Details

sample35.0ms

Algorithm

intervals

Results

9.0ms	191×	body	80	valid
8.0ms	30×	body	2560	valid
3.0ms	14×	body	1280	valid
2.0ms	11×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	15
1	31	15

prune7.0ms

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: 38.9b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.0b	(+ (* re re) (* im im))
0.9b	(- (sqrt (+ (* re re) (* im im))) re)
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`pow1` `add-log-exp`
7×	`*-un-lft-identity`
5×	`add-cube-cbrt` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`sqrt-pow1`
2×	`flip3--` `flip3-+` `pow1/2` `associate-*r/` `flip--` `flip-+` `difference-of-squares`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `diff-log` `pow-prod-down` `sum-log` `distribute-lft-out--`

Counts

4 → 54

Calls

4 calls:

7.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
4.0ms	(+ (* re re) (* im im))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series43.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
5.0ms	(+ (* re re) (* im im))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify42.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5269	741

prune129.0ms

Filtered

52 candidates to 66 candidates (-26.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	57	9	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	9	67

Merged error: 18.9b

Counts

67 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.7b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.2b	(sqrt (+ (* re re) (* im im)))
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
51×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
8×	`flip3-+` `flip-+`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod` `difference-of-squares`

Counts

4 → 126

Calls

4 calls:

15.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
14.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series27.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
10.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5835	1498

prune143.0ms

Filtered

73 candidates to 138 candidates (-89.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	138	9	147

Merged error: 18.9b

Counts

147 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

11.1b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (* (pow (sqrt (cbrt (sqrt (+ (* re re) (* im im))))) 4) (cbrt (sqrt (+ (* re re) (* im im))))))) re)
29.2b	(sqrt (+ (* re re) (* im im)))
29.2b	(sqrt (+ (* re re) (* im im)))
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `add-cbrt-cube`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 57

Calls

4 calls:

22.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (* (pow (sqrt (cbrt (sqrt (+ (* re re) (* im im))))) 4) (cbrt (sqrt (+ (* re re) (* im im))))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series25.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (* (pow (sqrt (cbrt (sqrt (+ (* re re) (* im im))))) 4) (cbrt (sqrt (+ (* re re) (* im im))))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
5.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4937	638
1	4937	638

prune136.0ms

Filtered

56 candidates to 69 candidates (-23.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	69	9	78

Merged error: 18.9b

Counts

78 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.9b	(pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4)
14.0b	(- (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4) (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 2)) re)
29.2b	(sqrt (+ (* re re) (* im im)))
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

15×	`sqrt-prod`
13×	`add-sqr-sqrt`
12×	`unpow-prod-down`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod`
7×	`pow1`
6×	`add-log-exp`
5×	`add-exp-log`
4×	`sqrt-div` `add-cbrt-cube`
3×	`pow-unpow`
2×	`rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow1/3` `diff-log` `pow-exp` `flip--` `sqr-pow`

Counts

4 → 69

Calls

4 calls:

6.0ms	(pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4)
14.0ms	(- (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4) (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 2)) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series53.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4)
7.0ms	(- (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4) (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 2)) re)
5.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify45.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4962	971
1	4962	971

prune125.0ms

Filtered

60 candidates to 81 candidates (-35.0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	81	9	90

Merged error: 18.9b

Counts

90 → 9

regimes282.0ms

Accuracy

57.6% (9.1b remaining)

Error of 26.6b against oracle of 17.5b and baseline of 39.0b

bsearch49.0ms

Steps

Iters	Range	Point
9	-7.676761036242019e-305	3.3654627424431923e-307	1.9838435047488465e-308
8	-9.68551370084772e-266	-3.1195446902457074e-268	-4.786656859853452e-266
7	-3.8095654050866245e+140	-5.961519079968264e+138	-1.1681449413097545e+139

Iters

Range

Point

-7.676761036242019e-305

3.3654627424431923e-307

1.9838435047488465e-308

-9.68551370084772e-266

-3.1195446902457074e-268

-4.786656859853452e-266

-3.8095654050866245e+140

-5.961519079968264e+138

-1.1681449413097545e+139

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	74
1	49	74

end0.0ms

sample991.0ms

Algorithm

intervals

Results

296.0ms	6060×	body	80	valid
204.0ms	718×	body	2560	valid
114.0ms	482×	body	1280	valid
89.0ms	264×	body	5120	valid
51.0ms	273×	body	640	valid
21.0ms	134×	body	320	valid
6.0ms	69×	body	160	valid

Details

sample35.0ms

simplify3.0ms

prune7.0ms

localize10.0ms

rewrite23.0ms

series43.0ms

simplify42.0ms

prune129.0ms

localize12.0ms

rewrite41.0ms

series27.0ms

simplify51.0ms

prune143.0ms

localize23.0ms

rewrite34.0ms

series25.0ms

simplify56.0ms

prune136.0ms

localize18.0ms

rewrite30.0ms

series53.0ms

simplify45.0ms

prune125.0ms

regimes282.0ms

bsearch49.0ms

simplify1.0ms

end0.0ms

sample991.0ms

Profiling