Details

analyze670.0ms (17.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
14%	85.8%	0.1%	7
22.6%	77.2%	0.1%	8
23.8%	74.5%	1.7%	9
40%	56.4%	3.7%	10
46.9%	48.7%	4.4%	11
48%	45.8%	6.2%	12
58.1%	32.2%	9.7%	13
62.1%	27.2%	10.6%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample1.1s (28.3%)

Symmetry

(sort x y z)

Results

861.0ms	8256×	body	128	valid
119.0ms	1132×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify25.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

438×	`fma-neg_binary64`
221×	`fma-def_binary64`
190×	`rules-40_binary64`
190×	`rules-41_binary64`
190×	`rules-42_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	55	11
2	175	11
3	702	11
4	18	11

prune4.0ms (0.1%)

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

54.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	54.5b	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)

Compiler

Compiled 44 to 26 computations (40.9% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (+.f64 (-.f64 y z) 1))
✓	11.0b	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)

series22.0ms (0.6%)

Counts

2 → 72

Calls

2 calls:

15.0ms	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)
7.0ms	(*.f64 x (+.f64 (-.f64 y z) 1))

rewrite81.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

884×	`fma-neg_binary64`
612×	`prod-diff_binary64`
192×	`egg-rr`
168×	`expm1-udef_binary64`
168×	`log1p-udef_binary64`

Counts

2 → 192

Calls

2 calls:

73.0ms	(*.f64 x (+.f64 (-.f64 y z) 1))
73.0ms	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	215	19
2	2812	19
3	5204	19
0	0	0
1	0	0

simplify81.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1154×	`rules-40_binary64`
1154×	`rules-42_binary64`
782×	`rules-41_binary64`
782×	`rules-43_binary64`
394×	`rules-20_binary64`

Counts

264 → 205

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	936
1	155	936
2	567	792
3	2100	792
4	4046	792
5	16	792

prune214.0ms (5.7%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	183	22	205
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	184	22	206

Error

45.1b

Counts

206 → 22

Alt Table

Status	Error	Program
	59.1b	(/.f64 (exp.f64 (log.f64 (fma.f64 x (-.f64 y z) x))) z)
	53.2b	(*.f64 (+.f64 (-.f64 y z) 1) (/.f64 x z))
	58.8b	(exp.f64 (log.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)))
	59.4b	(/.f64 (*.f64 (+.f64 1 y) x) z)
	55.7b	(/.f64 (fma.f64 (cbrt.f64 x) (cbrt.f64 (.f64 x x)) (neg.f64 (-.f64 0 (.f64 x (-.f64 y z))))) z)
	58.8b	(/.f64 (*.f64 y x) z)
	62.9b	(/.f64 (log.f64 (exp.f64 (fma.f64 x (-.f64 y z) x))) z)
	60.1b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z) 3))
	54.4b	(/.f64 (*.f64 (-.f64 1 z) x) z)
	54.7b	(/.f64 (pow.f64 (cbrt.f64 (fma.f64 x (-.f64 y z) x)) 3) z)
	57.7b	(fabs.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z))
	60.1b	(/.f64 (/.f64 (*.f64 x (+.f64 1 (pow.f64 (-.f64 y z) 3))) (+.f64 (pow.f64 (-.f64 y z) 2) (-.f64 1 (-.f64 y z)))) z)
	54.7b	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) 3)
	54.5b	(/.f64 (/.f64 x (/.f64 1 (+.f64 (-.f64 y z) 1))) z)
	61.2b	(pow.f64 (pow.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z) 3) 1/3)
	54.7b	(*.f64 (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) 2))
	54.7b	(/.f64 (fma.f64 (pow.f64 (cbrt.f64 (+.f64 (-.f64 y z) 1)) 2) (*.f64 (cbrt.f64 (+.f64 (-.f64 y z) 1)) x) 0) z)
	60.1b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z))) 1)
	55.3b	(/.f64 (.f64 -1 (.f64 z x)) z)
▶	52.0b	(*.f64 -1 x)
	62.2b	(/.f64 (pow.f64 (pow.f64 (fma.f64 x (-.f64 y z) x) 3) 1/3) z)
	59.3b	(/.f64 (-.f64 (exp.f64 (log1p.f64 (fma.f64 x (-.f64 y z) x))) 1) z)

Compiler

Compiled 4414 to 1986 computations (55% saved)

localize2.0ms (0%)

prune47.0ms (1.2%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	21	21
Picked	1	1
Done	0	0
Total	22	22

