Details

Time bar (total: 6.5s)

sample389.0ms

Algorithm
intervals
Results
39.0ms85×body1280valid
15.0ms60×body640valid
5.0ms79×body80valid
3.0ms19×body320valid
2.0ms13×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: 16.0b

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)))
3.8b
(cos (+ a b))

rewrite42.0ms

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))

series172.0ms

Counts
3 → 9
Calls
3 calls:
100.0ms
(* 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

prune211.0ms

Pruning

6 alts after pruning (6 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)))
27.0ms
(/ (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))

series475.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
116.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
225.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
50.0ms
(* (sin a) (sin b))

simplify57.0ms

Counts
122 → 122
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04321384
118471255
250011249
done50011249

prune395.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
23×add-cube-cbrt *-un-lft-identity
19×times-frac
18×associate-*r*
13×add-exp-log add-cbrt-cube
8×pow1
6×associate-*l* add-log-exp
4×expm1-log1p-u associate-/r/ log1p-expm1-u
3×flip3-- prod-diff prod-exp associate-/r* flip-- cbrt-unprod associate-/l* unswap-sqr
2×cbrt-undiv div-exp pow-prod-down *-commutative div-inv
1×sub-neg frac-2neg fma-neg diff-log associate-*r/ clear-num sin-mult expm1-udef associate--r-
Counts
4 → 107
Calls
4 calls:
12.0ms
(- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b)))))
23.0ms
(/ (sin b) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))))
52.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b)))))))
12.0ms
(* (sin a) (sin b))

series599.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b)))))
155.0ms
(/ (sin b) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))))
278.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b)))))))
46.0ms
(* (sin a) (sin b))

simplify59.0ms

Counts
119 → 119
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
04361600
118731337
250021333
done50021333

prune435.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.3b
(pow (* (sin a) (sin b)) 3)
0.4b
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.5b
(pow (* (cos a) (cos b)) 3)

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
88×pow1
36×pow-prod-down
34×add-exp-log add-cbrt-cube
18×prod-exp cbrt-unprod
8×pow-sqr pow-prod-up
6×add-sqr-sqrt add-cube-cbrt pow-unpow *-un-lft-identity
5×cos-mult sin-mult
4×expm1-log1p-u pow-pow pow-plus pow-exp log1p-expm1-u add-log-exp rem-cube-cbrt
2×cube-div pow2 cube-mult frac-times pow-to-exp unpow-prod-down unpow3 cube-prod associate-*r/ swap-sqr associate-*r* associate-*l* associate-*l/ *-commutative sqr-pow
Counts
4 → 128
Calls
4 calls:
46.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
11.0ms
(pow (* (sin a) (sin b)) 3)
41.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
9.0ms
(pow (* (cos a) (cos b)) 3)

series252.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
66.0ms
(pow (* (sin a) (sin b)) 3)
60.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
65.0ms
(pow (* (cos a) (cos b)) 3)

simplify76.0ms

Counts
140 → 140
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
0463618
12316583
25002580
done5002580

prune399.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes152.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01712
11712
done1712

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.2s2934×body1280valid
463.0ms1844×body640valid
130.0ms734×body320valid
119.0ms2128×body80valid
45.0ms362×body160valid