Details

sample179.0ms

Algorithm

intervals

Results

58.0ms	265×	body	80	valid
51.0ms	46×	body	640	valid
30.0ms	22×	body	1280	valid
11.0ms	17×	body	320	valid
3.0ms	8×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1878
4	761
3	231
2	72
1	34
0	17

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
2.9b	(cos (/ (+ phi2 phi1) 2))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
6×	`associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`hypot-udef` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 67

Calls

4 calls:

0.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
6.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
24.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
19.0ms	(cos (/ (+ phi2 phi1) 2))

series1.2s

Counts

4 → 12

Calls

4 calls:

497.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
602.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
107.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
29.0ms	(cos (/ (+ phi2 phi1) 2))

simplify2.9s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
3	4185
2	1076
1	360
0	144

prune700.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
2.9b	(cos (/ (+ phi1 phi2) 2))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
6×	`associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`hypot-udef` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 67

Calls

4 calls:

0.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2))
9.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2)) R)
19.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
10.0ms	(cos (/ (+ phi1 phi2) 2))

series1.4s

Counts

4 → 12

Calls

4 calls:

565.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2))
651.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2)) R)
156.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
45.0ms	(cos (/ (+ phi1 phi2) 2))

simplify2.5s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
3	4260
2	1075
1	363
0	144

prune615.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.5b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2)))))
0.2b	(expm1 (log1p (cos (/ (+ phi1 phi2) 2))))
0.4b	(log1p (cos (/ (+ phi1 phi2) 2)))
2.9b	(cos (/ (+ phi1 phi2) 2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`expm1-log1p-u` `associate-l`
4×	`insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`associate-*l/`
1×	`log1p-udef` `expm1-log1p` `flip3--` `pow-prod-down` `prod-exp` `log1p-expm1` `*-commutative` `cbrt-unprod` `flip--` `distribute-lft-out--` `expm1-udef` `difference-of-squares` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

16.0ms	(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2)))))
0.0ms	(expm1 (log1p (cos (/ (+ phi1 phi2) 2))))
0.0ms	(log1p (cos (/ (+ phi1 phi2) 2)))
8.0ms	(cos (/ (+ phi1 phi2) 2))

series324.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2)))))
64.0ms	(expm1 (log1p (cos (/ (+ phi1 phi2) 2))))
76.0ms	(log1p (cos (/ (+ phi1 phi2) 2)))
30.0ms	(cos (/ (+ phi1 phi2) 2))

simplify2.1s

Counts

71 → 71

Iterations

Iter	Nodes
done	5003
3	1612
2	481
1	205
0	100

prune636.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.5b

localize56.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))
2.9b	(cos (/ (+ phi1 phi2) 2))
2.9b	(cos (/ (+ phi1 phi2) 2))
2.9b	(cos (/ (+ phi1 phi2) 2))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `pow3` `associate-*l/` `cos-mult` `rem-cbrt-cube`

Counts

4 → 44

Calls

4 calls:

25.0ms	(cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))
8.0ms	(cos (/ (+ phi1 phi2) 2))
7.0ms	(cos (/ (+ phi1 phi2) 2))
8.0ms	(cos (/ (+ phi1 phi2) 2))

series155.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))
37.0ms	(cos (/ (+ phi1 phi2) 2))
37.0ms	(cos (/ (+ phi1 phi2) 2))
44.0ms	(cos (/ (+ phi1 phi2) 2))

simplify2.5s

Counts

56 → 56

Iterations

Iter	Nodes
done	5006
5	2542
4	761
3	284
2	130
1	80
0	48

prune554.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.5b

regimes909.0ms

Accuracy

0% (0.2b remaining)

Error of 3.4b against oracle of 3.3b and baseline of 3.4b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.2s	8345×	body	80	valid
2.1s	1197×	body	640	valid
1.2s	783×	body	1280	valid
482.0ms	687×	body	320	valid
207.0ms	343×	body	160	valid