	117	9	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	9	127

Error

2.4b

Counts

127 → 9

Alt Table

Status	Error	Program
	37.0b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 z a))) 3))
	30.2b	(/.f64 x (-.f64 t (*.f64 a z)))
	45.0b	(.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 (pow.f64 t 3) (pow.f64 (.f64 a z) 3))) (+.f64 (.f64 t t) (+.f64 (.f64 (.f64 a z) (.f64 a z)) (.f64 t (*.f64 a z)))))
	34.8b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y z) (.f64 y z))) (.f64 (-.f64 t (.f64 z a)) (fma.f64 y z x)))
▶	10.8b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
	11.0b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
	37.6b	(.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (/.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a))))
	42.3b	(/.f64 y a)
	11.5b	(.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a))))

Compiler

Compiled 3684 to 1136 computations (69.2% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 x (*.f64 y z))
✓	0.7b	(/.f64 1 (-.f64 t (*.f64 a z)))
✓	10.1b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))

series82.0ms (1.3%)

Counts

2 → 96

Calls

2 calls:

62.0ms	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
20.0ms	(/.f64 1 (-.f64 t (*.f64 a z)))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
15×	`associate-r_binary64`

Counts

2 → 79

Calls

2 calls:

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

simplify145.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

717×	`cancel-sign-sub-inv_binary64`
335×	`fma-neg_binary64`
295×	`distribute-rgt-in_binary64`
210×	`times-frac_binary64`
205×	`sub-neg_binary64`

Counts

175 → 176

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	225	5382
1	682	4890
2	2696	4652
3	4643	4651
4	4987	4651

prune178.0ms (2.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	199	4	203
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	201	11	212

Error

1.4b

Counts

212 → 11

Alt Table

Status	Error	Program
▶	11.0b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
	36.0b	(.f64 (-.f64 x (.f64 y z)) (+.f64 (/.f64 1 t) (/.f64 (*.f64 a z) (pow.f64 t 2))))
	11.5b	(.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a))))
	35.2b	(-.f64 (.f64 (+.f64 (/.f64 (.f64 z a) t) 1) (/.f64 x t)) (.f64 (/.f64 y t) (+.f64 z (/.f64 (.f64 z (*.f64 z a)) t))))
	35.0b	(.f64 (.f64 (-.f64 x (.f64 y z)) (sqrt.f64 (/.f64 1 (-.f64 t (.f64 a z))))) (sqrt.f64 (/.f64 1 (-.f64 t (*.f64 a z)))))
	37.0b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 z a))) 3))
	30.2b	(/.f64 x (-.f64 t (*.f64 a z)))
	34.8b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y z) (.f64 y z))) (.f64 (-.f64 t (.f64 z a)) (fma.f64 y z x)))
	37.6b	(.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (/.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a))))
	42.3b	(/.f64 y a)
	33.3b	(.f64 (.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 (.f64 t t) (.f64 (.f64 a z) (.f64 a z))))) (+.f64 t (.f64 a z)))

Compiler

Compiled 5602 to 1988 computations (64.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 x (*.f64 y z))
✓	0.4b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
✓	10.4b	(/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z)))

series124.0ms (1.9%)

Counts

2 → 120

Calls

2 calls:

63.0ms	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
61.0ms	(/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z)))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`times-frac_binary64`
54×	`*-un-lft-identity_binary64`
54×	`add-sqr-sqrt_binary64`
54×	`add-cube-cbrt_binary64`
18×	`associate-/r*_binary64`

Counts

2 → 120

Calls

2 calls:

7.0ms	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
5.0ms	(/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z)))

simplify219.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

398×	`sub-neg_binary64`
351×	`times-frac_binary64`
310×	`fma-neg_binary64`
262×	`associate-/l*_binary64`
231×	`associate-/r*_binary64`

Counts

240 → 261

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	338	8921
1	1048	8344
2	4130	8272
3	4944	8272
4	4953	8272

prune241.0ms (3.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	283	5	288
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	288	11	299

Error

1.4b

Counts

299 → 11

Alt Table

Status	Error	Program
	35.0b	(.f64 (.f64 (-.f64 x (.f64 y z)) (sqrt.f64 (/.f64 1 (-.f64 t (.f64 a z))))) (sqrt.f64 (/.f64 1 (-.f64 t (*.f64 a z)))))
	36.6b	(/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 z y))) 3)))
▶	10.7b	(/.f64 (-.f64 x (.f64 z y)) (-.f64 t (.f64 a z)))
	34.8b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y z) (.f64 y z))) (.f64 (-.f64 t (.f64 z a)) (fma.f64 y z x)))
	24.1b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 x (.f64 z y)) (-.f64 t (.f64 a z)))))
	36.0b	(.f64 (-.f64 x (.f64 y z)) (+.f64 (/.f64 1 t) (/.f64 (*.f64 a z) (pow.f64 t 2))))
	37.7b	(/.f64 1 (+.f64 (/.f64 (.f64 y (.f64 z t)) (.f64 x x)) (/.f64 (-.f64 t (.f64 a z)) x)))
	42.3b	(/.f64 y a)
	35.2b	(-.f64 (.f64 (+.f64 (/.f64 (.f64 z a) t) 1) (/.f64 x t)) (.f64 (/.f64 y t) (+.f64 z (/.f64 (.f64 z (*.f64 z a)) t))))
	11.0b	(/.f64 1 (.f64 (-.f64 t (.f64 a z)) (/.f64 1 (-.f64 x (*.f64 y z)))))
	33.3b	(.f64 (.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 (.f64 t t) (.f64 (.f64 a z) (.f64 a z))))) (+.f64 t (.f64 a z)))

