Details

analyze431.0ms (9.2%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
23.4%	51.5%	25.1%	7
24.2%	50.7%	25.1%	8
24.6%	50.3%	25.1%	9
36.9%	25.5%	37.6%	10
37.2%	25.3%	37.6%	11
37.3%	25.1%	37.6%	12
43.5%	12.7%	43.8%	13
43.6%	12.6%	43.8%	14

Compiler

Compiled 29 to 21 computations (27.6% saved)

sample36.0ms (0.8%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	80	valid
3.0ms	30×	body	80	nan

Compiler

Compiled 57 to 44 computations (22.8% saved)

simplify130.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (120.0ms)

Iter	Nodes	Cost
0	5538	19

prune10.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 33.0b

Counts

2 → 2

Compiler

Compiled 52 to 40 computations (23.1% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.4b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
30.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64`
22×	`log-pow_binary64`
20×	`pow1_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`pow1/2_binary64` `sqrt-pow1_binary64` `associate-/l*_binary64`
4×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`sqrt-prod_binary64`
2×	`flip3-+_binary64` `add-log-exp_binary64` `div-sub_binary64` `log-div_binary64` `flip-+_binary64`
1×	`cbrt-undiv_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

2 → 63

Calls

2 calls:

8.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series32.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

25.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify87.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5800	1640

prune87.0ms (1.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	58	11	69
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	59	12	71

Merged error: 7.7b

Counts

71 → 12

Compiler

Compiled 1521 to 383 computations (74.8% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.3b	(/.f64 1 (log.f64 base))
0.4b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 1 (log.f64 base)))
30.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite21.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
26×	`times-frac_binary64`
23×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
16×	`pow1_binary64` `associate-r_binary64` `add-exp-log_binary64`
10×	`log-pow_binary64` `add-cbrt-cube_binary64`
6×	`associate-l_binary64`
4×	`associate-/r*_binary64` `prod-exp_binary64` `div-exp_binary64`
3×	`add-log-exp_binary64` `unswap-sqr_binary64` `associate-/l*_binary64` `sqrt-prod_binary64`
2×	`pow1/2_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rec-exp_binary64` `div-inv_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-r/_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `pow-flip_binary64` `flip-+_binary64` `-commutative_binary64`

Counts

3 → 92

Calls

3 calls:

10.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 1 (log.f64 base)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(/.f64 1 (log.f64 base))

series46.0ms (1%)

Counts

3 → 9

Calls

3 calls:

27.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 1 (log.f64 base)))
13.0ms	(/.f64 1 (log.f64 base))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify94.0ms (2%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5575	1589

prune89.0ms (1.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	94	7	101
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	98	15	113

Merged error: 7.7b

Counts

113 → 15

Compiler

Compiled 2069 to 674 computations (67.4% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.3b	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
0.4b	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
31.8b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

140×	`times-frac_binary64`
71×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
46×	`pow1_binary64`
43×	`log-pow_binary64`
24×	`associate-/r*_binary64`
11×	`add-exp-log_binary64`
10×	`add-cbrt-cube_binary64`
7×	`associate-/l*_binary64`
6×	`div-inv_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`add-log-exp_binary64` `log-prod_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `log-div_binary64`
1×	`flip3-+_binary64` `rem-log-exp_binary64` `associate-/r/_binary64` `flip-+_binary64`

Counts

3 → 148

Calls

3 calls:

7.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
4.0ms	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
4.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

series76.0ms (1.6%)

Counts

3 → 9

Calls

3 calls:

34.0ms	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
33.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
9.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify118.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5411	4669

prune123.0ms (2.6%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	151	6	157
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	154	18	172

Merged error: 7.7b

Counts

172 → 18

Compiler

Compiled 3897 to 1078 computations (72.3% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
0.4b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
0.6b	(*.f64 (log.f64 base) (log.f64 base))
30.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite30.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
23×	`pow1_binary64` `add-cube-cbrt_binary64`
12×	`log-prod_binary64`
10×	`log-pow_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
9×	`times-frac_binary64`
8×	`associate-r_binary64`
6×	`swap-sqr_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`add-log-exp_binary64`
3×	`flip3-+_binary64` `associate-/r_binary64` `associate-/l_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`pow-prod-up_binary64` `cbrt-undiv_binary64` `pow-plus_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow-sqr_binary64` `pow2_binary64`

Counts

4 → 110

Calls

4 calls:

11.0ms	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
6.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
5.0ms	(*.f64 (log.f64 base) (log.f64 base))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series63.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

26.0ms	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
20.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
10.0ms	(*.f64 (log.f64 base) (log.f64 base))
6.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify94.0ms (2%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5260	2445

prune79.0ms (1.7%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	1	16	17
Picked	0	1	1
Done	0	0	0
Total	120	20	140

Merged error: 7.7b

Counts

140 → 20

Compiler

Compiled 3835 to 1247 computations (67.5% saved)

regimes550.0ms (11.7%)

Compiler: Compiled 1721 to 1326 computations (23% saved)

bsearch135.0ms (2.9%)

Steps

Iters	Range		Point
2	1.1564828128829714e+40	1.3925002093196445e+40	1.1859849874375555e+40
9	1.1506657958549418e-232	6.80726697281899e-227	1.2029630995824736e-228
11	-6.508309011806639e-160	-2.711778503539071e-181	-1.5366008112942153e-167
5	-2.4652733754771875e+97	-1.0810056581737977e+97	-1.3796695805914547e+97

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	126
1	49	126

end0.0ms (0%)

sample2.3s (48.4%)

Algorithm

1×

intervals

Results

743.0ms	8000×	body	80	valid
87.0ms	994×	body	80	nan

Compiler

Compiled 440 to 315 computations (28.4% saved)

Details

analyze431.0ms (9.2%)

sample36.0ms (0.8%)

simplify130.0ms (2.8%)

prune10.0ms (0.2%)

localize11.0ms (0.2%)

rewrite15.0ms (0.3%)

series32.0ms (0.7%)

simplify87.0ms (1.9%)

prune87.0ms (1.9%)

localize12.0ms (0.3%)

rewrite21.0ms (0.5%)

series46.0ms (1%)

simplify94.0ms (2%)

prune89.0ms (1.9%)

localize12.0ms (0.2%)

rewrite23.0ms (0.5%)

series76.0ms (1.6%)

simplify118.0ms (2.5%)

prune123.0ms (2.6%)

localize18.0ms (0.4%)

rewrite30.0ms (0.6%)

series63.0ms (1.3%)

simplify94.0ms (2%)

prune79.0ms (1.7%)

regimes550.0ms (11.7%)

bsearch135.0ms (2.9%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.3s (48.4%)

Profiling