Details

sample182.0ms

Algorithm

intervals

Results

19.0ms	198×	body	80	valid
11.0ms	21×	body	2560	valid
7.0ms	16×	body	1280	valid
5.0ms	7×	body	5120	valid
3.0ms	9×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify37.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	35
4	35
3	30
2	24
1	17
0	12

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.0b	(sqrt (* (- (sqrt (+ (* re re) (* im im))) re) 2.0))
0.2b	(- (sqrt (+ (* re re) (* im im))) re)
28.4b	(sqrt (+ (* re re) (* im im)))

rewrite89.0ms

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-cbrt-cube` `sqrt-div` `add-exp-log`
3×	`sqrt-pow1`
2×	`flip3-+` `flip3--` `pow1/2` `associate-*l/` `flip-+` `flip--` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sub-neg` `diff-log` `pow-prod-down` `distribute-lft-out--`

Counts

4 → 54

Calls

4 calls:

6.0ms	(+ (* re re) (* im im))
38.0ms	(sqrt (* (- (sqrt (+ (* re re) (* im im))) re) 2.0))
32.0ms	(- (sqrt (+ (* re re) (* im im))) re)
9.0ms	(sqrt (+ (* re re) (* im im)))

series390.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (* re re) (* im im))
237.0ms	(sqrt (* (- (sqrt (+ (* re re) (* im im))) re) 2.0))
60.0ms	(- (sqrt (+ (* re re) (* im im))) re)
50.0ms	(sqrt (+ (* re re) (* im im)))

simplify677.0ms

Counts

66 → 66

Iterations

Iter	Nodes
done	5001
2	1261
1	276
0	114

prune403.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.3b

localize33.0ms

Local error

Found 4 expressions with local error:

3.0b	(exp (log (+ (* im im) (* re re))))
13.7b	(- (sqrt (exp (log (+ (* im im) (* re re))))) re)
28.4b	(sqrt (exp (log (+ (* im im) (* re re)))))
29.5b	(log (+ (* im im) (* re re)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

13.0ms	(exp (log (+ (* im im) (* re re))))
63.0ms	(- (sqrt (exp (log (+ (* im im) (* re re))))) re)
20.0ms	(sqrt (exp (log (+ (* im im) (* re re)))))
10.0ms	(log (+ (* im im) (* re re)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(exp (log (+ (* im im) (* re re))))
80.0ms	(- (sqrt (exp (log (+ (* im im) (* re re))))) re)
47.0ms	(sqrt (exp (log (+ (* im im) (* re re)))))
82.0ms	(log (+ (* im im) (* re re)))

simplify631.0ms

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	1068
1	251
0	120

prune493.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.6b

localize58.0ms

Local error

Found 4 expressions with local error:

13.7b	(- (sqrt (* (exp (* 2 (log (cbrt (+ (pow re 2) (pow im 2)))))) (cbrt (+ (pow re 2) (pow im 2))))) re)
28.4b	(sqrt (* (exp (* 2 (log (cbrt (+ (pow re 2) (pow im 2)))))) (cbrt (+ (pow re 2) (pow im 2)))))
29.4b	(cbrt (+ (pow re 2) (pow im 2)))
29.4b	(cbrt (+ (pow re 2) (pow im 2)))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

98.0ms	(- (sqrt (* (exp (* 2 (log (cbrt (+ (pow re 2) (pow im 2)))))) (cbrt (+ (pow re 2) (pow im 2))))) re)
58.0ms	(sqrt (* (exp (* 2 (log (cbrt (+ (pow re 2) (pow im 2)))))) (cbrt (+ (pow re 2) (pow im 2)))))
18.0ms	(cbrt (+ (pow re 2) (pow im 2)))
20.0ms	(cbrt (+ (pow re 2) (pow im 2)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (sqrt (* (exp (* 2 (log (cbrt (+ (pow re 2) (pow im 2)))))) (cbrt (+ (pow re 2) (pow im 2))))) re)
61.0ms	(sqrt (* (exp (* 2 (log (cbrt (+ (pow re 2) (pow im 2)))))) (cbrt (+ (pow re 2) (pow im 2)))))
133.0ms	(cbrt (+ (pow re 2) (pow im 2)))
125.0ms	(cbrt (+ (pow re 2) (pow im 2)))

simplify1.5s

Counts

69 → 69

Iterations

Iter	Nodes
done	5002
3	2932
2	615
1	195
0	99

prune574.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (- (exp (log (sqrt (+ (* re re) (* im im))))) re) 2.0))
5.8b	(exp (log (sqrt (+ (* re re) (* im im)))))
13.7b	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
28.4b	(sqrt (+ (* re re) (* im im)))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

97.0ms	(sqrt (* (- (exp (log (sqrt (+ (* re re) (* im im))))) re) 2.0))
16.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
54.0ms	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

260.0ms	(sqrt (* (- (exp (log (sqrt (+ (* re re) (* im im))))) re) 2.0))
61.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
82.0ms	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
47.0ms	(sqrt (+ (* re re) (* im im)))

simplify648.0ms

Counts

78 → 78

Iterations

Iter	Nodes
done	5001
2	1105
1	296
0	147

prune399.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.6b

regimes527.0ms

Accuracy

47.4% (15.3b remaining)

Error of 25.0b against oracle of 9.7b and baseline of 38.7b

bsearch195.0ms

Steps

Iters	Range		Point
9	2.598286552721665e-80	1.1482561294715716e-71	7.975663580255671e-75
5	-1.1135581929510197e-64	-2.986264416976082e-65	-3.2671908360155654e-65
7	-1.723051907656132e+78	-5.006770742094819e+76	-8.327291769824927e+77

simplify12.0ms

Iterations

Iter	Nodes
done	49
2	49
1	48
0	37

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.0s	6030×	body	80	valid
299.0ms	683×	body	2560	valid
220.0ms	301×	body	5120	valid
196.0ms	487×	body	1280	valid
62.0ms	245×	body	640	valid
35.0ms	175×	body	320	valid
11.0ms	79×	body	160	valid