Details

Time bar (total: 41.6s)

sample1.1s

Algorithm
intervals
Results
586.0ms56×body640valid
332.0ms93×body1280valid
19.0ms30×body320valid
13.0ms69×body80valid
6.0ms8×body160valid

simplify50.0ms

Calls
1 calls:
Slowest
49.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune54.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize43.0ms

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))

rewrite24.0ms

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
11.0ms
(/ (* r (sin b)) (cos (+ a b)))
7.0ms
(cos (+ a b))
3.0ms
(* r (sin b))

series226.0ms

Calls
3 calls:
Slowest
126.0ms
(/ (* r (sin b)) (cos (+ a b)))
60.0ms
(* r (sin b))
39.0ms
(cos (+ a b))

simplify1.1s

Calls
24 calls:
Slowest
357.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
207.0ms
(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
184.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
94.0ms
(- (log (* r (sin b))) (log (cos (+ a b))))
50.0ms
(/ (* (sin b) r) (cos (+ a b)))

prune816.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize48.0ms

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)) (* (sin a) (sin b)))

rewrite59.0ms

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
27.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
18.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms
(* (sin a) (sin b))
3.0ms
(* r (sin b))

series435.0ms

Calls
4 calls:
Slowest
215.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
122.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
55.0ms
(* (sin a) (sin b))
42.0ms
(* r (sin b))

simplify2.9s

Calls
42 calls:
Slowest
393.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
386.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
296.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
287.0ms
(/ (* (* (* 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)))))
260.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

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
25.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
25.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
9.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
5.0ms
(* (sin a) (sin b))

series644.0ms

Calls
4 calls:
Slowest
316.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
145.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
101.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
82.0ms
(* (sin a) (sin b))

simplify4.7s

Calls
70 calls:
Slowest
413.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
379.0ms
(/ (* (* (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)))))
377.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
318.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
282.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

27.7b
(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
0.3b
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.2b
(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
0.2b
(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b)))))))

rewrite352.0ms

Algorithm
rewrite-expression-head
Rules
40×sin-mult
31×pow1
23×associate-*r*
21×cbrt-div
19×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×times-frac add-cbrt-cube add-exp-log associate-/r/
16×frac-times associate-*l/
14×cos-mult frac-sub
13×pow-prod-down
11×associate-*r/
8×prod-exp cbrt-unprod
4×pow-prod-up insert-posit16 add-log-exp
3×associate-/r* associate-/l*
2×pow-plus flip3-- *-commutative div-inv flip--
1×cbrt-prod pow2 cbrt-undiv clear-num frac-2neg pow1/3 div-exp associate-*l* pow3 rem-cbrt-cube
Calls
4 calls:
Slowest
144.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b)))))))
91.0ms
(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
77.0ms
(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
38.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))

series644.0ms

Calls
4 calls:
Slowest
339.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b)))))))
179.0ms
(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
66.0ms
(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
60.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))

simplify13.6s

Calls
105 calls:
Slowest
704.0ms
(* (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))) (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))))
413.0ms
(cbrt (* (* (- (cos (- a b)) (cos (+ a b))) (- (cos (- a b)) (cos (+ a b)))) (- (cos (- a b)) (cos (+ a b)))))
397.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b)))) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))) (* (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b)))))))
381.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
379.0ms
(* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))) (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))

prune2.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes488.0ms

Accuracy

0% (0.3b remaining)

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

bsearch6.0ms

end0.0ms

sample8.5s

Algorithm
intervals
Results
5.2s2906×body1280valid
1.9s1842×body640valid
476.0ms2184×body80valid
446.0ms739×body320valid
227.0ms330×body160valid