Details

Time bar (total: 39.7s)

sample562.0ms

Algorithm
intervals
Results
248.0ms103×body1280valid
100.0ms59×body640valid
21.0ms22×body320valid
19.0ms64×body80valid
4.0ms8×body160valid

simplify55.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
54.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.2b

localize61.0ms

Local error

Found 3 expressions with local error:

2.2b
(cos (+ a b))
0.3b
(/ (* r (sin b)) (cos (+ a b)))
0.2b
(* r (sin b))

rewrite37.0ms

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
15.0ms
(cos (+ a b))
12.0ms
(/ (* r (sin b)) (cos (+ a b)))
8.0ms
(* r (sin b))

series296.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
184.0ms
(/ (* r (sin b)) (cos (+ a b)))
70.0ms
(* r (sin b))
42.0ms
(cos (+ a b))

simplify1.5s

Counts
33 → 65
Calls
33 calls:
Slowest
328.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
235.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
227.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
221.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
190.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))

prune675.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

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

rewrite90.0ms

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×expm1-log1p-u prod-exp associate-/r/ cbrt-unprod insert-posit16 log1p-expm1-u 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 → 93
Calls
4 calls:
Slowest
60.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
11.0ms
(* (sin a) (sin b))
9.0ms
(* (cos a) (cos b))
8.0ms
(* r (sin b))

series464.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
269.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
70.0ms
(* r (sin b))
69.0ms
(* (sin a) (sin b))
57.0ms
(* (cos a) (cos b))

simplify3.3s

Counts
60 → 105
Calls
60 calls:
Slowest
381.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
375.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
326.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
303.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (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)))))
296.0ms
(* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b)))

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

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))

rewrite171.0ms

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×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u 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 → 117
Calls
4 calls:
Slowest
88.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
46.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
19.0ms
(* (cos a) (cos b))
14.0ms
(* (sin a) (sin b))

series632.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
342.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
166.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
68.0ms
(* (cos a) (cos b))
56.0ms
(* (sin a) (sin b))

simplify5.7s

Counts
90 → 129
Calls
90 calls:
Slowest
792.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
342.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
338.0ms
(* (* (* 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))))))
325.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
315.0ms
(/ (* (* (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)))))

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize73.0ms

Local error

Found 4 expressions with local error:

23.5b
(cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))
0.3b
(* (* (sin b) (sin a)) (* (sin b) (sin a)))
0.3b
(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))))
0.2b
(* (sin b) (sin a))

rewrite401.0ms

Algorithm
rewrite-expression-head
Rules
45×pow1
29×sin-mult
20×add-cbrt-cube add-exp-log
18×pow-prod-down
16×add-sqr-sqrt
14×cbrt-div *-un-lft-identity add-cube-cbrt
11×frac-times associate-*l/
9×times-frac prod-exp associate-/r/ cbrt-unprod
7×associate-*r/ cos-mult frac-sub
4×expm1-log1p-u associate-*r* associate-*l* pow-sqr pow-prod-up insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×pow-plus *-commutative
1×cbrt-prod pow2 cbrt-undiv clear-num frac-2neg flip3-- pow1/3 swap-sqr div-exp pow3 rem-cbrt-cube div-inv flip-- unswap-sqr
Counts
4 → 121
Calls
4 calls:
Slowest
166.0ms
(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))))
164.0ms
(cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))
58.0ms
(* (* (sin b) (sin a)) (* (sin b) (sin a)))
12.0ms
(* (sin b) (sin a))

series394.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
163.0ms
(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))))
83.0ms
(* (sin b) (sin a))
78.0ms
(cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))
70.0ms
(* (* (sin b) (sin a)) (* (sin b) (sin a)))

simplify12.6s

Counts
103 → 133
Calls
103 calls:
Slowest
768.0ms
(* (* (* (* (sin b) (sin b)) (sin b)) (* (* (sin a) (sin a)) (sin a))) (* (* (* (sin b) (sin b)) (sin b)) (* (* (sin a) (sin a)) (sin a))))
735.0ms
(* (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))) (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))
441.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a)))))) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a)))))))
390.0ms
(/ (sqrt (sin b)) (sqrt (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a)))))))
380.0ms
(cbrt (* (* (- (cos (- b a)) (cos (+ b a))) (- (cos (- b a)) (cos (+ b a)))) (- (cos (- b a)) (cos (+ b a)))))

prune2.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes220.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample7.4s

Algorithm
intervals
Results
4.4s2972×body1280valid
1.9s1821×body640valid
384.0ms726×body320valid
342.0ms2118×body80valid
133.0ms364×body160valid