Details

Time bar (total: 21.8s)

sample268.0ms

Algorithm
intervals
Results
94.0ms94×body1280valid
50.0ms63×body80valid
43.0ms59×body640valid
14.0ms26×body320valid
5.0ms14×body160valid

simplify146.0ms

Calls
1 calls:
Slowest
146.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize117.0ms

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))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×add-cbrt-cube add-exp-log
3×pow1 associate-/r* times-frac associate-*r* insert-posit16 add-log-exp
1×cbrt-undiv cos-sum clear-num frac-2neg div-exp *-commutative div-inv associate-/l*
Calls
3 calls:
Slowest
10.0ms
(/ (* r (sin b)) (cos (+ a b)))
7.0ms
(cos (+ a b))
3.0ms
(* r (sin b))

series249.0ms

Calls
3 calls:
Slowest
132.0ms
(/ (* r (sin b)) (cos (+ a b)))
64.0ms
(* r (sin b))
53.0ms
(cos (+ a b))

simplify923.0ms

Calls
24 calls:
Slowest
350.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
183.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
149.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
90.0ms
(- (log (* r (sin b))) (log (cos (+ a b))))
41.0ms
(/ (* (sin b) r) (cos (+ a b)))

prune510.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

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))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×add-cbrt-cube add-exp-log
6×pow1 associate-*r* add-log-exp
5×sin-mult
4×associate-/r/ cos-mult insert-posit16
3×associate-/r* times-frac associate-*l*
2×flip3-- *-commutative frac-sub flip-- sub-div
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-exp pow-prod-down prod-exp cbrt-unprod div-inv associate-/l*
Calls
4 calls:
Slowest
20.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
10.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms
(* (sin a) (sin b))
1.0ms
(* r (sin b))

series462.0ms

Calls
4 calls:
Slowest
262.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
90.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
57.0ms
(* (sin a) (sin b))
53.0ms
(* r (sin b))

simplify2.7s

Calls
42 calls:
Slowest
377.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
352.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
268.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
235.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
211.0ms
(/ (* (* (* 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)))))

prune981.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

3.7b
(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)))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×add-cbrt-cube add-exp-log
7×pow1
6×log-prod add-log-exp
4×insert-posit16
3×associate-/r* times-frac associate-*r* associate-*l* log-pow associate--r+
2×flip3-- associate-/r/ flip--
1×cbrt-undiv exp-prod clear-num sub-neg frac-2neg exp-to-pow diff-log div-exp rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod div-inv sin-mult associate-/l*
Calls
4 calls:
Slowest
12.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
8.0ms
(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
4.0ms
(* (sin a) (sin b))
3.0ms
(log (exp (* (sin a) (sin b))))

series504.0ms

Calls
4 calls:
Slowest
275.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
112.0ms
(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
59.0ms
(* (sin a) (sin b))
58.0ms
(log (exp (* (sin a) (sin b))))

simplify2.2s

Calls
44 calls:
Slowest
279.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
246.0ms
(+ (* (* (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)))))))
190.0ms
(/ (* (* (* 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)))))))
156.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
147.0ms
(- (log (* r (sin b))) (log (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×add-cbrt-cube add-exp-log
6×pow1 associate-*r* add-log-exp
5×sin-mult
4×associate-/r/ cos-mult insert-posit16
3×associate-/r* times-frac associate-*l*
2×flip3-- *-commutative frac-sub flip-- sub-div
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-exp pow-prod-down prod-exp cbrt-unprod div-inv associate-/l*
Calls
4 calls:
Slowest
18.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
8.0ms
(- (* (cos a) (cos b)) (* (sin b) (sin a)))
4.0ms
(* (sin b) (sin a))
1.0ms
(* r (sin b))

series449.0ms

Calls
4 calls:
Slowest
240.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
94.0ms
(- (* (cos a) (cos b)) (* (sin b) (sin a)))
68.0ms
(* (sin b) (sin a))
47.0ms
(* r (sin b))

simplify2.5s

Calls
42 calls:
Slowest
358.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- b a)) (cos (+ b a)))))
286.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
226.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- b a)) (cos (+ b a))))
210.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
209.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (* (cos a) (cos b)) (* (sin b) (sin a)))))

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes281.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample7.2s

Algorithm
intervals
Results
4.4s2903×body1280valid
1.6s1812×body640valid
452.0ms835×body320valid
422.0ms2100×body80valid
123.0ms350×body160valid