Details

Time bar (total: 1.1m)

sample263.0ms

Algorithm
intervals
Results
72.0ms91×body1280valid
63.0ms59×body640valid
10.0ms26×body320valid
7.0ms63×body80valid
5.0ms17×body160valid

simplify49.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
48.0ms
(* r (/ (sin b) (cos (+ a b))))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize36.0ms

Local error

Found 3 expressions with local error:

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

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×*-un-lft-identity times-frac add-cube-cbrt
13×associate-*r*
10×add-cbrt-cube add-exp-log
5×pow1
3×associate-/r* associate-*l* insert-posit16 associate-/l* add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×cos-sum clear-num frac-2neg pow-prod-down associate-*r/ *-commutative
Counts
3 → 70
Calls
3 calls:
Slowest
35.0ms
(cos (+ a b))
13.0ms
(* r (/ (sin b) (cos (+ a b))))
10.0ms
(/ (sin b) (cos (+ a b)))

series248.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
139.0ms
(* r (/ (sin b) (cos (+ a b))))
79.0ms
(/ (sin b) (cos (+ a b)))
30.0ms
(cos (+ a b))

simplify4.5s

Counts
91 → 79
Calls
91 calls:
Slowest
491.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
340.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
319.0ms
(* (* (* r (/ (sin b) (cos (+ a b)))) (* r (/ (sin b) (cos (+ a b))))) (* r (/ (sin b) (cos (+ a b)))))
268.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
260.0ms
(* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b))))

prune960.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

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))

rewrite178.0ms

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
93.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
54.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
20.0ms
(* (sin a) (sin b))
9.0ms
(* (cos a) (cos b))

series632.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
312.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
177.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
82.0ms
(* (sin a) (sin b))
61.0ms
(* (cos a) (cos b))

simplify11.6s

Counts
132 → 121
Calls
132 calls:
Slowest
646.0ms
(* (* (* 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))))))
398.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
389.0ms
(* (* (* 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))))))
386.0ms
(* r (/ (sin b) (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))))
366.0ms
(/ (sin b) (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)))

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite180.0ms

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
119.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
39.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
11.0ms
(* (sin b) (sin a))
9.0ms
(* (cos a) (cos b))

series652.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
336.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
172.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
86.0ms
(* (sin b) (sin a))
58.0ms
(* (cos a) (cos b))

simplify11.4s

Counts
132 → 121
Calls
132 calls:
Slowest
462.0ms
(/ (sin b) (- (pow (* (cos a) (cos b)) 3) (pow (* (sin b) (sin a)) 3)))
430.0ms
(/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin b) (sin a)) (* (sin b) (sin a)))))
412.0ms
(/ (sin b) (- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- b a)) (cos (+ b a))))))
407.0ms
(* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b)))
391.0ms
(* (* (* (sin b) (sin b)) (sin b)) (* (* (sin a) (sin a)) (sin a)))

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

25.3b
(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))

rewrite342.0ms

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×associate-*r* associate-*l* pow-sqr pow-prod-up insert-posit16 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 → 113
Calls
4 calls:
Slowest
147.0ms
(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))))
129.0ms
(cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))
53.0ms
(* (* (sin b) (sin a)) (* (sin b) (sin a)))
11.0ms
(* (sin b) (sin a))

series382.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
175.0ms
(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))))
73.0ms
(cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))
70.0ms
(* (* (sin b) (sin a)) (* (sin b) (sin a)))
65.0ms
(* (sin b) (sin a))

simplify23.6s

Counts
141 → 125
Calls
141 calls:
Slowest
782.0ms
(* (* (* (* (sin b) (sin b)) (sin b)) (* (* (sin a) (sin a)) (sin a))) (* (* (* (sin b) (sin b)) (sin b)) (* (* (sin a) (sin a)) (sin a))))
741.0ms
(* (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))) (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))
728.0ms
(/ (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))) (sin b))
479.0ms
(/ (cbrt (sin b)) (sqrt (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a)))))))
429.0ms
(* (* (* (sin b) (sin b)) (sin b)) (* (* (sin a) (sin a)) (sin a)))

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes231.0ms

Accuracy

0% (0.3b remaining)

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

bsearch9.0ms

end0.0ms

sample7.3s

Algorithm
intervals
Results
3.8s2873×body1280valid
1.7s1833×body640valid
796.0ms2218×body80valid
470.0ms743×body320valid
234.0ms337×body160valid