Details

analyze19.0ms (0.3%)

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
74.9%	25%	0.1%	3
87.4%	12.5%	0.1%	4
93.7%	6.2%	0.1%	5
96.8%	3.1%	0.1%	6
98.3%	1.6%	0.1%	7
99.1%	0.8%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample36.0ms (0.5%)

Algorithm

1×

intervals

Results

21.0ms

256×

body

128

valid

Compiler

Compiled 31 to 23 computations (25.8% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`hypot-def_binary64`
2×	`fma-def_binary64`
1×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	11
1	14	11
2	16	11
3	16	11

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

0.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.6b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))

Compiler

Compiled 39 to 29 computations (25.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 re im)
✓	0.6b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))

series47.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

35.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))
12.0ms	(hypot.f64 re im)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`times-frac_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
12×	`pow1_binary64`

Counts

2 → 48

Calls

2 calls:

3.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))
0.0ms	(hypot.f64 re im)

simplify81.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

783×	`times-frac_binary64`
715×	`fma-neg_binary64`
436×	`associate-/r*_binary64`
404×	`associate-/l*_binary64`
347×	`fma-def_binary64`

Counts

96 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	2237
1	472	2152
2	1292	2092
3	4552	2092
4	5054	2092

prune84.0ms (1.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	101	12	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	12	114

Error

0.1b

Counts

114 → 12

Alt Table

Status	Error	Program
	16.6b	(/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 10) (sqrt.f64 (log.f64 (hypot.f64 re im)))))
	16.9b	(exp.f64 (log.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	0.7b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3))
	1.3b	(/.f64 (*.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (/.f64 (log.f64 10) (cbrt.f64 (log.f64 (hypot.f64 re im)))))
	16.9b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	0.6b	(/.f64 1 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))))
	16.7b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (log.f64 10)))
	1.3b	(.f64 (/.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (sqrt.f64 (log.f64 10))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (sqrt.f64 (log.f64 10))))
▶	0.6b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))
	16.6b	(*.f64 (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))) (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	0.7b	(cbrt.f64 (/.f64 (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (.f64 (.f64 (log.f64 10) (log.f64 10)) (log.f64 10))))
	1.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))

Compiler

Compiled 2636 to 1807 computations (31.4% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.3b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))
✓	0.4b	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))

series72.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

38.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))
33.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`times-frac_binary64`
96×	`add-sqr-sqrt_binary64`
59×	`sqrt-prod_binary64`
56×	`*-un-lft-identity_binary64`
50×	`add-cube-cbrt_binary64`

Counts

2 → 151

Calls

2 calls:

19.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))
4.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))

simplify217.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

605×	`fma-def_binary64`
563×	`associate-/r*_binary64`
405×	`fma-neg_binary64`
308×	`associate-/l/_binary64`
218×	`cancel-sign-sub-inv_binary64`

Counts

199 → 236

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	265	5977
1	731	5300
2	2185	5063
3	4589	5035
4	4992	5035
5	4986	5035
6	4960	5035

prune229.0ms (3.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	272	6	278
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	280	10	290

Error

0.0b

Counts

290 → 10

Alt Table

Status	Error	Program
	0.7b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3))
	0.6b	(/.f64 (*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (hypot.f64 re im))) (sqrt.f64 (log.f64 10)))
	1.3b	(/.f64 (*.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (/.f64 (log.f64 10) (cbrt.f64 (log.f64 (hypot.f64 re im)))))
	16.9b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	16.7b	(*.f64 (/.f64 (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))) (sqrt.f64 (log.f64 10))) (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))))
	1.2b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (*.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))))
▶	0.3b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
	16.9b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (exp.f64 (log.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))))
	0.7b	(cbrt.f64 (/.f64 (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (.f64 (.f64 (log.f64 10) (log.f64 10)) (log.f64 10))))
	0.7b	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))))

Compiler

Compiled 7628 to 5756 computations (24.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.3b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
✓	1.0b	(/.f64 1 (log.f64 10))
✓	3.7b	(pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))

series161.0ms (2.4%)

Counts

3 → 48

Calls

3 calls:

95.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
65.0ms	(pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))
0.0ms	(/.f64 1 (log.f64 10))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`add-sqr-sqrt_binary64`
49×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`
30×	`sqrt-prod_binary64`

Counts

3 → 139

Calls

3 calls:

12.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
3.0ms	(pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))
3.0ms	(/.f64 1 (log.f64 10))

simplify182.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

343×	`associate-r_binary64`
295×	`fma-neg_binary64`
291×	`associate-l_binary64`
257×	`fma-def_binary64`
243×	`associate-/l*_binary64`