Error

45.1b

Counts

22 → 22

Alt Table

Status	Error	Program
	59.1b	(/.f64 (exp.f64 (log.f64 (fma.f64 x (-.f64 y z) x))) z)
▶	53.2b	(*.f64 (+.f64 (-.f64 y z) 1) (/.f64 x z))
	58.8b	(exp.f64 (log.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)))
	59.4b	(/.f64 (*.f64 (+.f64 1 y) x) z)
	55.7b	(/.f64 (fma.f64 (cbrt.f64 x) (cbrt.f64 (.f64 x x)) (neg.f64 (-.f64 0 (.f64 x (-.f64 y z))))) z)
	58.8b	(/.f64 (*.f64 y x) z)
	62.9b	(/.f64 (log.f64 (exp.f64 (fma.f64 x (-.f64 y z) x))) z)
	60.1b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z) 3))
	54.4b	(/.f64 (*.f64 (-.f64 1 z) x) z)
	54.7b	(/.f64 (pow.f64 (cbrt.f64 (fma.f64 x (-.f64 y z) x)) 3) z)
	57.7b	(fabs.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z))
	60.1b	(/.f64 (/.f64 (*.f64 x (+.f64 1 (pow.f64 (-.f64 y z) 3))) (+.f64 (pow.f64 (-.f64 y z) 2) (-.f64 1 (-.f64 y z)))) z)
	54.7b	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) 3)
	54.5b	(/.f64 (/.f64 x (/.f64 1 (+.f64 (-.f64 y z) 1))) z)
	61.2b	(pow.f64 (pow.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z) 3) 1/3)
	54.7b	(*.f64 (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) 2))
	54.7b	(/.f64 (fma.f64 (pow.f64 (cbrt.f64 (+.f64 (-.f64 y z) 1)) 2) (*.f64 (cbrt.f64 (+.f64 (-.f64 y z) 1)) x) 0) z)
	60.1b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z))) 1)
	55.3b	(/.f64 (.f64 -1 (.f64 z x)) z)
✓	52.0b	(*.f64 -1 x)
	62.2b	(/.f64 (pow.f64 (pow.f64 (fma.f64 x (-.f64 y z) x) 3) 1/3) z)
	59.3b	(/.f64 (-.f64 (exp.f64 (log1p.f64 (fma.f64 x (-.f64 y z) x))) 1) z)

Compiler

Compiled 626 to 399 computations (36.3% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	7.0b	(*.f64 (+.f64 (-.f64 y z) 1) (/.f64 x z))

series13.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

13.0ms

(*.f64 (+.f64 (-.f64 y z) 1) (/.f64 x z))

rewrite74.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

853×	`fma-neg_binary64`
592×	`prod-diff_binary64`
168×	`expm1-udef_binary64`
168×	`log1p-udef_binary64`
131×	`egg-rr`

Counts

1 → 131

Calls

1 calls:

71.0ms

(*.f64 (+.f64 (-.f64 y z) 1) (/.f64 x z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	215	13
2	2802	13
3	5129	13
0	0	0
1	0	0

simplify74.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1275×	`rules-42_binary64`
1005×	`rules-41_binary64`
1005×	`rules-43_binary64`
581×	`rules-40_binary64`
377×	`rules-14-rev_binary64`

Counts

167 → 138

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	360
1	125	360
2	432	252
3	2019	252
4	3556	252
5	16	252

prune119.0ms (3.1%)

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	126	12	138
Fresh	6	14	20
Picked	1	0	1
Done	0	1	1
Total	133	27	160

