Details

analyze71.0ms (1.2%)

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)

sample39.0ms (0.6%)

Algorithm

1×

intervals

Results

24.0ms

256×

body

128

valid

Compiler

Compiled 31 to 23 computations (25.8% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 1

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	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

0.6b

Counts

2 → 1

Alt Table

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

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(hypot.f64 re im)
0.6b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))

rewrite98.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

19×	`pow1_binary64`
11×	`log-pow_binary64`
10×	`add-cbrt-cube_binary64`
10×	`add-cube-cbrt_binary64`
8×	`add-exp-log_binary64`

Counts

2 → 77

Calls

2 calls:

13.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))
10.0ms	(hypot.f64 re im)

Compiler

Compiled 746 to 408 computations (45.3% saved)

series72.0ms (1.2%)

Error

0.6b

Counts

2 → 30

Calls

2 calls:

33.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))
28.0ms	(hypot.f64 re im)

Compiler

Compiled 1214 to 1004 computations (17.3% saved)

simplify84.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

610×	`div-exp_binary64`
576×	`fma-neg_binary64`
459×	`times-frac_binary64`
408×	`fma-def_binary64`
371×	`cancel-sign-sub-inv_binary64`

Counts

107 → 47

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	125	1141
1	273	1070
2	760	1043
3	2550	1025
4	4664	1019
5	5719	1019

prune25.0ms (0.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	42	5	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	42	6	48

Error

0.3b

Counts

48 → 6

Alt Table

Status	Error	Program
✓	0.6b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))
	32.0b	(/.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (hypot.f64 re im) 2)) (cbrt.f64 (hypot.f64 re im)))) (log.f64 10))
	17.6b	(*.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))))
	0.8b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 2)) (cbrt.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))
	1.0b	(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 10))))

Compiler

Compiled 593 to 390 computations (34.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(hypot.f64 re im)
0.5b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3))
0.6b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))
0.8b	(pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3)

rewrite178.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

24×	`pow1_binary64`
24×	`add-cube-cbrt_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`

Counts

4 → 164

Calls

4 calls:

14.0ms	(pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3)
12.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))
12.0ms	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3))
9.0ms	(hypot.f64 re im)

Compiler

Compiled 1921 to 1230 computations (36% saved)

series201.0ms (3.3%)

Error

0.2b

Counts

4 → 53

Calls

4 calls:

70.0ms	(pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3)
41.0ms	(hypot.f64 re im)
31.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))
29.0ms	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3))

Compiler

Compiled 2919 to 2501 computations (14.3% saved)

simplify90.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

705×	`associate-*l/_binary64`
273×	`unswap-sqr_binary64`
226×	`times-frac_binary64`
190×	`associate-/r/_binary64`
166×	`associate-/r*_binary64`

Counts

217 → 112

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	235	2712
1	525	2516
2	1980	2420
3	5445	2420

prune64.0ms (1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	104	8	112
Fresh	1	3	4
Picked	1	0	1
Done	1	0	1
Total	107	11	118

Error

0.1b

Counts

118 → 11

Alt Table

Status	Error	Program
	0.8b	(cbrt.f64 (pow.f64 (*.f64 (cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 2)) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)))) 3))
	0.7b	(cbrt.f64 (cbrt.f64 (pow.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3) 3)))
	0.9b	(*.f64 (cbrt.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3)) (/.f64 1 (log.f64 10)))
	32.0b	(/.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (hypot.f64 re im) 2)) (cbrt.f64 (hypot.f64 re im)))) (log.f64 10))
▶	0.7b	(/.f64 1 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))))
	0.8b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 2)) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	18.1b	(cbrt.f64 (exp.f64 (*.f64 3 (log.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))))
	0.7b	(cbrt.f64 (/.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3) (*.f64 (log.f64 10) (log.f64 10))) (log.f64 10)))
	17.6b	(*.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))))
	17.6b	(cbrt.f64 (*.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3/2) (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3/2)))
	0.7b	(cbrt.f64 (*.f64 (cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 6)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))

Compiler

Compiled 1499 to 1047 computations (30.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(hypot.f64 re im)
0.3b	(/.f64 1 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))))
0.6b	(/.f64 (log.f64 10) (log.f64 (hypot.f64 re im)))

rewrite157.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

26×	`add-cube-cbrt_binary64`
23×	`pow1_binary64`
18×	`add-exp-log_binary64`
17×	`add-cbrt-cube_binary64`
12×	`add-sqr-sqrt_binary64`

Counts

3 → 129

Calls

3 calls:

47.0ms	(/.f64 1 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))))
12.0ms	(/.f64 (log.f64 10) (log.f64 (hypot.f64 re im)))
10.0ms	(hypot.f64 re im)

Compiler

Compiled 1556 to 958 computations (38.4% saved)

series270.0ms (4.4%)

Error

0.1b

Counts

3 → 48

Calls

3 calls:

176.0ms	(/.f64 (log.f64 10) (log.f64 (hypot.f64 re im)))
33.0ms	(/.f64 1 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))))
31.0ms	(hypot.f64 re im)

Compiler

Compiled 3346 to 2804 computations (16.2% saved)

simplify158.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

462×	`fma-def_binary64`
301×	`times-frac_binary64`
299×	`fma-neg_binary64`
272×	`cancel-sign-sub-inv_binary64`
238×	`unswap-sqr_binary64`

