Details

analyze320.0ms (6.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
25%	25%	50%	2
25%	25%	50%	3
31.2%	18.7%	50%	4
31.2%	18.7%	50%	5
34.3%	15.6%	50%	6
34.3%	15.6%	50%	7
35.9%	14%	50%	8
35.9%	14%	50%	9
36.7%	13.3%	50%	10
36.7%	13.3%	50%	11
37.1%	12.9%	50%	12
37.1%	12.9%	50%	13
37.3%	12.7%	50%	14

Compiler

Compiled 18 to 14 computations (22.2% saved)

sample40.0ms (0.8%)

Algorithm

1×

intervals

Results

8.0ms	189×	body	128	valid
6.0ms	256×	pre	128	true
6.0ms	25×	body	2048	valid
5.0ms	17×	body	4096	valid
2.0ms	14×	body	1024	valid
1.0ms	7×	body	512	valid
0.0ms	4×	body	256	valid

Compiler

Compiled 33 to 28 computations (15.2% saved)

simplify107.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	249	23
1	249	23

prune2.0ms (0%)

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

Error

40.6b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.0b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.8b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
31.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite93.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

40.5b

Rules

11×	`add-sqr-sqrt_binary64_441`
8×	`pow1_binary64_480` `add-log-exp_binary64_458` `*-un-lft-identity_binary64_419`
6×	`add-cube-cbrt_binary64_454`
5×	`sqrt-prod_binary64_435`
4×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455` `sqrt-div_binary64_436`
3×	`sqrt-pow1_binary64_437` `cancel-sign-sub-inv_binary64_385`
2×	`pow1/2_binary64_499` `flip3-+_binary64_422` `flip-+_binary64_393` `flip3--_binary64_423` `flip--_binary64_394` `difference-of-squares_binary64_388` `associate-*r/_binary64_361`
1×	`rem-sqrt-square_binary64_432` `diff-log_binary64_511` `sub-neg_binary64_412` `distribute-lft-out--_binary64_371` `pow-prod-down_binary64_490` `sum-log_binary64_510` `+-commutative_binary64_349`

Counts

4 → 56

Calls

4 calls:

9.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 1418 to 497 computations (65% saved)

series365.0ms (7.2%)

Error

0.5b

Counts

4 → 45

Calls

4 calls:

88.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
84.0ms	(+.f64 (.f64 re re) (.f64 im im))
78.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
75.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 1736 to 1528 computations (12% saved)

simplify52.0ms (1%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5066	1486

prune96.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	94	7	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	7	102

Error

0.5b

Counts

102 → 7

Compiler

Compiled 1891 to 920 computations (51.3% saved)

localize4.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 0.5b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune7.0ms (0.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	6	6
Picked	1	1
Done	0	0
Total	7	7

Error

0.5b

Counts

7 → 7

Compiler

Compiled 99 to 80 computations (19.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 1 im))
0.3b	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
0.5b	(*.f64 re (sqrt.f64 2))
0.5b	(*.f64 (sqrt.f64 im) (sqrt.f64 2))

rewrite193.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

42×	`add-sqr-sqrt_binary64_441`
40×	`sqrt-prod_binary64_435`
28×	`associate-r_binary64_359`
27×	`*-un-lft-identity_binary64_419`
26×	`add-cube-cbrt_binary64_454`
20×	`times-frac_binary64_425`
17×	`pow1_binary64_480`
13×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
10×	`associate-l_binary64_360`
7×	`pow-prod-down_binary64_490`
6×	`unswap-sqr_binary64_387`
5×	`sqrt-pow1_binary64_437` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
4×	`add-log-exp_binary64_458`
3×	`pow1/2_binary64_499` `*-commutative_binary64_350` `rem-sqrt-square_binary64_432`
2×	`sqrt-div_binary64_436` `div-inv_binary64_416`
1×	`sqrt-unprod_binary64_439` `associate-*r/_binary64_361` `inv-pow_binary64_504` `pow-flip_binary64_493`

Counts

4 → 112

Calls

4 calls:

10.0ms	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
7.0ms	(*.f64 (sqrt.f64 im) (sqrt.f64 2))
5.0ms	(*.f64 re (sqrt.f64 2))
3.0ms	(sqrt.f64 (/.f64 1 im))

Compiler

Compiled 2828 to 2228 computations (21.2% saved)

series185.0ms (3.7%)

