Details

Time bar (total: 19.4s)

sample229.0ms

Algorithm
intervals
Results
50.0ms94×body1280valid
49.0ms11×body160valid
20.0ms62×body640valid
5.0ms68×body80valid
5.0ms21×body320valid

simplify46.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
08243
112243
216243
319243
420243
done20243

prune145.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize24.0ms

Local error

Found 3 expressions with local error:

0.1b
(* r (sin b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
2.2b
(cos (+ a b))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
10×add-cbrt-cube add-exp-log
9×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
5×pow1
3×expm1-log1p-u associate-/r* times-frac associate-*r* associate-*l* log1p-expm1-u add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod
1×cos-sum clear-num frac-2neg pow-prod-down *-commutative div-inv associate-/l* unswap-sqr
Counts
3 → 53
Calls
3 calls:
12.0ms
(* r (sin b))
11.0ms
(/ (* r (sin b)) (cos (+ a b)))
11.0ms
(cos (+ a b))

series428.0ms

Counts
3 → 9
Calls
3 calls:
98.0ms
(* r (sin b))
280.0ms
(/ (* r (sin b)) (cos (+ a b)))
49.0ms
(cos (+ a b))

simplify1.3s

Counts
62 → 62
Iterations

Useful iterations: done (1.3s)

IterNodesCost
09814743
122013752
288313592
done500113402

prune442.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-cbrt-cube add-exp-log
10×*-un-lft-identity add-cube-cbrt
8×pow1
6×associate-*r* associate-*l* add-log-exp
5×sin-mult
4×expm1-log1p-u associate-/r/ cos-mult log1p-expm1-u
3×associate-/r* times-frac prod-exp cbrt-unprod
2×cbrt-undiv flip3-- div-exp pow-prod-down *-commutative frac-sub flip-- sub-div unswap-sqr
1×clear-num sub-neg frac-2neg fma-neg diff-log prod-diff div-inv associate-/l*
Counts
4 → 86
Calls
4 calls:
8.0ms
(* r (sin b))
14.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
10.0ms
(* (sin a) (sin b))
27.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series538.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* r (sin b))
120.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
62.0ms
(* (sin a) (sin b))
287.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.7s

Counts
98 → 98
Iterations

Useful iterations: done (2.7s)

IterNodesCost
015334918
138933094
2168832599
done500132043

prune758.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin a) (sin b))
0.2b
(expm1 (log1p (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.3b
(/ (* r (sin b)) (expm1 (log1p (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
0.4b
(log1p (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
11×add-cbrt-cube add-exp-log
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×pow1
5×expm1-log1p-u
4×log1p-expm1-u add-log-exp
3×associate-/r* times-frac associate-*r* associate-*l*
2×cbrt-undiv div-exp prod-exp cbrt-unprod
1×log1p-udef expm1-log1p clear-num frac-2neg pow-prod-down log1p-expm1 *-commutative div-inv sin-mult associate-/l* expm1-udef unswap-sqr
Counts
4 → 66
Calls
4 calls:
10.0ms
(* (sin a) (sin b))
0.0ms
(expm1 (log1p (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
11.0ms
(/ (* r (sin b)) (expm1 (log1p (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
2.0ms
(log1p (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series874.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (sin a) (sin b))
156.0ms
(expm1 (log1p (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
450.0ms
(/ (* r (sin b)) (expm1 (log1p (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
205.0ms
(log1p (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.6s

Counts
78 → 78
Iterations

Useful iterations: done (1.6s)

IterNodesCost
013536645
130830019
2133629784
done500029259

prune554.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
0.2b
(* (sin a) (sin b))
0.3b
(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
2.8b
(log (exp (* (sin a) (sin b))))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
11×*-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
8×pow1
7×add-log-exp
6×log-prod prod-diff log-pow
4×expm1-log1p-u log1p-expm1-u
3×associate-/r* times-frac associate-*r* associate-*l* associate--r+
2×cbrt-undiv exp-prod flip3-- exp-to-pow div-exp prod-exp associate-/r/ cbrt-unprod flip--
1×clear-num sub-neg frac-2neg fma-neg diff-log rem-log-exp pow-prod-down *-commutative div-inv sin-mult associate-/l* unswap-sqr
Counts
4 → 86
Calls
4 calls:
13.0ms
(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
10.0ms
(* (sin a) (sin b))
34.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
4.0ms
(log (exp (* (sin a) (sin b))))

series594.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
61.0ms
(* (sin a) (sin b))
355.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
66.0ms
(log (exp (* (sin a) (sin b))))

simplify2.3s

Counts
98 → 98
Iterations

Useful iterations: done (2.3s)

IterNodesCost
016948639
143737114
2243936187
done500136027

prune699.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes414.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
014583
117583
done17583

end0.0ms

sample5.3s

Algorithm
intervals
Results
3.0s2960×body1280valid
1.3s1897×body640valid
282.0ms707×body320valid
244.0ms2060×body80valid
144.0ms376×body160valid