Compiler

Compiled 9018 to 2864 computations (68.2% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 z y))
✓	10.4b	(/.f64 (-.f64 x (.f64 z y)) (-.f64 t (.f64 a z)))

series69.0ms (1.1%)

Counts

2 → 96

Calls

2 calls:

63.0ms	(/.f64 (-.f64 x (.f64 z y)) (-.f64 t (.f64 a z)))
5.0ms	(-.f64 x (*.f64 z y))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 54

Calls

2 calls:

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

simplify140.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

811×	`fma-def_binary64`
732×	`cancel-sign-sub-inv_binary64`
207×	`sub-neg_binary64`
192×	`fma-neg_binary64`
173×	`times-frac_binary64`

Counts

150 → 138

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	207	3986
1	632	3761
2	2365	3631
3	4904	3631
4	4982	3631
5	4944	3631

prune98.0ms (1.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	138	11	149

Error

1.4b

Counts

149 → 11

Alt Table

Status	Error	Program
	35.0b	(.f64 (.f64 (-.f64 x (.f64 y z)) (sqrt.f64 (/.f64 1 (-.f64 t (.f64 a z))))) (sqrt.f64 (/.f64 1 (-.f64 t (*.f64 a z)))))
	36.6b	(/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 z y))) 3)))
✓	10.7b	(/.f64 (-.f64 x (.f64 z y)) (-.f64 t (.f64 a z)))
	34.8b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y z) (.f64 y z))) (.f64 (-.f64 t (.f64 z a)) (fma.f64 y z x)))
	24.1b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 x (.f64 z y)) (-.f64 t (.f64 a z)))))
	36.0b	(.f64 (-.f64 x (.f64 y z)) (+.f64 (/.f64 1 t) (/.f64 (*.f64 a z) (pow.f64 t 2))))
	37.7b	(/.f64 1 (+.f64 (/.f64 (.f64 y (.f64 z t)) (.f64 x x)) (/.f64 (-.f64 t (.f64 a z)) x)))
	42.3b	(/.f64 y a)
	35.2b	(-.f64 (.f64 (+.f64 (/.f64 (.f64 z a) t) 1) (/.f64 x t)) (.f64 (/.f64 y t) (+.f64 z (/.f64 (.f64 z (*.f64 z a)) t))))
	11.0b	(/.f64 1 (.f64 (-.f64 t (.f64 a z)) (/.f64 1 (-.f64 x (*.f64 y z)))))
	33.3b	(.f64 (.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 (.f64 t t) (.f64 (.f64 a z) (.f64 a z))))) (+.f64 t (.f64 a z)))

Compiler

Compiled 3721 to 1097 computations (70.5% saved)

regimes1.9s (29.8%)

Accuracy

Total 3.2b remaining (63.8%)

Threshold costs 0b (0%)

Counts

199 → 3

Compiler

Compiled 27188 to 17034 computations (37.3% saved)

bsearch7.0ms (0.1%)

Compiler: Compiled 16 to 10 computations (37.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	64
1	42	64
2	57	64
3	67	64
4	72	64
5	71	64

end161.0ms (2.5%)

Compiler: Compiled 340 to 187 computations (45% saved)

Details

analyze1.3s (20%)

sample1.3s (19.7%)

simplify114.0ms (1.8%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series72.0ms (1.1%)

rewrite10.0ms (0.2%)

simplify120.0ms (1.8%)

prune100.0ms (1.5%)

localize9.0ms (0.1%)

series82.0ms (1.3%)

rewrite24.0ms (0.4%)

simplify145.0ms (2.2%)

prune178.0ms (2.8%)

localize9.0ms (0.1%)

series124.0ms (1.9%)

rewrite23.0ms (0.4%)

simplify219.0ms (3.4%)

prune241.0ms (3.7%)

localize12.0ms (0.2%)

series69.0ms (1.1%)

rewrite12.0ms (0.2%)

simplify140.0ms (2.2%)

prune98.0ms (1.5%)

regimes1.9s (29.8%)

bsearch7.0ms (0.1%)

simplify4.0ms (0.1%)

end161.0ms (2.5%)

Profiling