Details

sample57.0ms

Algorithm

intervals

Results

15.0ms	196×	body	80	valid
10.0ms	23×	body	2560	valid
6.0ms	17×	body	1280	valid
4.0ms	7×	body	5120	valid
1.0ms	5×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	4×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	24
2	24
1	22
0	12

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

localize106.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
1.3b	(+ (sqrt (+ (* re re) (* im im))) re)
28.4b	(sqrt (+ (* re re) (* im im)))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

113.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
60.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
15.0ms	(sqrt (+ (* re re) (* im im)))

series568.0ms

Counts

3 → 9

Calls

3 calls:

324.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
148.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
95.0ms	(sqrt (+ (* re re) (* im im)))

simplify4.1s

Counts

49 → 49

Iterations

Iter	Nodes
done	5000
3	2094
2	666
1	243
0	99

prune536.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.1b

localize61.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (exp (log (sqrt (+ (* re re) (* im im))))) re)))
5.9b	(exp (log (sqrt (+ (* re re) (* im im)))))
14.0b	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
28.4b	(sqrt (+ (* re re) (* im im)))

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

82.0ms	(sqrt (* 2.0 (+ (exp (log (sqrt (+ (* re re) (* im im))))) re)))
22.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
129.0ms	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
16.0ms	(sqrt (+ (* re re) (* im im)))

series654.0ms

Counts

4 → 12

Calls

4 calls:

395.0ms	(sqrt (* 2.0 (+ (exp (log (sqrt (+ (* re re) (* im im))))) re)))
73.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
112.0ms	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
73.0ms	(sqrt (+ (* re re) (* im im)))

simplify4.0s

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
3	2213
2	746
1	293
0	138

prune819.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 18.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (pow (sqrt E) (log (+ (* re re) (* im im)))) re)))
6.3b	(pow (sqrt E) (log (+ (* re re) (* im im))))
14.2b	(+ (pow (sqrt E) (log (+ (* re re) (* im im)))) re)
29.5b	(log (+ (* re re) (* im im)))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `*-un-lft-identity`
9×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`add-exp-log` `unpow-prod-down` `log-prod` `add-log-exp`
4×	`log-div` `pow-unpow` `flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+`
3×	`unpow-prod-up` `pow-pow` `sqrt-pow1`
2×	`pow1/2` `sqrt-div` `associate-*r/` `log-pow` `pow-sub`
1×	`+-commutative` `pow-to-exp` `rem-log-exp` `pow-prod-down` `pow-exp` `sum-log` `sqrt-pow2` `distribute-lft-out` `sqr-pow`

Counts

4 → 68

Calls

4 calls:

67.0ms	(sqrt (* 2.0 (+ (pow (sqrt E) (log (+ (* re re) (* im im)))) re)))
24.0ms	(pow (sqrt E) (log (+ (* re re) (* im im))))
87.0ms	(+ (pow (sqrt E) (log (+ (* re re) (* im im)))) re)
13.0ms	(log (+ (* re re) (* im im)))

series1.5s

Counts

4 → 12

Calls

4 calls:

506.0ms	(sqrt (* 2.0 (+ (pow (sqrt E) (log (+ (* re re) (* im im)))) re)))
430.0ms	(pow (sqrt E) (log (+ (* re re) (* im im))))
450.0ms	(+ (pow (sqrt E) (log (+ (* re re) (* im im)))) re)
89.0ms	(log (+ (* re re) (* im im)))

simplify5.9s

Counts

80 → 80

Iterations

Iter	Nodes
done	5007
3	4184
2	1339
1	520
0	192

prune942.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 17.9b

localize131.0ms

Local error

Found 4 expressions with local error:

14.2b	(+ (* (* (cbrt (pow (sqrt E) (log (+ (* re re) (* im im))))) (cbrt (pow (sqrt E) (log (+ (* re re) (* im im)))))) (cbrt (pow (sqrt E) (log (+ (* re re) (* im im)))))) re)
29.5b	(log (+ (* re re) (* im im)))
29.5b	(log (+ (* re re) (* im im)))
29.5b	(log (+ (* re re) (* im im)))

rewrite285.0ms

Algorithm

rewrite-expression-head

Rules

9×	`log-prod`
7×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`log-div` `add-log-exp`
4×	`flip3-+` `add-cbrt-cube` `flip-+`
3×	`rem-log-exp` `log-pow`
1×	`+-commutative` `sum-log`

Counts

4 → 53

Calls

4 calls:

246.0ms	(+ (* (* (cbrt (pow (sqrt E) (log (+ (* re re) (* im im))))) (cbrt (pow (sqrt E) (log (+ (* re re) (* im im)))))) (cbrt (pow (sqrt E) (log (+ (* re re) (* im im)))))) re)
12.0ms	(log (+ (* re re) (* im im)))
12.0ms	(log (+ (* re re) (* im im)))
13.0ms	(log (+ (* re re) (* im im)))

series657.0ms

Counts

4 → 12

Calls

4 calls:

397.0ms	(+ (* (* (cbrt (pow (sqrt E) (log (+ (* re re) (* im im))))) (cbrt (pow (sqrt E) (log (+ (* re re) (* im im)))))) (cbrt (pow (sqrt E) (log (+ (* re re) (* im im)))))) re)
86.0ms	(log (+ (* re re) (* im im)))
83.0ms	(log (+ (* re re) (* im im)))
91.0ms	(log (+ (* re re) (* im im)))

simplify6.1s

Counts

65 → 65

Iterations

Iter	Nodes
done	5003
4	4821
3	1401
2	540
1	224
0	88

prune861.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 17.9b

regimes1.9s

Accuracy

59.5% (8.8b remaining)

Error of 25.7b against oracle of 16.9b and baseline of 38.6b

bsearch251.0ms

Steps

Iters	Range	Point
9	8.232280728626634e+118	1.616260079881983e+124	2.4332203230453174e+119
7	2.0138989610737437e-223	3.513292998456653e-221	1.3675002061575564e-222
6	-5.820797299615256e-262	-4.929572255277891e-263	-5.5536305775998016e-263

Iters

Range

Point

8.232280728626634e+118

1.616260079881983e+124

2.4332203230453174e+119

2.0138989610737437e-223

3.513292998456653e-221

1.3675002061575564e-222

-5.820797299615256e-262

-4.929572255277891e-263

-5.5536305775998016e-263

simplify19.0ms

Iterations

Iter	Nodes
done	47
1	47
0	37

end0.0ms

sample2.7s

Algorithm

intervals

Results

926.0ms	695×	body	2560	valid
611.0ms	6026×	body	80	valid
354.0ms	300×	body	5120	valid
205.0ms	485×	body	1280	valid
141.0ms	265×	body	640	valid
89.0ms	152×	body	320	valid
56.0ms	77×	body	160	valid