Details

Time bar (total: 2.8m)

sample337.0ms

Algorithm
intervals
Results
183.0ms98×body1280valid
48.0ms51×body640valid
20.0ms29×body320valid
18.0ms70×body80valid
4.0ms8×body160valid

simplify70.0ms

Calls
1 calls:
Slowest
31.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize18.0ms

Local error

Found 3 expressions with local error:

2.9b
(cos (+ a b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
0.1b
(* r (sin b))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
36×times-frac
30×*-un-lft-identity add-cube-cbrt
15×associate-*r* associate-*l*
12×associate-/l*
10×add-cbrt-cube add-exp-log
5×pow1 *-commutative unswap-sqr
3×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-undiv cos-sum div-exp prod-exp cbrt-unprod
1×+-commutative clear-num frac-2neg pow-prod-down div-inv
Calls
3 calls:
Slowest
31.0ms
(/ (* r (sin b)) (cos (+ a b)))
13.0ms
(* r (sin b))
10.0ms
(cos (+ a b))

series230.0ms

Calls
3 calls:
Slowest
161.0ms
(/ (* r (sin b)) (cos (+ a b)))
43.0ms
(* r (sin b))
26.0ms
(cos (+ a b))

simplify3.8s

Calls
109 calls:
Slowest
345.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
271.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
260.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
239.0ms
(/ (* r (* (cbrt (sin b)) (cbrt (sin b)))) (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b)))))
235.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
378×add-sqr-sqrt
244×*-un-lft-identity
173×associate-*l*
144×prod-diff
132×times-frac add-cube-cbrt
117×associate-*r*
95×unswap-sqr
56×distribute-lft-out-- difference-of-squares
39×*-commutative
13×add-cbrt-cube add-exp-log
12×fma-neg associate-/l*
11×associate-/r*
8×pow1
6×add-log-exp
5×sin-mult
4×expm1-log1p-u associate-/r/ cos-mult insert-posit16 log1p-expm1-u
3×prod-exp cbrt-unprod
2×cbrt-undiv flip3-- div-exp pow-prod-down frac-sub flip-- sub-div
1×clear-num sub-neg frac-2neg diff-log div-inv
Calls
4 calls:
Slowest
62.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
50.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
15.0ms
(* (sin a) (sin b))
8.0ms
(* r (sin b))

series573.0ms

Calls
4 calls:
Slowest
339.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
117.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
67.0ms
(* r (sin b))
50.0ms
(* (sin a) (sin b))

simplify49.4s

Calls
638 calls:
Slowest
551.0ms
(/ (* (sqrt r) (sin b)) (- (* (sqrt (cos a)) (sqrt (cos b))) (* (sqrt (sin a)) (sqrt (sin b)))))
457.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
341.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
341.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
337.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))

prune5.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite426.0ms

Algorithm
rewrite-expression-head
Rules
280×add-sqr-sqrt
188×*-un-lft-identity
144×prod-diff
119×associate-*r*
117×associate-*l*
115×add-cube-cbrt
67×times-frac
64×unswap-sqr
36×distribute-lft-out-- difference-of-squares
27×*-commutative
22×associate-/r*
17×associate-*r/
13×add-cbrt-cube add-exp-log
12×fma-neg
8×pow1 associate-/r/
7×sin-mult associate-/l*
6×cos-mult add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×clear-num flip3-- prod-exp frac-sub cbrt-unprod flip-- sub-div
2×cbrt-undiv frac-2neg div-exp pow-prod-down un-div-inv div-inv
1×sub-neg diff-log
Calls
4 calls:
Slowest
244.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
92.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
67.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
15.0ms
(* (sin a) (sin b))

series641.0ms

Calls
4 calls:
Slowest
331.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
139.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
123.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
48.0ms
(* (sin a) (sin b))

simplify40.1s

Calls
491 calls:
Slowest
543.0ms
(fma (cos a) (cos b) (- (* (cbrt (* (sin a) (sin b))) (* (cbrt (* (sin a) (sin b))) (cbrt (* (sin a) (sin b)))))))
436.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
388.0ms
(* (* (* 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))))))
380.0ms
(/ (* (* (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)))))
380.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune4.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
250×add-sqr-sqrt
211×times-frac
181×*-un-lft-identity
171×add-cube-cbrt
120×prod-diff
51×associate-*r* associate-*l*
40×fma-neg
22×unswap-sqr
17×*-commutative
15×associate-/l* difference-of-squares
13×add-cbrt-cube add-exp-log
10×associate-/r*
6×pow1 div-inv add-log-exp
5×distribute-lft-out--
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv div-exp
2×clear-num frac-2neg flip3-- prod-exp associate-/r/ cos-mult cbrt-unprod flip--
1×sub-neg diff-log pow-prod-down associate-/l/
Calls
4 calls:
Slowest
68.0ms
(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
67.0ms
(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
27.0ms
(/ (* (cos a) (cos b)) (sin b))
21.0ms
(* (cos a) (cos b))

series586.0ms

Calls
4 calls:
Slowest
266.0ms
(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
151.0ms
(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
118.0ms
(/ (* (cos a) (cos b)) (sin b))
50.0ms
(* (cos a) (cos b))

simplify46.3s

Calls
455 calls:
Slowest
554.0ms
(fma (/ (* (cos a) (* (cbrt (cos b)) (cbrt (cos b)))) 1) (/ (cbrt (cos b)) (sin b)) (- (* (sqrt (sin a)) (sqrt (sin a)))))
529.0ms
(fma (/ (* (cbrt (cos a)) (cbrt (cos a))) 1) (/ (* (cbrt (cos a)) (cos b)) (sin b)) (- (* (sqrt (sin a)) (sqrt (sin a)))))
513.0ms
(fma (/ (cos a) (sqrt (sin b))) (/ (cos b) (sqrt (sin b))) (- (* (sin a) 1)))
506.0ms
(fma (/ (* (cbrt (cos a)) (cbrt (cos a))) (* (cbrt (sin b)) (cbrt (sin b)))) (/ (* (cbrt (cos a)) (cos b)) (cbrt (sin b))) (- (* (sin a) 1)))
500.0ms
(fma (/ (* (cbrt (cos a)) (cbrt (cos a))) 1) (/ (* (cbrt (cos a)) (cos b)) (sin b)) (- (* (sin a) 1)))

prune4.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes285.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample7.3s

Algorithm
intervals
Results
4.1s3020×body1280valid
1.5s1778×body640valid
893.0ms792×body320valid
454.0ms2079×body80valid
145.0ms332×body160valid