Error

45.1b

Counts

160 → 27

Alt Table

Status	Error	Program
	54.7b	(/.f64 (fma.f64 (pow.f64 (cbrt.f64 (+.f64 (-.f64 y z) 1)) 2) (*.f64 (cbrt.f64 (+.f64 (-.f64 y z) 1)) x) 0) z)
	53.4b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 x z)) 2) (*.f64 (cbrt.f64 (/.f64 x z)) (+.f64 (-.f64 y z) 1)) 0)
▶	51.0b	(-.f64 (/.f64 x z) x)
	53.4b	(fma.f64 (cbrt.f64 (+.f64 (-.f64 y z) 1)) (*.f64 (/.f64 x z) (pow.f64 (cbrt.f64 (+.f64 (-.f64 y z) 1)) 2)) 0)
	55.3b	(/.f64 (.f64 -1 (.f64 z x)) z)
	60.1b	(cbrt.f64 (pow.f64 (*.f64 (+.f64 (-.f64 y z) 1) (/.f64 x z)) 3))
✓	52.0b	(*.f64 -1 x)
	55.9b	(fabs.f64 (*.f64 (+.f64 (-.f64 y z) 1) (/.f64 x z)))
	59.4b	(/.f64 (*.f64 (+.f64 1 y) x) z)
	58.8b	(exp.f64 (log.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)))
	55.7b	(/.f64 (fma.f64 (cbrt.f64 x) (cbrt.f64 (.f64 x x)) (neg.f64 (-.f64 0 (.f64 x (-.f64 y z))))) z)
	58.8b	(/.f64 (*.f64 y x) z)
	62.9b	(/.f64 (log.f64 (exp.f64 (fma.f64 x (-.f64 y z) x))) z)
	61.2b	(pow.f64 (pow.f64 (*.f64 (+.f64 (-.f64 y z) 1) (/.f64 x z)) 3) 1/3)
	54.7b	(/.f64 (pow.f64 (cbrt.f64 (fma.f64 x (-.f64 y z) x)) 3) z)
	57.7b	(fabs.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z))
	62.2b	(/.f64 (pow.f64 (pow.f64 (fma.f64 x (-.f64 y z) x) 3) 1/3) z)
	58.7b	(/.f64 (/.f64 (.f64 (+.f64 (-.f64 y z) 1) x) (cbrt.f64 (.f64 z z))) (cbrt.f64 z))
	56.0b	(expm1.f64 (log1p.f64 (*.f64 (+.f64 (-.f64 y z) 1) (/.f64 x z))))
	61.2b	(pow.f64 (pow.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z) 3) 1/3)
	53.2b	(/.f64 (+.f64 (-.f64 y z) 1) (/.f64 1 (/.f64 x z)))
	59.3b	(/.f64 (-.f64 (exp.f64 (log1p.f64 (fma.f64 x (-.f64 y z) x))) 1) z)
	62.3b	(fma.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (/.f64 z (+.f64 (-.f64 y z) 1))) 0)
	57.5b	(-.f64 (exp.f64 (log1p.f64 (*.f64 (+.f64 (-.f64 y z) 1) (/.f64 x z)))) 1)
	53.4b	(fma.f64 (cbrt.f64 (.f64 (+.f64 (-.f64 y z) 1) (/.f64 x z))) (pow.f64 (cbrt.f64 (.f64 (+.f64 (-.f64 y z) 1) (/.f64 x z))) 2) 0)
	59.1b	(/.f64 (exp.f64 (log.f64 (fma.f64 x (-.f64 y z) x))) z)
	54.7b	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) 3)

Compiler

Compiled 3842 to 1992 computations (48.2% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 x z) x)

series6.0ms (0.2%)

Counts

1 → 15

Calls

1 calls:

6.0ms

(-.f64 (/.f64 x z) x)

rewrite55.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

599×	`log1p-expm1-u_binary64`
599×	`expm1-log1p-u_binary64`
447×	`prod-diff_binary64`
105×	`expm1-udef_binary64`
105×	`log1p-udef_binary64`

Counts

1 → 67

Calls

1 calls:

53.0ms

(-.f64 (/.f64 x z) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	123	7
2	1696	7
3	4990	7
0	0	0
1	0	0

simplify32.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

485×	`fma-neg_binary64`
271×	`rules-40_binary64`
271×	`rules-41_binary64`
271×	`rules-42_binary64`
271×	`rules-43_binary64`

Counts

82 → 73

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	132
1	83	96
2	229	96
3	926	96
4	958	96

prune71.0ms (1.9%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	64	9	73
Fresh	10	15	25
Picked	1	0	1
Done	0	1	1
Total	75	25	100