Error

0.5b

Counts

4 → 15

Calls

4 calls:

97.0ms	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
36.0ms	(*.f64 re (sqrt.f64 2))
22.0ms	(*.f64 (sqrt.f64 im) (sqrt.f64 2))
14.0ms	(sqrt.f64 (/.f64 1 im))

Compiler

Compiled 918 to 816 computations (11.1% saved)

simplify86.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4891	1398
1	4891	1398

prune173.0ms (3.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	126	8	134

Error

0.5b

Counts

134 → 8

Compiler

Compiled 3008 to 2363 computations (21.4% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
0.5b	(*.f64 re (sqrt.f64 2))
0.5b	(*.f64 (sqrt.f64 2) (sqrt.f64 im))
4.8b	(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 im))))

rewrite189.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

32×	`add-sqr-sqrt_binary64_441`
28×	`associate-r_binary64_359`
27×	`sqrt-prod_binary64_435`
20×	`pow1_binary64_480` `add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
13×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
10×	`pow-prod-down_binary64_490` `associate-l_binary64_360`
9×	`times-frac_binary64_425`
7×	`exp-prod_binary64_471`
6×	`unswap-sqr_binary64_387`
5×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
4×	`pow1/2_binary64_499` `log-pow_binary64_508` `sqrt-pow1_binary64_437` `add-log-exp_binary64_458`
3×	`*-commutative_binary64_350`
1×	`log-prod_binary64_505` `exp-sum_binary64_465` `rem-exp-log_binary64_459` `sqrt-unprod_binary64_439` `sqrt-div_binary64_436` `associate-*r/_binary64_361` `div-inv_binary64_416`

Counts

4 → 100

Calls

4 calls:

10.0ms	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
7.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 im))
6.0ms	(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 im))))
5.0ms	(*.f64 re (sqrt.f64 2))

Compiler

Compiled 2725 to 2196 computations (19.4% saved)

series211.0ms (4.2%)

Error

0.5b

Counts

4 → 15

Calls

4 calls:

103.0ms	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
37.0ms	(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 im))))
32.0ms	(*.f64 re (sqrt.f64 2))
21.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 im))

Compiler

Compiled 1039 to 939 computations (9.6% saved)

simplify83.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5157	1285

prune163.0ms (3.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	115	8	123

Error

0.5b

Counts

123 → 8

Compiler

Compiled 2838 to 2289 computations (19.3% saved)

regimes765.0ms (15.1%)

Accuracy

Total 15.1b remaining (97%)

Threshold costs 0b (0%)

Compiler

Compiled 5552 to 4316 computations (22.3% saved)

bsearch74.0ms (1.5%)

Steps

Iters	Range		Point
7	4.3650973378345744e-61	1.971126332909892e-59	1.8325515919274365e-60
5	1.2882580288630576e-168	4.240800318280748e-168	1.3178163098264688e-168
7	3.561542614034214e-181	9.254579470387835e-180	1.754922286482946e-180
8	-1.6575500661622083e+37	-4.519289074705631e+34	-4.588012152373333e+34

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	81
1	63	81

end0.0ms (0%)

sample1.8s (35.7%)

Algorithm

1×

intervals

Results

287.0ms	6054×	body	128	valid
157.0ms	530×	body	4096	valid
146.0ms	651×	body	2048	valid
106.0ms	8000×	pre	128	true
73.0ms	419×	body	1024	valid
29.0ms	223×	body	512	valid
11.0ms	123×	body	256	valid

Compiler

Compiled 759 to 600 computations (20.9% saved)

Details

analyze320.0ms (6.3%)

sample40.0ms (0.8%)

simplify107.0ms (2.1%)

prune2.0ms (0%)

localize10.0ms (0.2%)

rewrite93.0ms (1.8%)

series365.0ms (7.2%)

simplify52.0ms (1%)

prune96.0ms (1.9%)

localize4.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0.1%)

prune7.0ms (0.1%)

localize12.0ms (0.2%)

rewrite193.0ms (3.8%)

series185.0ms (3.7%)

simplify86.0ms (1.7%)

prune173.0ms (3.4%)

localize15.0ms (0.3%)

rewrite189.0ms (3.7%)

series211.0ms (4.2%)

simplify83.0ms (1.6%)

prune163.0ms (3.2%)

regimes765.0ms (15.1%)

bsearch74.0ms (1.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.8s (35.7%)

Profiling