Details

Time bar (total: 34.8s)

sample691.0ms

Algorithm
intervals
Results
102.0ms87×body1280valid
86.0ms70×body640valid
14.0ms63×body80valid
12.0ms23×body320valid
5.0ms13×body160valid

simplify57.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
56.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize37.0ms

Local error

Found 3 expressions with local error:

3.2b
(cos (+ a b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
0.1b
(* r (sin b))

rewrite32.0ms

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* insert-posit16 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 → 56
Calls
3 calls:
Slowest
12.0ms
(/ (* r (sin b)) (cos (+ a b)))
9.0ms
(cos (+ a b))
8.0ms
(* r (sin b))

series220.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
126.0ms
(/ (* r (sin b)) (cos (+ a b)))
51.0ms
(* r (sin b))
42.0ms
(cos (+ a b))

simplify1.4s

Counts
33 → 65
Calls
33 calls:
Slowest
282.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
202.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
200.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
200.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
181.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))

prune574.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite97.0ms

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 insert-posit16 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 → 90
Calls
4 calls:
Slowest
34.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
30.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
22.0ms
(* (sin a) (sin b))
9.0ms
(* r (sin b))

series535.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
297.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
125.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
59.0ms
(* (sin a) (sin b))
54.0ms
(* r (sin b))

simplify3.9s

Counts
56 → 102
Calls
56 calls:
Slowest
470.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
343.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
328.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
303.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
293.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

3.0b
(log (exp (* (sin a) (sin b))))
0.2b
(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
0.2b
(* (sin a) (sin b))
0.1b
(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))

rewrite83.0ms

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 insert-posit16 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 → 90
Calls
4 calls:
Slowest
51.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
14.0ms
(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
11.0ms
(* (sin a) (sin b))
5.0ms
(log (exp (* (sin a) (sin b))))

series561.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
315.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
110.0ms
(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
72.0ms
(* (sin a) (sin b))
65.0ms
(log (exp (* (sin a) (sin b))))

simplify8.5s

Counts
61 → 102
Calls
61 calls:
Slowest
544.0ms
(fma (cos a) (cos b) (- (* (cbrt (log (exp (* (sin a) (sin b))))) (* (cbrt (log (exp (* (sin a) (sin b))))) (cbrt (log (exp (* (sin a) (sin b)))))))))
429.0ms
(fma (cos a) (cos b) (- (* (log (exp (* (sin a) (sin b)))) 1)))
383.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (log (exp (* (sin a) (sin b)))) (log (exp (* (sin a) (sin b))))) (* (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
380.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
354.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
29×*-un-lft-identity add-cube-cbrt
28×times-frac
13×add-cbrt-cube associate-*l* add-exp-log
6×pow1 associate-/r* associate-/l* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv div-exp associate-*r* prod-diff div-inv
2×clear-num frac-2neg flip3-- prod-exp associate-/r/ cbrt-unprod flip-- unswap-sqr
1×sub-neg fma-neg diff-log pow-prod-down associate-*l/ *-commutative
Counts
4 → 116
Calls
4 calls:
Slowest
31.0ms
(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
30.0ms
(* (/ (cos a) (sin b)) (cos b))
26.0ms
(/ r (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))
17.0ms
(/ (cos a) (sin b))

series565.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
249.0ms
(/ r (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))
117.0ms
(* (/ (cos a) (sin b)) (cos b))
117.0ms
(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
82.0ms
(/ (cos a) (sin b))

simplify4.9s

Counts
97 → 128
Calls
97 calls:
Slowest
430.0ms
(/ (* (* (cos a) (cos a)) (cos a)) (* (* (sin b) (sin b)) (sin b)))
303.0ms
(* (* (* (/ (cos a) (sin b)) (/ (cos a) (sin b))) (/ (cos a) (sin b))) (* (* (cos b) (cos b)) (cos b)))
298.0ms
(/ (* (* r r) r) (* (* (- (* (/ (cos a) (sin b)) (cos b)) (sin a)) (- (* (/ (cos a) (sin b)) (cos b)) (sin a))) (- (* (/ (cos a) (sin b)) (cos b)) (sin a))))
285.0ms
(+ (* (* (/ (cos a) (sin b)) (cos b)) (* (/ (cos a) (sin b)) (cos b))) (+ (* (sin a) (sin a)) (* (* (/ (cos a) (sin b)) (cos b)) (sin a))))
271.0ms
(/ (exp (* (/ (cos a) (sin b)) (cos b))) (exp (sin a)))

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes570.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample7.3s

Algorithm
intervals
Results
3.8s2921×body1280valid
2.2s1775×body640valid
474.0ms796×body320valid
462.0ms2156×body80valid
126.0ms353×body160valid