Details

analyze448.0ms (2.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	338	46
1	338	46
0	2	2
1	2	2

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)

sample36.0ms (0.2%)

Algorithm

1×

intervals

Results

12.0ms	196×	body	128	valid
5.0ms	19×	body	4096	valid
5.0ms	21×	body	2048	valid
4.0ms	256×	pre	128	true
2.0ms	12×	body	1024	valid
1.0ms	5×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 33 to 28 computations (15.2% saved)

simplify24.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	249	23
1	249	23

prune3.0ms (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

39.1b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.1b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.7b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite31.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

series192.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

112.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
32.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
20.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify83.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4930	1140
1	4930	1140

prune87.0ms (0.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	60	8	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	8	69

Error

8.8b

Counts

69 → 8

Compiler

Compiled 1491 to 664 computations (55.5% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

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

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow1_binary64_480`
2×	`sqrt-div_binary64_436` `associate-*r/_binary64_361` `sqrt-pow1_binary64_437`
1×	`*-un-lft-identity_binary64_419` `pow-prod-down_binary64_490` `add-log-exp_binary64_458` `add-cube-cbrt_binary64_454` `pow1/2_binary64_499` `add-sqr-sqrt_binary64_441` `flip3--_binary64_423` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `flip--_binary64_394` `sqrt-prod_binary64_435`

Counts

1 → 13

Calls

1 calls:

5.0ms

(sqrt.f64 (*.f64 2 (-.f64 im re)))

series55.0ms (0.3%)

Counts

1 → 3

Calls

1 calls:

55.0ms

(sqrt.f64 (*.f64 2 (-.f64 im re)))

simplify57.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4956	255
1	4956	255

prune23.0ms (0.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	15	1	16
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	15	9	24

Error

8.8b

Counts

24 → 9

Compiler

Compiled 376 to 258 computations (31.4% saved)

localize8.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (*.f64 2 (-.f64 im re)))
3.5b	(exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1_binary64_480`
7×	`exp-prod_binary64_471`
4×	`-un-lft-identity_binary64_419` `sqrt-div_binary64_436` `add-cube-cbrt_binary64_454` `log-prod_binary64_505` `add-sqr-sqrt_binary64_441` `associate-r/_binary64_361` `log-pow_binary64_508` `exp-sum_binary64_465` `sqrt-pow1_binary64_437`
2×	`pow-prod-down_binary64_490` `exp-diff_binary64_467` `add-log-exp_binary64_458` `pow1/2_binary64_499` `flip3--_binary64_423` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `flip--_binary64_394` `sqrt-prod_binary64_435` `log-div_binary64_506`
1×	`rem-exp-log_binary64_459`

Counts

2 → 34

Calls

2 calls:

7.0ms	(exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))
5.0ms	(sqrt.f64 (*.f64 2 (-.f64 im re)))

series234.0ms (1.1%)

Counts

2 → 6

Calls

2 calls:

183.0ms	(exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))
51.0ms	(sqrt.f64 (*.f64 2 (-.f64 im re)))

simplify42.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5259	606

prune45.0ms (0.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	39	1	40
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	40	9	49

Error

8.8b

Counts

49 → 9

Compiler

Compiled 789 to 544 computations (31.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(cbrt.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))
0.4b	(cbrt.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))
2.0b	(exp.f64 (.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))) (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))))
3.5b	(pow.f64 (exp.f64 (.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))))) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))))

rewrite28.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`cbrt-prod_binary64_450`
17×	`pow1_binary64_480`
12×	`log-pow_binary64_508`
10×	`pow-unpow_binary64_496`
9×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
7×	`add-log-exp_binary64_458`
6×	`sqrt-pow1_binary64_437`
4×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`pow-prod-down_binary64_490` `unpow-prod-down_binary64_498` `pow1/2_binary64_499` `pow-pow_binary64_491`
2×	`pow1/3_binary64_501` `exp-to-pow_binary64_481` `exp-prod_binary64_471`
1×	`pow-exp_binary64_487` `sqr-pow_binary64_391` `pow-to-exp_binary64_488` `rem-exp-log_binary64_459`

Counts

4 → 66

Calls

4 calls:

7.0ms	(cbrt.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))
7.0ms	(pow.f64 (exp.f64 (.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))))) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))))
5.0ms	(cbrt.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))
2.0ms	(exp.f64 (.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))) (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))))

series16.7s (77.4%)

Counts

4 → 12

Calls

4 calls:

10.6s	(pow.f64 (exp.f64 (.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))))) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))))
2.1s	(cbrt.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))
2.1s	(cbrt.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))
1.8s	(exp.f64 (.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))) (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))))

simplify131.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5037	14250

prune637.0ms (3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	77	10	87

Error

8.8b

Counts

87 → 10

Compiler

Compiled 9635 to 7198 computations (25.3% saved)

regimes764.0ms (3.5%)

Accuracy

Total 10.4b remaining (51.1%)

Threshold costs 0b (0%)

Compiler

Compiled 6587 to 4800 computations (27.1% saved)

bsearch69.0ms (0.3%)

Steps

Iters	Range		Point
10	2.5275864304172245e-61	2.621070765314153e-51	2.5529104624380686e-61
9	-8.482556092597006e-37	-1.903745674079318e-42	-1.9300912174625423e-42
6	-2.29028409903959e+76	-1.8323520695723772e+75	-2.2499199913069257e+76

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	96
1	61	96

end0.0ms (0%)

sample1.8s (8.4%)

Algorithm

1×

intervals

Results

304.0ms	6130×	body	128	valid
151.0ms	653×	body	2048	valid
141.0ms	493×	body	4096	valid
114.0ms	8000×	pre	128	true
75.0ms	405×	body	1024	valid
29.0ms	205×	body	512	valid
10.0ms	114×	body	256	valid

Compiler

Compiled 903 to 656 computations (27.4% saved)

Details

analyze448.0ms (2.1%)

sample36.0ms (0.2%)

simplify24.0ms (0.1%)

prune3.0ms (0%)

localize10.0ms (0%)

rewrite31.0ms (0.1%)

series192.0ms (0.9%)

simplify83.0ms (0.4%)

prune87.0ms (0.4%)

localize5.0ms (0%)

rewrite5.0ms (0%)

series55.0ms (0.3%)

simplify57.0ms (0.3%)

prune23.0ms (0.1%)

localize8.0ms (0%)

rewrite14.0ms (0.1%)

series234.0ms (1.1%)

simplify42.0ms (0.2%)

prune45.0ms (0.2%)

localize14.0ms (0.1%)

rewrite28.0ms (0.1%)

series16.7s (77.4%)

simplify131.0ms (0.6%)

prune637.0ms (3%)

regimes764.0ms (3.5%)

bsearch69.0ms (0.3%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.8s (8.4%)

Profiling