Details

sample140.0ms

Algorithm

intervals

Results

49.0ms	43×	body	640	valid
41.0ms	293×	body	80	valid
17.0ms	21×	body	1280	valid
12.0ms	27×	body	320	valid
3.0ms	9×	body	160	valid

simplify3.6s

Counts

1 → 1

Iterations

Iter	Nodes
6	5440
5	1878
4	761
3	231
2	72
1	34
0	17

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.7b

localize24.0ms

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)))
1.5b	(cos (/ (+ phi2 phi1) 2))

rewrite38.0ms

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)
23.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
8.0ms	(cos (/ (+ phi2 phi1) 2))

series1.8s

Counts

4 → 12

Calls

4 calls:

962.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
644.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
121.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
24.0ms	(cos (/ (+ phi2 phi1) 2))

simplify1.4s

Counts

79 → 79

Iterations

Iter	Nodes
3	3897
2	1082
1	359
0	144

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 1.6b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
0.1b	(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)))
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
1.5b	(cos (/ (+ phi2 phi1) 2))

rewrite67.0ms

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))
9.0ms	(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)))
42.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
15.0ms	(cos (/ (+ phi2 phi1) 2))

series1.4s

Counts

4 → 12

Calls

4 calls:

536.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
703.0ms	(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)))
112.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
24.0ms	(cos (/ (+ phi2 phi1) 2))

simplify1.4s

Counts

79 → 79

Iterations

Iter	Nodes
3	3783
2	1027
1	354
0	143

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 1.6b

localize54.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
1.5b	(cos (/ (+ phi2 phi1) 2))
1.5b	(cos (/ (+ phi2 phi1) 2))
1.5b	(cos (/ (+ phi2 phi1) 2))

rewrite62.0ms

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:

12.0ms	(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
10.0ms	(cos (/ (+ phi2 phi1) 2))
25.0ms	(cos (/ (+ phi2 phi1) 2))
15.0ms	(cos (/ (+ phi2 phi1) 2))

series106.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
28.0ms	(cos (/ (+ phi2 phi1) 2))
29.0ms	(cos (/ (+ phi2 phi1) 2))
24.0ms	(cos (/ (+ phi2 phi1) 2))

simplify3.5s

Counts

56 → 56

Iterations

Iter	Nodes
8	2735
7	1309
6	887
5	668
4	443
3	227
2	120
1	77
0	49

prune980.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 1.6b

localize54.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (/ (+ phi2 phi1) 2)))
1.5b	(cos (/ (+ phi2 phi1) 2))
1.5b	(cos (/ (+ phi2 phi1) 2))
1.5b	(cos (/ (+ phi2 phi1) 2))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 44

Calls

4 calls:

1.0ms	(cbrt (cos (/ (+ phi2 phi1) 2)))
22.0ms	(cos (/ (+ phi2 phi1) 2))
15.0ms	(cos (/ (+ phi2 phi1) 2))
15.0ms	(cos (/ (+ phi2 phi1) 2))

series187.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(cbrt (cos (/ (+ phi2 phi1) 2)))
23.0ms	(cos (/ (+ phi2 phi1) 2))
23.0ms	(cos (/ (+ phi2 phi1) 2))
23.0ms	(cos (/ (+ phi2 phi1) 2))

simplify1.4s

Counts

56 → 56

Iterations

Iter	Nodes
6	2049
5	1116
4	666
3	300
2	147
1	88
0	49

prune1.1s

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 1.6b

regimes897.0ms

Accuracy

0% (0.2b remaining)

Error of 3.8b against oracle of 3.6b and baseline of 3.8b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	17
1	17
0	14

end0.0ms

sample7.1s

Algorithm

intervals

Results

2.2s	8314×	body	80	valid
2.0s	1334×	body	640	valid
1.6s	790×	body	1280	valid
512.0ms	715×	body	320	valid
260.0ms	384×	body	160	valid