Details

Time bar (total: 22.9s)

sample360.0ms

Algorithm
intervals
Results
226.0ms117×body1280valid
78.0ms76×body640valid
18.0ms29×body320valid
6.0ms15×body160valid
3.0ms19×body80valid

simplify32.0ms

Counts
1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize101.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (sin (- lambda1 lambda2)))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.6b
(cos (- lambda1 lambda2))
3.6b
(sin (- lambda1 lambda2))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity sin-sum add-cbrt-cube add-log-exp
4×sub-neg
3×distribute-rgt-in cos-diff distribute-lft-in associate-*r* associate-*l*
2×cos-sum associate-+r+
1×+-commutative flip3-+ pow-prod-down prod-exp sum-log sin-diff *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 55
Calls
4 calls:
66.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
11.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
12.0ms
(cos (- lambda1 lambda2))
18.0ms
(sin (- lambda1 lambda2))

series265.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
144.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
25.0ms
(cos (- lambda1 lambda2))
30.0ms
(sin (- lambda1 lambda2))

simplify1.3s

Counts
67 → 67

prune472.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.7b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (cos (- lambda1 lambda2)))
0.2b
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.6b
(cos (- lambda1 lambda2))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×associate-*l* add-log-exp
5×cos-diff
4×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×distribute-rgt-in cos-sum associate-+r+ distribute-lft-in *-commutative distribute-rgt-neg-out
1×+-commutative sub-neg flip3-+ sin-neg sum-log cos-mult flip-+ unswap-sqr
Counts
4 → 63
Calls
4 calls:
28.0ms
(* (cos phi2) (cos (- lambda1 lambda2)))
75.0ms
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
14.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
12.0ms
(cos (- lambda1 lambda2))

series421.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(* (cos phi2) (cos (- lambda1 lambda2)))
154.0ms
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
150.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
22.0ms
(cos (- lambda1 lambda2))

simplify685.0ms

Counts
75 → 75

prune620.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (* (cos lambda1) (cos lambda2)))
0.2b
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
0.2b
(* (sin lambda1) (sin lambda2))
0.5b
(+ (cos phi1) (+ (* (cos phi2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1 add-exp-log add-cbrt-cube
10×add-sqr-sqrt *-un-lft-identity
9×associate-*l* add-log-exp
8×add-cube-cbrt
7×pow-prod-down prod-exp cbrt-unprod
5×associate-*r*
3×sum-log *-commutative
2×distribute-rgt-neg-out
1×+-commutative associate-+r+ flip3-+ associate-*r/ sin-neg cos-mult flip-+ sin-mult distribute-lft-out unswap-sqr
Counts
4 → 71
Calls
4 calls:
34.0ms
(* (cos phi2) (* (cos lambda1) (cos lambda2)))
56.0ms
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
14.0ms
(* (sin lambda1) (sin lambda2))
63.0ms
(+ (cos phi1) (+ (* (cos phi2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))

series633.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(* (cos phi2) (* (cos lambda1) (cos lambda2)))
117.0ms
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
52.0ms
(* (sin lambda1) (sin lambda2))
345.0ms
(+ (cos phi1) (+ (* (cos phi2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))

simplify820.0ms

Counts
83 → 83

prune667.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.5b
(+ (cos phi1) (+ (cbrt (pow (* (cos lambda1) (* (cos phi2) (cos lambda2))) 3)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.6b
(cbrt (pow (* (cos lambda1) (* (cos phi2) (cos lambda2))) 3))
0.7b
(pow (* (cos lambda1) (* (cos phi2) (cos lambda2))) 3)

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1 add-exp-log add-cbrt-cube
10×add-sqr-sqrt *-un-lft-identity
9×add-log-exp
8×cbrt-prod add-cube-cbrt
4×pow-prod-down prod-exp cbrt-unprod
3×pow-unpow pow-pow associate-*r* associate-*l* pow-exp sum-log rem-cube-cbrt
2×cube-div cube-mult unpow-prod-down unpow3 cube-prod associate-*r/ cos-mult sqr-pow
1×+-commutative pow-to-exp cbrt-div associate-+r+ flip3-+ pow1/3 *-commutative rem-cbrt-cube flip-+ sin-mult distribute-lft-out unswap-sqr
Counts
4 → 77
Calls
4 calls:
26.0ms
(* (sin lambda1) (sin lambda2))
58.0ms
(+ (cos phi1) (+ (cbrt (pow (* (cos lambda1) (* (cos phi2) (cos lambda2))) 3)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
9.0ms
(cbrt (pow (* (cos lambda1) (* (cos phi2) (cos lambda2))) 3))
21.0ms
(pow (* (cos lambda1) (* (cos phi2) (cos lambda2))) 3)

series697.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(* (sin lambda1) (sin lambda2))
322.0ms
(+ (cos phi1) (+ (cbrt (pow (* (cos lambda1) (* (cos phi2) (cos lambda2))) 3)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
137.0ms
(cbrt (pow (* (cos lambda1) (* (cos phi2) (cos lambda2))) 3))
154.0ms
(pow (* (cos lambda1) (* (cos phi2) (cos lambda2))) 3)

simplify799.0ms

Counts
89 → 89

prune768.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes680.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0s

end0.0ms

sample11.8s

Algorithm
intervals
Results
6.9s3590×body1280valid
3.4s2349×body640valid
602.0ms922×body320valid
206.0ms423×body160valid
177.0ms716×body80valid