Details

Time bar (total: 23.7s)

sample309.0ms

Algorithm
intervals
Results
90.0ms81×body1280valid
55.0ms28×body320valid
47.0ms54×body640valid
14.0ms83×body80valid
4.0ms10×body160valid

simplify58.0ms

Calls
1 calls:
Slowest
57.0ms
(* r (/ (sin b) (cos (+ a b))))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize407.0ms

Local error

Found 3 expressions with local error:

2.5b
(cos (+ a b))
0.2b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
13×associate-*r*
5×add-cbrt-cube add-exp-log
3×pow1 associate-/r* insert-posit16 associate-/l* add-log-exp
2×div-inv
1×cbrt-undiv cos-sum clear-num frac-2neg div-exp associate-*r/ *-commutative
Calls
3 calls:
Slowest
9.0ms
(/ (sin b) (cos (+ a b)))
7.0ms
(cos (+ a b))
6.0ms
(* r (/ (sin b) (cos (+ a b))))

series214.0ms

Calls
3 calls:
Slowest
123.0ms
(* r (/ (sin b) (cos (+ a b))))
56.0ms
(/ (sin b) (cos (+ a b)))
34.0ms
(cos (+ a b))

simplify1.3s

Calls
49 calls:
Slowest
279.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
195.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
191.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
141.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
45.0ms
(/ (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b)))))

prune743.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

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

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
20×associate-*r*
18×times-frac
8×add-cbrt-cube add-exp-log associate-/r/
7×sin-mult
6×pow1 cos-mult add-log-exp
4×insert-posit16
3×associate-/r* flip3-- associate-*l* frac-sub flip-- associate-/l* sub-div
2×*-commutative div-inv
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-exp pow-prod-down prod-exp associate-*r/ cbrt-unprod
Calls
4 calls:
Slowest
27.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
24.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
17.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
8.0ms
(* (sin a) (sin b))

series542.0ms

Calls
4 calls:
Slowest
232.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
134.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
92.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
84.0ms
(* (sin a) (sin b))

simplify3.6s

Calls
70 calls:
Slowest
319.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
309.0ms
(/ (* (* (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)))))
291.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
244.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
222.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

2.7b
(log (exp (* (sin a) (sin b))))
0.2b
(* (sin a) (sin b))
0.2b
(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
0.1b
(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×times-frac associate-*r*
8×add-cbrt-cube add-exp-log
7×pow1
5×add-log-exp
4×associate-/r/ insert-posit16
3×log-prod associate-/r* associate-*l* log-pow associate-/l*
2×flip3-- *-commutative div-inv flip--
1×cbrt-undiv exp-prod clear-num frac-2neg exp-to-pow div-exp rem-log-exp pow-prod-down prod-exp associate-*r/ cbrt-unprod sin-mult
Calls
4 calls:
Slowest
20.0ms
(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
12.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
9.0ms
(* (sin a) (sin b))
5.0ms
(log (exp (* (sin a) (sin b))))

series487.0ms

Calls
4 calls:
Slowest
271.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
112.0ms
(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
60.0ms
(log (exp (* (sin a) (sin b))))
44.0ms
(* (sin a) (sin b))

simplify3.1s

Calls
70 calls:
Slowest
299.0ms
(/ (* (* (sin b) (sin b)) (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)))))))
282.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
220.0ms
(+ (* (* (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)))))))
210.0ms
(+ (* (* (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)))))))
127.0ms
(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (sin b))
0.7b
(cbrt (sin b))
0.7b
(cbrt (sin b))
0.5b
(* (cbrt (sin b)) (cbrt (sin b)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×pow1
7×pow1/3
6×associate-*r* associate-*l* add-exp-log
4×add-cbrt-cube insert-posit16 add-log-exp
2×pow-prod-down pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
6.0ms
(* (cbrt (sin b)) (cbrt (sin b)))
1.0ms
(cbrt (sin b))
1.0ms
(cbrt (sin b))
1.0ms
(cbrt (sin b))

series580.0ms

Calls
4 calls:
Slowest
152.0ms
(cbrt (sin b))
144.0ms
(cbrt (sin b))
144.0ms
(* (cbrt (sin b)) (cbrt (sin b)))
140.0ms
(cbrt (sin b))

simplify639.0ms

Calls
41 calls:
Slowest
141.0ms
(- (pow b 1/3) (+ (* 1/3240 (pow (pow b 13) 1/3)) (* 1/18 (pow (pow b 7) 1/3))))
128.0ms
(- (+ (pow b 2/3) (* 1/405 (pow (pow b 14) 1/3))) (* 1/9 (pow (pow b 8) 1/3)))
105.0ms
(- (pow b 1/3) (+ (* 1/3240 (pow (pow b 13) 1/3)) (* 1/18 (pow (pow b 7) 1/3))))
104.0ms
(- (pow b 1/3) (+ (* 1/3240 (pow (pow b 13) 1/3)) (* 1/18 (pow (pow b 7) 1/3))))
10.0ms
(pow (sin b) 1/3)

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes311.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch6.0ms

end0.0ms

sample7.1s

Algorithm
intervals
Results
4.3s2908×body1280valid
1.6s1801×body640valid
399.0ms2176×body80valid
390.0ms760×body320valid
198.0ms355×body160valid