Details

Time bar (total: 6.4s)

sample396.0ms

Algorithm
intervals
Results
62.0ms98×body1280valid
16.0ms64×body640valid
4.0ms25×body320valid
3.0ms60×body80valid
1.0ms9×body160valid

simplify12.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0125
1165
2205
3215
4215
done215

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b
(* r (/ (sin b) (cos (+ a b))))
0.2b
(/ (sin b) (cos (+ a b)))
3.5b
(cos (+ a b))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity times-frac
13×associate-*r*
10×add-exp-log add-cbrt-cube
5×pow1
3×expm1-log1p-u associate-*l* associate-/r* log1p-expm1-u associate-/l* add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×cos-sum frac-2neg associate-*r/ pow-prod-down clear-num *-commutative
Counts
3 → 73
Calls
3 calls:
17.0ms
(* r (/ (sin b) (cos (+ a b))))
10.0ms
(/ (sin b) (cos (+ a b)))
12.0ms
(cos (+ a b))

series176.0ms

Counts
3 → 9
Calls
3 calls:
102.0ms
(* r (/ (sin b) (cos (+ a b))))
41.0ms
(/ (sin b) (cos (+ a b)))
32.0ms
(cos (+ a b))

simplify40.0ms

Counts
82 → 82
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0263560
11093504
25002504
done5002504

prune220.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
20×associate-*r*
19×times-frac
13×add-exp-log add-cbrt-cube
8×pow1 associate-/r/
7×sin-mult
6×associate-*l* cos-mult add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×flip3-- prod-exp associate-/r* frac-sub flip-- cbrt-unprod associate-/l* sub-div unswap-sqr
2×cbrt-undiv div-exp pow-prod-down *-commutative div-inv
1×sub-neg frac-2neg fma-neg diff-log associate-*r/ prod-diff clear-num
Counts
4 → 110
Calls
4 calls:
18.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
28.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
73.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
12.0ms
(* (sin a) (sin b))

series483.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
120.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
226.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
51.0ms
(* (sin a) (sin b))

simplify57.0ms

Counts
122 → 122
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04321384
118471255
250011249
done50011249

prune412.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
19×times-frac
16×associate-*r*
13×add-exp-log add-cbrt-cube
8×pow1
6×associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×prod-exp associate-/r* cbrt-unprod associate-/l* unswap-sqr
2×cbrt-undiv div-exp pow-prod-down *-commutative div-inv
1×frac-2neg associate-*r/ clear-num fma-udef sin-mult
Counts
4 → 94
Calls
4 calls:
0.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))
9.0ms
(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
16.0ms
(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
12.0ms
(* (sin a) (sin b))

series490.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(fma (cos a) (cos b) (- (* (sin a) (sin b))))
120.0ms
(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
235.0ms
(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
47.0ms
(* (sin a) (sin b))

simplify47.0ms

Counts
106 → 106
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
03291173
114131043
250011043
done50011043

prune360.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))
0.2b
(/ (sin b) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b)))))))
0.2b
(* r (/ (sin b) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))))
0.2b
(* (sin a) (sin b))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
19×times-frac
16×associate-*r*
13×add-exp-log add-cbrt-cube
8×pow1
6×associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×prod-exp associate-/r* cbrt-unprod associate-/l* unswap-sqr
2×cbrt-undiv div-exp pow-prod-down *-commutative div-inv
1×frac-2neg associate-*r/ clear-num fma-udef sin-mult
Counts
4 → 94
Calls
4 calls:
0.0ms
(fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))
8.0ms
(/ (sin b) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b)))))))
16.0ms
(* r (/ (sin b) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))))
12.0ms
(* (sin a) (sin b))

series608.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))
156.0ms
(/ (sin b) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b)))))))
278.0ms
(* r (/ (sin b) (fma (cos a) (cos b) (- (expm1 (log1p (* (sin a) (sin b))))))))
46.0ms
(* (sin a) (sin b))

simplify47.0ms

Counts
106 → 106
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03281353
114061165
250011160
done50011160

prune388.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes159.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01612
11612
done1612

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.2s2908×body1280valid
453.0ms1875×body640valid
135.0ms778×body320valid
119.0ms2093×body80valid
42.0ms347×body160valid