Details

Time bar (total: 46.3s)

sample602.0ms

Algorithm
intervals
Results
376.0ms100×body1280valid
144.0ms71×body640valid
19.0ms14×body320valid
19.0ms59×body80valid
9.0ms12×body160valid

simplify48.0ms

Counts
1 → 1

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (sin theta) (sin delta)) (cos phi1))
0.3b
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.6b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite82.0ms

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-*r* add-log-exp
4×associate-*l* pow-prod-down prod-exp cbrt-unprod
2×*-commutative sin-mult
1×sub-neg asin-acos flip3-- diff-log associate-*l/ flip-- unswap-sqr
Counts
4 → 58
Calls
4 calls:
37.0ms
(* (* (sin theta) (sin delta)) (cos phi1))
27.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
13.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series646.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(* (* (sin theta) (sin delta)) (cos phi1))
222.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
17.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
280.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify684.0ms

Counts
70 → 70

prune550.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize77.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b
(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.3b
(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.4b
(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

rewrite266.0ms

Algorithm
rewrite-expression-head
Rules
43×pow1
18×add-exp-log add-cbrt-cube
17×pow-prod-down
16×sin-mult
13×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×times-frac
10×cos-mult
8×prod-exp cbrt-unprod
7×associate-/l/
6×frac-sub add-log-exp
5×associate-*r/ associate-*l/ difference-of-squares
4×pow-sqr pow-prod-up associate-/l* sub-div
3×frac-times associate-/r*
2×flip3-- pow-plus associate-/r/ flip--
1×cbrt-undiv pow2 sub-neg asin-acos sqr-cos frac-2neg flip3-+ diff-log div-sub swap-sqr div-exp associate-*r* associate-*l* associate--l+ clear-num *-commutative flip-+ div-inv
Counts
4 → 105
Calls
4 calls:
4.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
95.0ms
(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
77.0ms
(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
82.0ms
(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

series2.5s

Counts
4 → 12
Calls
4 calls:
16.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
1.4s
(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
293.0ms
(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
792.0ms
(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

simplify1.7s

Counts
117 → 117

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize131.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin phi1) 3)
0.4b
(pow (sin phi1) 3)
0.4b
(- (pow (cos delta) 2) (+ (* (pow (sin phi1) 3) (* (cos phi1) (* (cos delta) (* (sin delta) (cos theta))))) (+ (* (pow (sin phi1) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin delta) 2)))) (+ (* (pow (sin phi1) 4) (pow (cos delta) 2)) (* (pow (sin phi1) 3) (* (cos phi1) (* (sin delta) (* (cos delta) (cos theta)))))))))
0.5b
(pow (sin phi1) 4)

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt add-log-exp
14×*-un-lft-identity
12×add-cube-cbrt
10×unpow-prod-down
9×pow-unpow
7×pow1 add-exp-log
6×cube-prod sum-log add-cbrt-cube
4×diff-log difference-of-squares sqr-pow
3×pow-to-exp pow-pow pow-exp
2×cube-mult unpow3 rem-cube-cbrt
1×sub-neg flip3-- flip-- associate--r+ distribute-lft-out-- unpow2
Counts
4 → 84
Calls
4 calls:
4.0ms
(pow (sin phi1) 3)
4.0ms
(pow (sin phi1) 3)
1.4s
(- (pow (cos delta) 2) (+ (* (pow (sin phi1) 3) (* (cos phi1) (* (cos delta) (* (sin delta) (cos theta))))) (+ (* (pow (sin phi1) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin delta) 2)))) (+ (* (pow (sin phi1) 4) (pow (cos delta) 2)) (* (pow (sin phi1) 3) (* (cos phi1) (* (sin delta) (* (cos delta) (cos theta)))))))))
4.0ms
(pow (sin phi1) 4)

series898.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(pow (sin phi1) 3)
57.0ms
(pow (sin phi1) 3)
762.0ms
(- (pow (cos delta) 2) (+ (* (pow (sin phi1) 3) (* (cos phi1) (* (cos delta) (* (sin delta) (cos theta))))) (+ (* (pow (sin phi1) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin delta) 2)))) (+ (* (pow (sin phi1) 4) (pow (cos delta) 2)) (* (pow (sin phi1) 3) (* (cos phi1) (* (sin delta) (* (cos delta) (cos theta)))))))))
46.0ms
(pow (sin phi1) 4)

