Details

Time bar (total: 20.0s)

sample174.0ms

Algorithm
intervals
Results
69.0ms261×body80valid
36.0ms39×body640valid
31.0ms26×body1280valid
13.0ms21×body320valid
3.0ms8×body160valid

simplify334.0ms

Counts
1 → 1

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.4b

localize32.0ms

Local error

Found 4 expressions with local error:

3.0b
(cos (/ (+ phi2 phi1) 2))
0.1b
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
0.1b
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.0b
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

rewrite37.0ms

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:
Slowest
18.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
7.0ms
(cos (/ (+ phi2 phi1) 2))
6.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
5.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
605.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
449.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
106.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
22.0ms
(cos (/ (+ phi2 phi1) 2))

simplify490.0ms

Counts
79 → 79

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.2b

localize24.0ms

Local error

Found 4 expressions with local error:

3.0b
(cos (* (+ phi1 phi2) 1/2))
0.1b
(* (cos (* (+ phi1 phi2) 1/2)) (- lambda1 lambda2))
0.1b
(* (hypot (* (cos (* (+ phi1 phi2) 1/2)) (- lambda1 lambda2)) (- phi1 phi2)) R)
0.0b
(hypot (* (cos (* (+ phi1 phi2) 1/2)) (- lambda1 lambda2)) (- phi1 phi2))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
18×prod-diff
11×distribute-rgt-in distribute-lft-in
8×pow1 add-cbrt-cube associate-*r* add-exp-log
6×associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×sub-neg pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod unswap-sqr
1×hypot-udef flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 89
Calls
4 calls:
Slowest
32.0ms
(* (cos (* (+ phi1 phi2) 1/2)) (- lambda1 lambda2))
11.0ms
(cos (* (+ phi1 phi2) 1/2))
6.0ms
(* (hypot (* (cos (* (+ phi1 phi2) 1/2)) (- lambda1 lambda2)) (- phi1 phi2)) R)
0.0ms
(hypot (* (cos (* (+ phi1 phi2) 1/2)) (- lambda1 lambda2)) (- phi1 phi2))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
668.0ms
(hypot (* (cos (* (+ phi1 phi2) 1/2)) (- lambda1 lambda2)) (- phi1 phi2))
478.0ms
(* (hypot (* (cos (* (+ phi1 phi2) 1/2)) (- lambda1 lambda2)) (- phi1 phi2)) R)
137.0ms
(* (cos (* (+ phi1 phi2) 1/2)) (- lambda1 lambda2))
30.0ms
(cos (* (+ phi1 phi2) 1/2))

simplify547.0ms

Counts
123 → 101

prune1.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.2b

localize41.0ms

Local error

Found 4 expressions with local error:

3.0b
(cos (* (+ phi1 phi2) 1/2))
0.5b
(expm1 (cos (* (+ phi1 phi2) 1/2)))
0.2b
(log1p (expm1 (cos (* (+ phi1 phi2) 1/2))))
0.1b
(* (log1p (expm1 (cos (* (+ phi1 phi2) 1/2)))) (- lambda1 lambda2))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
20×*-un-lft-identity
18×prod-diff add-cube-cbrt
11×distribute-rgt-in distribute-lft-in
6×pow1 add-cbrt-cube add-exp-log
5×associate-*r* log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×associate-*l*
2×sub-neg associate-*r/
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 → 81
Calls
4 calls:
Slowest
26.0ms
(* (log1p (expm1 (cos (* (+ phi1 phi2) 1/2)))) (- lambda1 lambda2))
10.0ms
(cos (* (+ phi1 phi2) 1/2))
0.0ms
(expm1 (cos (* (+ phi1 phi2) 1/2)))
0.0ms
(log1p (expm1 (cos (* (+ phi1 phi2) 1/2))))

series425.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
240.0ms
(* (log1p (expm1 (cos (* (+ phi1 phi2) 1/2)))) (- lambda1 lambda2))
85.0ms
(log1p (expm1 (cos (* (+ phi1 phi2) 1/2))))
74.0ms
(expm1 (cos (* (+ phi1 phi2) 1/2)))
26.0ms
(cos (* (+ phi1 phi2) 1/2))

simplify791.0ms

Counts
113 → 93

prune1.6s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.2b

localize52.0ms

Local error

Found 4 expressions with local error:

3.0b
(cos (/ (+ phi2 phi1) 2))
3.0b
(cos (/ (+ phi2 phi1) 2))
3.0b
(cos (/ (+ phi2 phi1) 2))
0.4b
(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (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:
Slowest
29.0ms
(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
14.0ms
(cos (/ (+ phi2 phi1) 2))
11.0ms
(cos (/ (+ phi2 phi1) 2))
7.0ms
(cos (/ (+ phi2 phi1) 2))

series115.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
36.0ms
(cos (/ (+ phi2 phi1) 2))
30.0ms
(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
27.0ms
(cos (/ (+ phi2 phi1) 2))
22.0ms
(cos (/ (+ phi2 phi1) 2))

simplify842.0ms

Counts
56 → 56

prune979.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.2b

regimes904.0ms

Accuracy

0% (0.2b remaining)

Error of 4.1b against oracle of 3.9b and baseline of 4.1b

bsearch3.0ms

end0.0ms

sample7.4s

Algorithm
intervals
Results
2.4s8365×body80valid
1.8s1312×body640valid
1.6s806×body1280valid
1.0s729×body320valid
154.0ms345×body160valid