Details

Time bar (total: 47.4s)

sample718.0ms

Algorithm
intervals
Results
278.0ms91×body1280valid
137.0ms59×body640valid
78.0ms63×body80valid
42.0ms17×body160valid
21.0ms26×body320valid

simplify32.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
32.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize18.0ms

Local error

Found 3 expressions with local error:

2.4b
(cos (+ a b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
0.1b
(* r (sin b))

rewrite41.0ms

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×associate-/r* times-frac associate-*r* associate-*l* insert-posit16 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 → 50
Calls
3 calls:
Slowest
18.0ms
(cos (+ a b))
12.0ms
(/ (* r (sin b)) (cos (+ a b)))
8.0ms
(* r (sin b))

series241.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
145.0ms
(/ (* r (sin b)) (cos (+ a b)))
66.0ms
(* r (sin b))
30.0ms
(cos (+ a b))

simplify2.7s

Counts
64 → 59
Calls
64 calls:
Slowest
354.0ms
(* (* (/ (* r (sin b)) (cos (+ a b))) (/ (* r (sin b)) (cos (+ a b)))) (/ (* r (sin b)) (cos (+ a b))))
347.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
229.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
225.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
212.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))

prune675.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×add-cbrt-cube add-exp-log
12×*-un-lft-identity add-cube-cbrt
10×pow1
9×associate-*r* associate-*l*
4×prod-exp associate-/r/ cbrt-unprod insert-posit16 add-log-exp
3×associate-/r* times-frac pow-prod-down cos-mult *-commutative sin-mult unswap-sqr
2×cbrt-undiv div-exp
1×clear-num frac-2neg flip3-- frac-sub div-inv flip-- associate-/l* sub-div
Counts
4 → 85
Calls
4 calls:
Slowest
36.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
21.0ms
(* (sin a) (sin b))
18.0ms
(* (cos a) (cos b))
15.0ms
(* r (sin b))

series838.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
451.0ms
(* (sin a) (sin b))
293.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
54.0ms
(* (cos a) (cos b))
40.0ms
(* r (sin b))

simplify7.2s

Counts
101 → 97
Calls
101 calls:
Slowest
453.0ms
(/ (* r (sin b)) (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b)))))
422.0ms
(* (* (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
402.0ms
(* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b)))
387.0ms
(/ (* (* (* r r) r) (* (* (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)))))
374.0ms
(/ (* r (sin b)) (- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b))))))

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

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))

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
24×*-un-lft-identity add-cube-cbrt
23×associate-*r*
19×times-frac
15×add-cbrt-cube add-exp-log
10×pow1
9×associate-*l*
8×associate-/r/
5×cos-mult sin-mult
4×prod-exp cbrt-unprod insert-posit16 add-log-exp unswap-sqr
3×associate-/r* pow-prod-down *-commutative associate-/l*
2×cbrt-undiv flip3-- div-exp frac-sub div-inv flip-- sub-div
1×clear-num frac-2neg associate-*r/
Counts
4 → 109
Calls
4 calls:
Slowest
87.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
25.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
13.0ms
(* (sin a) (sin b))
9.0ms
(* (cos a) (cos b))

series657.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
341.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
161.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
79.0ms
(* (sin a) (sin b))
76.0ms
(* (cos a) (cos b))

simplify11.4s

Counts
132 → 121
Calls
132 calls:
Slowest
454.0ms
(/ (sin b) (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)))
432.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
410.0ms
(* (* (* 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))))))
409.0ms
(/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
408.0ms
(* r (/ (sin b) (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))))

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.3b
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.2b
(* (sin a) (sin b))
0.2b
(* (sin a) (sin b))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
86×pow1
36×pow-prod-down
32×add-cbrt-cube add-exp-log
18×prod-exp cbrt-unprod
12×add-sqr-sqrt
8×*-un-lft-identity associate-*r* associate-*l* pow-sqr pow-prod-up add-cube-cbrt
6×sin-mult
4×pow-plus cos-mult *-commutative insert-posit16 add-log-exp
2×pow2 frac-times swap-sqr associate-*l/ associate-*r/ unswap-sqr
Counts
4 → 116
Calls
4 calls:
Slowest
70.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
53.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
22.0ms
(* (sin a) (sin b))
21.0ms
(* (sin a) (sin b))

series291.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
84.0ms
(* (sin a) (sin b))
80.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))
72.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
56.0ms
(* (sin a) (sin b))

simplify9.0s

Counts
128 → 128
Calls
128 calls:
Slowest
896.0ms
(* (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))) (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))))
868.0ms
(* (* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b))) (* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b))))
806.0ms
(* (* (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (cos a) (cos b))) (* (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (cos a) (cos b))))
681.0ms
(* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))) (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
382.0ms
(exp (* (* (sin a) (sin b)) (* (sin a) (sin b))))

prune2.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes308.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample7.7s

Algorithm
intervals
Results
4.2s2873×body1280valid
2.0s1833×body640valid
495.0ms743×body320valid
427.0ms2218×body80valid
203.0ms337×body160valid