Error

44.9b

Counts

100 → 25

Alt Table

Status	Error	Program
	60.8b	(pow.f64 (pow.f64 (-.f64 (/.f64 x z) x) 3) 1/3)
	53.4b	(fma.f64 (cbrt.f64 (.f64 (+.f64 (-.f64 y z) 1) (/.f64 x z))) (pow.f64 (cbrt.f64 (.f64 (+.f64 (-.f64 y z) 1) (/.f64 x z))) 2) 0)
	59.9b	(/.f64 x z)
	53.4b	(fma.f64 (cbrt.f64 (+.f64 (-.f64 y z) 1)) (*.f64 (/.f64 x z) (pow.f64 (cbrt.f64 (+.f64 (-.f64 y z) 1)) 2)) 0)
	55.3b	(/.f64 (.f64 -1 (.f64 z x)) z)
	54.2b	(fabs.f64 (-.f64 (/.f64 x z) x))
✓	52.0b	(*.f64 -1 x)
	58.6b	(/.f64 (/.f64 (-.f64 x (.f64 x z)) (cbrt.f64 (.f64 z z))) (cbrt.f64 z))
	55.9b	(fabs.f64 (*.f64 (+.f64 (-.f64 y z) 1) (/.f64 x z)))
	59.4b	(/.f64 (*.f64 (+.f64 1 y) x) z)
	62.9b	(/.f64 (log.f64 (exp.f64 (fma.f64 x (-.f64 y z) x))) z)
	54.8b	(+.f64 (fma.f64 (cbrt.f64 (*.f64 x x)) (/.f64 (cbrt.f64 x) z) (neg.f64 x)) (fma.f64 -1 x x))
	55.5b	(exp.f64 (log.f64 (-.f64 (/.f64 x z) x)))
	53.2b	(/.f64 (+.f64 (-.f64 y z) 1) (/.f64 1 (/.f64 x z)))
	51.2b	(pow.f64 (cbrt.f64 (-.f64 (/.f64 x z) x)) 3)
	62.3b	(fma.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (/.f64 z (+.f64 (-.f64 y z) 1))) 0)
	59.3b	(/.f64 (-.f64 (exp.f64 (log1p.f64 (fma.f64 x (-.f64 y z) x))) 1) z)
	57.5b	(-.f64 (exp.f64 (log1p.f64 (*.f64 (+.f64 (-.f64 y z) 1) (/.f64 x z)))) 1)
	56.3b	(+.f64 (fma.f64 x (/.f64 1 z) (neg.f64 x)) (fma.f64 (neg.f64 (cbrt.f64 x)) (cbrt.f64 (*.f64 x x)) x))
	54.7b	(/.f64 (fma.f64 (pow.f64 (cbrt.f64 (+.f64 (-.f64 y z) 1)) 2) (*.f64 (cbrt.f64 (+.f64 (-.f64 y z) 1)) x) 0) z)
	59.1b	(/.f64 (exp.f64 (log.f64 (fma.f64 x (-.f64 y z) x))) z)
	59.6b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 x z) x) 3))
	58.8b	(/.f64 (*.f64 y x) z)
	54.7b	(/.f64 (pow.f64 (cbrt.f64 (fma.f64 x (-.f64 y z) x)) 3) z)
	62.2b	(/.f64 (pow.f64 (pow.f64 (fma.f64 x (-.f64 y z) x) 3) 1/3) z)

Compiler

Compiled 1314 to 501 computations (61.9% saved)

regimes701.0ms (18.5%)

Accuracy

Total 9.3b remaining (99.6%)

Threshold costs 0b (0%)

Counts

115 → 4

Compiler

Compiled 8500 to 5354 computations (37% saved)

bsearch83.0ms (2.2%)

Steps

Iters	Range		Point
8	-2.0563373464143146	-0.0015979814906276466	-2.01574423849711
6	-4.166338600322385e+154	-8.231825795729234e+153	-4.11761413583795e+154
7	-5.753744155196295e+209	-2.570467836780386e+208	-2.606579495399084e+208

Compiler

Compiled 4 to 3 computations (25% saved)

simplify16.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	46
1	25	46
2	24	46

end305.0ms (8.1%)

Remove: (sort x y z)
Compiler: Compiled 491 to 329 computations (33% saved)

Details

analyze670.0ms (17.7%)

sample1.1s (28.3%)

simplify25.0ms (0.7%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series22.0ms (0.6%)

rewrite81.0ms (2.1%)

simplify81.0ms (2.2%)

prune214.0ms (5.7%)

localize2.0ms (0%)

prune47.0ms (1.2%)

localize6.0ms (0.2%)

series13.0ms (0.3%)

rewrite74.0ms (2%)

simplify74.0ms (2%)

prune119.0ms (3.1%)

localize3.0ms (0.1%)

series6.0ms (0.2%)

rewrite55.0ms (1.4%)

simplify32.0ms (0.8%)

prune71.0ms (1.9%)

regimes701.0ms (18.5%)

bsearch83.0ms (2.2%)

simplify16.0ms (0.4%)

end305.0ms (8.1%)

Profiling