Details

Time bar (total: 18.0s)

sample299.0ms

Algorithm
intervals
Results
98.0ms62×body640valid
86.0ms94×body1280valid
9.0ms68×body80valid
8.0ms21×body320valid
7.0ms11×body160valid

simplify31.0ms

Counts
1 → 1
Iterations
IterNodes
done21
421
320
216
112
08

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.3b

localize17.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ r (cos (+ b a)))
0.2b
(* (sin b) (/ r (cos (+ b a))))
2.2b
(cos (+ b a))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×*-un-lft-identity times-frac add-cube-cbrt
13×associate-*r*
10×add-cbrt-cube add-exp-log
5×pow1
3×expm1-log1p-u associate-/r* associate-*l* log1p-expm1-u associate-/l* add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×cos-sum clear-num frac-2neg pow-prod-down associate-*r/ *-commutative
Counts
3 → 73
Calls
3 calls:
23.0ms
(/ r (cos (+ b a)))
36.0ms
(* (sin b) (/ r (cos (+ b a))))
14.0ms
(cos (+ b a))

series324.0ms

Counts
3 → 9
Calls
3 calls:
90.0ms
(/ r (cos (+ b a)))
191.0ms
(* (sin b) (/ r (cos (+ b a))))
42.0ms
(cos (+ b a))

simplify862.0ms

Counts
82 → 82
Iterations
IterNodes
done5000
21481
1287
0124

prune597.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize63.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b
(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b
(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b
(* (sin a) (sin b))

rewrite165.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
20×associate-*r*
19×times-frac
13×add-cbrt-cube add-exp-log
8×pow1 associate-/r/
7×sin-mult
6×associate-*l* cos-mult add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×associate-/r* flip3-- prod-exp frac-sub cbrt-unprod flip-- associate-/l* sub-div unswap-sqr
2×cbrt-undiv div-exp pow-prod-down *-commutative div-inv
1×clear-num sub-neg frac-2neg fma-neg diff-log prod-diff associate-*r/
Counts
4 → 110
Calls
4 calls:
28.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
32.0ms
(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
79.0ms
(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
19.0ms
(* (sin a) (sin b))

series780.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
241.0ms
(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
343.0ms
(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
87.0ms
(* (sin a) (sin b))

simplify1.8s

Counts
122 → 122
Iterations
IterNodes
done5000
22428
1472
0184

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (cos a) (cos b) (* (sin a) (- (sin b))))
0.2b
(/ r (fma (cos a) (cos b) (* (sin a) (- (sin b)))))
0.2b
(* (sin b) (/ r (fma (cos a) (cos b) (* (sin a) (- (sin b))))))
0.2b
(* (sin a) (- (sin b)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
24×*-un-lft-identity add-cube-cbrt
23×associate-*r*
19×times-frac
13×add-cbrt-cube add-exp-log
8×pow1
6×associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×distribute-lft-neg-in associate-/r* distribute-rgt-neg-in prod-exp cbrt-unprod associate-/l* unswap-sqr
2×cbrt-undiv div-exp pow-prod-down *-commutative div-inv
1×clear-num neg-mul-1 frac-2neg associate-*r/ distribute-rgt-neg-out fma-udef
Counts
4 → 101
Calls
4 calls:
0.0ms
(fma (cos a) (cos b) (* (sin a) (- (sin b))))
8.0ms
(/ r (fma (cos a) (cos b) (* (sin a) (- (sin b)))))
21.0ms
(* (sin b) (/ r (fma (cos a) (cos b) (* (sin a) (- (sin b))))))
16.0ms
(* (sin a) (- (sin b)))

series798.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(fma (cos a) (cos b) (* (sin a) (- (sin b))))
262.0ms
(/ r (fma (cos a) (cos b) (* (sin a) (- (sin b)))))
330.0ms
(* (sin b) (/ r (fma (cos a) (cos b) (* (sin a) (- (sin b))))))
92.0ms
(* (sin a) (- (sin b)))

simplify1.3s

Counts
113 → 113
Iterations
IterNodes
done5000
22133
1415
0172

prune870.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (cos b) (cos a) (* (sin b) (- (sin a))))
0.1b
(* (sin b) r)
0.2b
(* (sin b) (- (sin a)))
0.3b
(/ (* (sin b) r) (fma (cos b) (cos a) (* (sin b) (- (sin a)))))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
13×add-cbrt-cube associate-*r* add-exp-log
12×*-un-lft-identity add-cube-cbrt
8×pow1
6×associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×distribute-lft-neg-in associate-/r* distribute-rgt-neg-in times-frac prod-exp cbrt-unprod
2×cbrt-undiv div-exp pow-prod-down *-commutative unswap-sqr
1×clear-num neg-mul-1 frac-2neg distribute-rgt-neg-out fma-udef div-inv associate-/l*
Counts
4 → 81
Calls
4 calls:
0.0ms
(fma (cos b) (cos a) (* (sin b) (- (sin a))))
15.0ms
(* (sin b) r)
26.0ms
(* (sin b) (- (sin a)))
9.0ms
(/ (* (sin b) r) (fma (cos b) (cos a) (* (sin b) (- (sin a)))))

series622.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(fma (cos b) (cos a) (* (sin b) (- (sin a))))
49.0ms
(* (sin b) r)
79.0ms
(* (sin b) (- (sin a)))
345.0ms
(/ (* (sin b) r) (fma (cos b) (cos a) (* (sin b) (- (sin a)))))

simplify827.0ms

Counts
93 → 93
Iterations
IterNodes
done5000
21690
1331
0140

prune720.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes460.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done25
325
224
120
014

end0.0ms

sample5.7s

Algorithm
intervals
Results
3.0s2960×body1280valid
1.7s1897×body640valid
349.0ms2060×body80valid
245.0ms707×body320valid
130.0ms376×body160valid