Counts

187 → 262

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	413	7156
1	1220	6771
2	4788	6769
3	5016	6769

prune364.0ms (5.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	301	3	304
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	305	9	314

Error

Counts

314 → 9

Alt Table

Status	Error	Program
✓	0.3b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
▶	0.3b	(*.f64 (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10))) (log.f64 (hypot.f64 re im)))
	0.6b	(/.f64 (*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (hypot.f64 re im))) (sqrt.f64 (log.f64 10)))
	1.3b	(/.f64 (*.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (/.f64 (log.f64 10) (cbrt.f64 (log.f64 (hypot.f64 re im)))))
	0.7b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (log.f64 (hypot.f64 re im))) (sqrt.f64 (log.f64 10))) 3))
	1.2b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (*.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))))
	16.9b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (exp.f64 (log.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))))
	0.7b	(cbrt.f64 (/.f64 (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (.f64 (.f64 (log.f64 10) (log.f64 10)) (log.f64 10))))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10)))))))

Compiler

Compiled 11076 to 9230 computations (16.7% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.3b	(*.f64 (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10))) (log.f64 (hypot.f64 re im)))
	1.0b	(/.f64 1 (log.f64 10))

series34.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

33.0ms

(*.f64 (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10))) (log.f64 (hypot.f64 re im)))

rewrite57.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

229×	`times-frac_binary64`
198×	`sqrt-prod_binary64`
137×	`associate-l_binary64`
134×	`add-sqr-sqrt_binary64`
108×	`*-un-lft-identity_binary64`

Counts

1 → 172

Calls

1 calls:

27.0ms

(*.f64 (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10))) (log.f64 (hypot.f64 re im)))

simplify169.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

736×	`fma-neg_binary64`
618×	`times-frac_binary64`
478×	`associate-/l*_binary64`
376×	`associate-l_binary64`
338×	`associate-/r*_binary64`

Counts

196 → 214

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	210	5783
1	504	5613
2	1312	5569
3	4589	5569
4	5204	5569

prune323.0ms (4.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	291	1	292
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	292	9	301

Error

Counts

301 → 9

Alt Table

Status	Error	Program
	0.2b	(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10)))))
	1.3b	(/.f64 (*.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (/.f64 (log.f64 10) (cbrt.f64 (log.f64 (hypot.f64 re im)))))
✓	0.3b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
✓	0.3b	(*.f64 (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10))) (log.f64 (hypot.f64 re im)))
	0.7b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (log.f64 (hypot.f64 re im))) (sqrt.f64 (log.f64 10))) 3))
	1.2b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (*.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))))
	16.9b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (exp.f64 (log.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))))
	0.7b	(cbrt.f64 (/.f64 (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (.f64 (.f64 (log.f64 10) (log.f64 10)) (log.f64 10))))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10)))))))

Compiler

Compiled 8080 to 6628 computations (18% saved)

regimes2.4s (36.4%)

Accuracy

Total 0.1b remaining (84.6%)

Threshold costs 0.1b (84.6%)

Counts

113 → 1

Compiler

Compiled 17930 to 14468 computations (19.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	26
1	16	26
2	15	26

end14.0ms (0.2%)

Remove: (sort re im)
Compiler: Compiled 54 to 48 computations (11.1% saved)

sample2.0s (30.4%)

Algorithm

1×

intervals

Results

1.2s

8000×

body

128

valid

Compiler

Compiled 233 to 183 computations (21.5% saved)

Details

analyze19.0ms (0.3%)

sample36.0ms (0.5%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series47.0ms (0.7%)

rewrite5.0ms (0.1%)

simplify81.0ms (1.2%)

prune84.0ms (1.3%)

localize10.0ms (0.1%)

series72.0ms (1.1%)

rewrite38.0ms (0.6%)

simplify217.0ms (3.3%)

prune229.0ms (3.4%)

localize14.0ms (0.2%)

series161.0ms (2.4%)

rewrite28.0ms (0.4%)

simplify182.0ms (2.7%)

prune364.0ms (5.5%)

localize11.0ms (0.2%)

series34.0ms (0.5%)

rewrite57.0ms (0.9%)

simplify169.0ms (2.5%)

prune323.0ms (4.8%)

regimes2.4s (36.4%)

simplify4.0ms (0.1%)

end14.0ms (0.2%)

sample2.0s (30.4%)

Profiling