Counts

177 → 93

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	266	2746
1	749	2479
2	2961	2444
3	4891	2438
4	4978	2438
5	5000	2438
6	4943	2438

prune65.0ms (1.1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	89	15	104

Error

0.0b

Counts

104 → 15

Alt Table

Status	Error	Program
	0.8b	(cbrt.f64 (pow.f64 (*.f64 (cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 2)) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)))) 3))
▶	0.7b	(cbrt.f64 (cbrt.f64 (pow.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3) 3)))
	18.1b	(cbrt.f64 (exp.f64 (*.f64 3 (log.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))))
	0.9b	(/.f64 1 (*.f64 (cbrt.f64 (pow.f64 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))) 2)) (cbrt.f64 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))))))
	0.7b	(cbrt.f64 (/.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3) (*.f64 (log.f64 10) (log.f64 10))) (log.f64 10)))
	0.7b	(/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))) 3)))
	0.9b	(*.f64 (cbrt.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3)) (/.f64 1 (log.f64 10)))
	32.0b	(/.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (hypot.f64 re im) 2)) (cbrt.f64 (hypot.f64 re im)))) (log.f64 10))
	17.6b	(*.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))))
	1.2b	(.f64 (cbrt.f64 (/.f64 1 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))))) (.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)))))
✓	0.7b	(/.f64 1 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))))
	0.8b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 2)) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	1.4b	(/.f64 (/.f64 1 (cbrt.f64 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))))) (*.f64 (cbrt.f64 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im)))) (cbrt.f64 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))))))
	17.6b	(cbrt.f64 (*.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3/2) (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3/2)))
	0.7b	(cbrt.f64 (*.f64 (cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 6)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))

Compiler

Compiled 1899 to 1301 computations (31.5% saved)

localize70.0ms (1.1%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (pow.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3) 3))
0.6b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))
0.7b	(pow.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3) 3)
0.8b	(pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3)

rewrite182.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

26×	`add-cube-cbrt_binary64`
22×	`cube-div_binary64`
22×	`pow1_binary64`
16×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`

Counts

4 → 181

Calls

4 calls:

14.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))
13.0ms	(pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3)
13.0ms	(pow.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3) 3)
10.0ms	(cbrt.f64 (pow.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3) 3))

Compiler

Compiled 2581 to 1819 computations (29.5% saved)

series319.0ms (5.2%)

Error

0.0b

Counts

4 → 41

Calls

4 calls:

141.0ms	(pow.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3) 3)
66.0ms	(cbrt.f64 (pow.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3) 3))
61.0ms	(pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3)
16.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))

Compiler

Compiled 3416 to 2998 computations (12.2% saved)

simplify127.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

633×	`unswap-sqr_binary64`
291×	`times-frac_binary64`
234×	`fma-def_binary64`
203×	`associate-/r*_binary64`
165×	`log-prod_binary64`

Counts

222 → 119

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	263	3289
1	617	3101
2	2497	3010
3	4867	3010
4	4993	3010

prune73.0ms (1.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	115	4	119
Fresh	5	8	13
Picked	1	0	1
Done	0	1	1
Total	121	13	134

Error

0.0b

Counts

134 → 13

Alt Table

Status	Error	Program
	0.7b	(cbrt.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (pow.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3) 3) 3))))
	0.9b	(/.f64 1 (*.f64 (cbrt.f64 (pow.f64 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))) 2)) (cbrt.f64 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))))))
	0.7b	(cbrt.f64 (/.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3) (*.f64 (log.f64 10) (log.f64 10))) (log.f64 10)))
	0.7b	(/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))) 3)))
	17.6b	(*.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))))
	1.2b	(.f64 (cbrt.f64 (/.f64 1 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))))) (.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)))))
	0.7b	(/.f64 1 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))))
	0.8b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 2)) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	17.9b	(cbrt.f64 (-.f64 (exp.f64 (log1p.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3))) 1))
	1.4b	(/.f64 (/.f64 1 (cbrt.f64 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))))) (*.f64 (cbrt.f64 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im)))) (cbrt.f64 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))))))
	17.6b	(cbrt.f64 (cbrt.f64 (*.f64 (pow.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3) 3/2) (pow.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3) 3/2))))
	18.1b	(cbrt.f64 (cbrt.f64 (pow.f64 (exp.f64 (*.f64 3 (log.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))) 3)))
	32.0b	(/.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (hypot.f64 re im) 2)) (cbrt.f64 (hypot.f64 re im)))) (log.f64 10))

Compiler

Compiled 1630 to 1200 computations (26.4% saved)

regimes2.7s (43.3%)

Accuracy

Total 0.5b remaining (90.6%)

Threshold costs 0.5b (90.6%)

Compiler

Compiled 36494 to 29897 computations (18.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	11	16

end7.0ms (0.1%)

Remove: (sort re im)
Compiler: Compiled 36 to 30 computations (16.7% saved)

sample1.1s (18%)

Algorithm

1×

intervals

Results

644.0ms

8000×

body

128

valid

Compiler

Compiled 290 to 223 computations (23.1% saved)

Details

analyze71.0ms (1.2%)

sample39.0ms (0.6%)

simplify11.0ms (0.2%)

prune3.0ms (0%)

localize7.0ms (0.1%)

rewrite98.0ms (1.6%)

series72.0ms (1.2%)

simplify84.0ms (1.4%)

prune25.0ms (0.4%)

localize10.0ms (0.2%)

rewrite178.0ms (2.9%)

series201.0ms (3.3%)

simplify90.0ms (1.5%)

prune64.0ms (1%)

localize8.0ms (0.1%)

rewrite157.0ms (2.5%)

series270.0ms (4.4%)

simplify158.0ms (2.6%)

prune65.0ms (1.1%)

localize70.0ms (1.1%)

rewrite182.0ms (2.9%)

series319.0ms (5.2%)

simplify127.0ms (2.1%)

prune73.0ms (1.2%)

regimes2.7s (43.3%)

simplify3.0ms (0%)

end7.0ms (0.1%)

sample1.1s (18%)

Profiling