simplify1.0s

Counts
96 → 96

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize145.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (pow (cos delta) 2) (+ (* (pow (sin phi1) 3) (* (cos phi1) (* (cos delta) (* (sin delta) (cos theta))))) (+ (* (pow (sin phi1) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin delta) 2)))) (+ (* (* (pow (sin phi1) 2) (pow (sin phi1) 2)) (pow (cos delta) 2)) (* (pow (sin phi1) 3) (* (cos phi1) (* (sin delta) (* (cos delta) (cos theta))))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.4b
(pow (sin phi1) 3)
0.4b
(pow (sin phi1) 3)
0.4b
(- (pow (cos delta) 2) (+ (* (pow (sin phi1) 3) (* (cos phi1) (* (cos delta) (* (sin delta) (cos theta))))) (+ (* (pow (sin phi1) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin delta) 2)))) (+ (* (* (pow (sin phi1) 2) (pow (sin phi1) 2)) (pow (cos delta) 2)) (* (pow (sin phi1) 3) (* (cos phi1) (* (sin delta) (* (cos delta) (cos theta)))))))))

rewrite7.4s

Algorithm
rewrite-expression-head
Rules
53×add-sqr-sqrt
33×*-un-lft-identity
24×times-frac
23×add-cube-cbrt
20×difference-of-squares
18×add-log-exp
11×unpow-prod-down
8×add-exp-log add-cbrt-cube associate-/l*
7×sqr-pow
6×pow1 pow-unpow cube-prod sum-log
5×distribute-lft-out-- unpow2
4×diff-log
3×associate-/r*
2×cube-mult pow-to-exp flip3-- pow-pow unpow3 pow-exp associate-/r/ flip-- associate-/l/ rem-cube-cbrt
1×cbrt-undiv sub-neg frac-2neg flip3-+ div-sub div-exp clear-num flip-+ div-inv associate--r+
Counts
4 → 119
Calls
4 calls:
5.1s
(/ (- (pow (cos delta) 2) (+ (* (pow (sin phi1) 3) (* (cos phi1) (* (cos delta) (* (sin delta) (cos theta))))) (+ (* (pow (sin phi1) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin delta) 2)))) (+ (* (* (pow (sin phi1) 2) (pow (sin phi1) 2)) (pow (cos delta) 2)) (* (pow (sin phi1) 3) (* (cos phi1) (* (sin delta) (* (cos delta) (cos theta))))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
7.0ms
(pow (sin phi1) 3)
7.0ms
(pow (sin phi1) 3)
2.3s
(- (pow (cos delta) 2) (+ (* (pow (sin phi1) 3) (* (cos phi1) (* (cos delta) (* (sin delta) (cos theta))))) (+ (* (pow (sin phi1) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin delta) 2)))) (+ (* (* (pow (sin phi1) 2) (pow (sin phi1) 2)) (pow (cos delta) 2)) (* (pow (sin phi1) 3) (* (cos phi1) (* (sin delta) (* (cos delta) (cos theta)))))))))

series2.2s

Counts
4 → 12
Calls
4 calls:
1.3s
(/ (- (pow (cos delta) 2) (+ (* (pow (sin phi1) 3) (* (cos phi1) (* (cos delta) (* (sin delta) (cos theta))))) (+ (* (pow (sin phi1) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin delta) 2)))) (+ (* (* (pow (sin phi1) 2) (pow (sin phi1) 2)) (pow (cos delta) 2)) (* (pow (sin phi1) 3) (* (cos phi1) (* (sin delta) (* (cos delta) (cos theta))))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
46.0ms
(pow (sin phi1) 3)
35.0ms
(pow (sin phi1) 3)
742.0ms
(- (pow (cos delta) 2) (+ (* (pow (sin phi1) 3) (* (cos phi1) (* (cos delta) (* (sin delta) (cos theta))))) (+ (* (pow (sin phi1) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin delta) 2)))) (+ (* (* (pow (sin phi1) 2) (pow (sin phi1) 2)) (pow (cos delta) 2)) (* (pow (sin phi1) 3) (* (cos phi1) (* (sin delta) (* (cos delta) (cos theta)))))))))

simplify1.6s

Counts
131 → 131

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes808.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify496.0ms

end0.0ms

sample18.5s

Algorithm
intervals
Results
10.8s3136×body1280valid
4.4s1818×body640valid
1.3s712×body320valid
746.0ms327×body160valid
556.0ms2007×body80valid