Details

Time bar (total: 33.0s)

sample692.0ms

Algorithm
intervals
Results
149.0ms87×body1280valid
61.0ms70×body640valid
14.0ms23×body320valid
12.0ms63×body80valid
6.0ms13×body160valid

simplify47.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
46.0ms
(* r (/ (sin b) (cos (+ a b))))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize40.0ms

Local error

Found 3 expressions with local error:

3.2b
(cos (+ a b))
0.3b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))

rewrite34.0ms

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* insert-posit16 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 → 76
Calls
3 calls:
Slowest
13.0ms
(* r (/ (sin b) (cos (+ a b))))
11.0ms
(cos (+ a b))
9.0ms
(/ (sin b) (cos (+ a b)))

series198.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
120.0ms
(* r (/ (sin b) (cos (+ a b))))
41.0ms
(/ (sin b) (cos (+ a b)))
37.0ms
(cos (+ a b))

simplify2.4s

Counts
60 → 85
Calls
60 calls:
Slowest
368.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
300.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
286.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
221.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
216.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite172.0ms

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 insert-posit16 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 → 114
Calls
4 calls:
Slowest
97.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
36.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
25.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
12.0ms
(* (sin a) (sin b))

series748.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
336.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
199.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
126.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
87.0ms
(* (sin a) (sin b))

simplify6.1s

Counts
86 → 126
Calls
86 calls:
Slowest
450.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
365.0ms
(* (* (* r r) r) (* (* (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
361.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
329.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
321.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

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))

rewrite69.0ms

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
20.0ms
(/ r (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))
20.0ms
(* (/ (cos a) (sin b)) (cos b))
18.0ms
(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
9.0ms
(/ (cos a) (sin b))

series609.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
274.0ms
(/ r (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))
167.0ms
(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
90.0ms
(* (/ (cos a) (sin b)) (cos b))
77.0ms
(/ (cos a) (sin b))

simplify4.9s

Counts
97 → 128
Calls
97 calls:
Slowest
387.0ms
(/ (* (* (cos a) (cos a)) (cos a)) (* (* (sin b) (sin b)) (sin b)))
351.0ms
(/ (* (* 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))))
341.0ms
(+ (* (* (/ (cos a) (sin b)) (cos b)) (* (/ (cos a) (sin b)) (cos b))) (+ (* (sin a) (sin a)) (* (* (/ (cos a) (sin b)) (cos b)) (sin a))))
328.0ms
(- (/ 1 b) (+ (* 1/3 b) (* 1/2 (/ (pow a 2) b))))
243.0ms
(+ (* 1/2 (* (pow a 2) (* r b))) (+ (* a (* r (pow b 2))) (* r b)))

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 3 expressions with local error:

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

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×times-frac
7×add-cbrt-cube add-exp-log
6×associate-/r* associate-/l*
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-undiv clear-num frac-2neg div-exp div-inv
1×fma-udef
Counts
3 → 71
Calls
3 calls:
Slowest
9.0ms
(/ (cos a) (sin b))
4.0ms
(/ r (fma (/ (cos a) (sin b)) (cos b) (- (sin a))))
0.0ms
(fma (/ (cos a) (sin b)) (cos b) (- (sin a)))

series541.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
310.0ms
(/ r (fma (/ (cos a) (sin b)) (cos b) (- (sin a))))
154.0ms
(fma (/ (cos a) (sin b)) (cos b) (- (sin a)))
76.0ms
(/ (cos a) (sin b))

simplify3.0s

Counts
59 → 80
Calls
59 calls:
Slowest
439.0ms
(/ (* (* (cos a) (cos a)) (cos a)) (* (* (sin b) (sin b)) (sin b)))
386.0ms
(/ (* (* r r) r) (* (* (fma (/ (cos a) (sin b)) (cos b) (- (sin a))) (fma (/ (cos a) (sin b)) (cos b) (- (sin a)))) (fma (/ (cos a) (sin b)) (cos b) (- (sin a)))))
260.0ms
(- (+ (/ 1 b) (* 1/6 b)) (* 1/2 (/ (pow a 2) b)))
215.0ms
(+ (* 1/2 (* (pow a 2) (* r b))) (+ (* a (* r (pow b 2))) (* r b)))
198.0ms
(- (/ 1 b) (+ a (* 1/2 (/ (pow a 2) b))))

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes247.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch1.0ms

end0.0ms

sample7.6s

Algorithm
intervals
Results
4.3s2921×body1280valid
2.0s1775×body640valid
522.0ms796×body320valid
468.0ms2156×body80valid
135.0ms353×body160valid