Details

Time bar (total: 49.5s)

sample345.0ms

Algorithm
intervals
Results
159.0ms83×body1280valid
35.0ms68×body640valid
8.0ms21×body320valid
8.0ms67×body80valid
6.0ms17×body160valid

simplify80.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
79.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize23.0ms

Local error

Found 3 expressions with local error:

3.5b
(cos (+ a b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
0.1b
(* r (sin b))

rewrite79.0ms

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
32.0ms
(cos (+ a b))
27.0ms
(/ (* r (sin b)) (cos (+ a b)))
16.0ms
(* r (sin b))

series285.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
141.0ms
(* r (sin b))
111.0ms
(/ (* r (sin b)) (cos (+ a b)))
32.0ms
(cos (+ a b))

simplify3.0s

Counts
70 → 65
Calls
70 calls:
Slowest
334.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
314.0ms
(* (* (/ (* r (sin b)) (cos (+ a b))) (/ (* r (sin b)) (cos (+ a b)))) (/ (* r (sin b)) (cos (+ a b))))
243.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
242.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
222.0ms
(* (* (* r (sin b)) (* r (sin b))) (* r (sin b)))

prune765.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

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
28.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
14.0ms
(* r (sin b))
14.0ms
(* (sin a) (sin b))
10.0ms
(* (cos a) (cos b))

series904.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
735.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
69.0ms
(* (cos a) (cos b))
61.0ms
(* (sin a) (sin b))
38.0ms
(* r (sin b))

simplify7.9s

Counts
109 → 105
Calls
109 calls:
Slowest
421.0ms
(/ (* r (sin b)) (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b)))))
388.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
379.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
375.0ms
(* (* (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
370.0ms
(/ (* r (sin b)) (- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b))))))

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (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))

rewrite212.0ms

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
139.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
30.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
22.0ms
(* (sin a) (sin b))
18.0ms
(* (cos a) (cos b))

series632.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
336.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
159.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
85.0ms
(* (sin a) (sin b))
52.0ms
(* (cos a) (cos b))

simplify11.5s

Counts
140 → 129
Calls
140 calls:
Slowest
523.0ms
(/ (sin b) (- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b))))))
372.0ms
(exp (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
366.0ms
(/ (* (* (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)))))
365.0ms
(* r (/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))))
360.0ms
(* r (/ (sin b) (- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))))

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

26.5b
(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 a) (sin b))
0.2b
(* (sin a) (sin b))

rewrite264.0ms

Algorithm
rewrite-expression-head
Rules
47×pow1
20×add-cbrt-cube add-exp-log
19×pow-prod-down
18×sin-mult
12×add-sqr-sqrt
10×prod-exp cbrt-unprod
8×*-un-lft-identity add-cube-cbrt
7×cbrt-div associate-*r* associate-*l*
6×frac-times associate-*l/
4×expm1-log1p-u associate-*r/ pow-sqr pow-prod-up insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×pow-plus unswap-sqr
1×cbrt-prod pow2 pow1/3 swap-sqr pow3 rem-cbrt-cube
Counts
4 → 104
Calls
4 calls:
Slowest
151.0ms
(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
79.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
19.0ms
(* (sin a) (sin b))
11.0ms
(* (sin a) (sin b))

series279.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
76.0ms
(* (sin a) (sin b))
71.0ms
(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
69.0ms
(* (sin a) (sin b))
63.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))

simplify10.1s

Counts
122 → 116
Calls
122 calls:
Slowest
838.0ms
(* (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))) (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))))
668.0ms
(* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))) (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
596.0ms
(* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b)))
406.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
363.0ms
(cbrt (* (* (- (cos (- a b)) (cos (+ a b))) (- (cos (- a b)) (cos (+ a b)))) (- (cos (- a b)) (cos (+ a b)))))

prune1.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes263.0ms

Accuracy

0% (0.3b remaining)

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

bsearch6.0ms

end0.0ms

sample7.7s

Algorithm
intervals
Results
4.3s2957×body1280valid
2.1s1852×body640valid
513.0ms739×body320valid
433.0ms2117×body80valid
125.0ms338×body160valid