Details

sample34.0ms

Algorithm

intervals

Results

10.0ms	197×	body	80	valid
5.0ms	18×	body	2560	valid
3.0ms	14×	body	1280	valid
3.0ms	8×	body	5120	valid
2.0ms	9×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	2×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	8
1	24	8
2	30	8
3	35	8
4	35	8

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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

Merged error: 37.5b

Counts

2 → 1

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.2b	(- (sqrt (+ (* re re) (* im im))) re)
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

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

series37.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify92.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	234	381
1	812	362
2	3077	355
3	5001	353

prune103.0ms

Filtered

52 candidates to 42 candidates (19.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	46	6	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	6	53

Merged error: 15.9b

Counts

53 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (sqrt (+ (* re re) (* im im))) re))
0.2b	(- (sqrt (+ (* re re) (* im im))) re)
0.3b	(* (sqrt 2.0) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
25×	`sqrt-prod`
16×	`*-un-lft-identity`
10×	`pow1` `add-cube-cbrt`
9×	`associate-r`
6×	`add-exp-log` `sqrt-div` `associate-l` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
4×	`sqrt-pow1` `pow1/2` `unswap-sqr`
3×	`flip3--` `pow-prod-down` `flip--` `distribute-lft-out--`
2×	`rem-sqrt-square` `associate-*r/`
1×	`sub-neg` `flip3-+` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 83

Calls

4 calls:

9.0ms	(sqrt (- (sqrt (+ (* re re) (* im im))) re))
6.0ms	(- (sqrt (+ (* re re) (* im im))) re)
13.0ms	(* (sqrt 2.0) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series51.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(sqrt (- (sqrt (+ (* re re) (* im im))) re))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
22.0ms	(* (sqrt 2.0) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify42.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	322	811
1	1273	781
2	5001	767

prune123.0ms

Filtered

95 candidates to 67 candidates (29.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	94	7	101

Merged error: 15.9b

Counts

101 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
6.6b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.3b	(sqrt (+ (* re re) (* im im)))
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite42.0ms

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)))
5.0ms	(sqrt (+ (* re re) (* im im)))

series26.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.0ms	(- (* (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)))

simplify46.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	261	1112
1	935	975
2	5001	951

prune264.0ms

Filtered

138 candidates to 75 candidates (45.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	138	7	145

Merged error: 15.9b

Counts

145 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (sqrt (+ (* re re) (* im im))) re)
5.2b	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
21.5b	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
32×	`times-frac`
25×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
15×	`unpow-prod-down`
10×	`distribute-lft-out`
9×	`add-exp-log`
8×	`pow1` `associate-/l*`
6×	`add-cbrt-cube` `add-log-exp`
5×	`unpow2` `sqr-pow`
4×	`associate-/r*` `sqrt-prod`
3×	`sqrt-pow1` `flip3-+` `sqrt-div` `div-exp` `flip-+`
2×	`pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 99

Calls

4 calls:

6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
11.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
10.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
4.0ms	(sqrt (+ (* re re) (* im im)))

series47.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
24.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
10.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	412	1076
1	1494	991
2	5002	987

prune142.0ms

Filtered

111 candidates to 78 candidates (29.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	108	10	118

Merged error: 7.1b

Counts

118 → 10

regimes359.0ms

Accuracy

48.4% (16.5b remaining)

Error of 23.3b against oracle of 6.8b and baseline of 38.7b

bsearch133.0ms

Steps

Iters	Range		Point
10	7.113085883623841e+50	1.078960105470046e+63	8.652791266125621e+60
10	4.081936154592251e-145	7.407484477097181e-132	4.288589544984824e-145
10	-1.1848656664474683e-136	-8.228269418273186e-150	-8.332553808951539e-150
3	-1.0401647864543139e-36	-7.462749473791532e-37	-1.021419081690422e-36
10	-1.2018840913203397e+174	-2.0456985869433597e+161	-2.0689817943266104e+161

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	51
1	81	51
2	82	51
3	82	51

end0.0ms

sample1.0s

Algorithm

intervals

Results

307.0ms	6008×	body	80	valid
210.0ms	718×	body	2560	valid
128.0ms	527×	body	1280	valid
96.0ms	265×	body	5120	valid
51.0ms	271×	body	640	valid
20.0ms	145×	body	320	valid
6.0ms	66×	body	160	valid

Details

sample34.0ms

simplify7.0ms

prune3.0ms

localize15.0ms

rewrite19.0ms

series37.0ms

simplify92.0ms

prune103.0ms

localize12.0ms

rewrite34.0ms

series51.0ms

simplify42.0ms

prune123.0ms

localize13.0ms

rewrite42.0ms

series26.0ms

simplify46.0ms

prune264.0ms

localize14.0ms

rewrite34.0ms

series47.0ms

simplify51.0ms

prune142.0ms

regimes359.0ms

bsearch133.0ms

simplify3.0ms

end0.0ms

sample1.0s

Profiling