Details

Time bar (total: 1.1m)

sample478.0ms

Algorithm
intervals
Results
163.0ms91×body1280valid
51.0ms59×body640valid
17.0ms26×body320valid
11.0ms63×body80valid
9.0ms17×body160valid

simplify35.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
34.0ms
(* r (/ (sin b) (cos (+ a b))))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize40.0ms

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))))

rewrite50.0ms

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×expm1-log1p-u associate-/r* associate-*l* insert-posit16 log1p-expm1-u 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 → 76
Calls
3 calls:
Slowest
18.0ms
(/ (sin b) (cos (+ a b)))
17.0ms
(cos (+ a b))
13.0ms
(* r (/ (sin b) (cos (+ a b))))

series177.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
99.0ms
(* r (/ (sin b) (cos (+ a b))))
52.0ms
(/ (sin b) (cos (+ a b)))
25.0ms
(cos (+ a b))

simplify4.3s

Counts
97 → 85
Calls
97 calls:
Slowest
483.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
262.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
260.0ms
(* (* (* r (/ (sin b) (cos (+ a b)))) (* r (/ (sin b) (cos (+ a b))))) (* r (/ (sin b) (cos (+ a b)))))
259.0ms
(* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))))
233.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune837.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

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))

rewrite146.0ms

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
83.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
39.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
12.0ms
(* (sin a) (sin b))
10.0ms
(* (cos a) (cos b))

series634.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
299.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
179.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
81.0ms
(* (sin a) (sin b))
74.0ms
(* (cos a) (cos b))

simplify12.0s

Counts
140 → 129
Calls
140 calls:
Slowest
596.0ms
(* (* (* 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))))))
514.0ms
(/ (sin b) (- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b))))))
463.0ms
(* r (/ (sin b) (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))))
418.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
416.0ms
(* (* (* 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))))))

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

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))

rewrite431.0ms

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×expm1-log1p-u associate-*r* associate-*l* pow-sqr pow-prod-up insert-posit16 log1p-expm1-u 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 → 121
Calls
4 calls:
Slowest
199.0ms
(cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))
168.0ms
(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))))
52.0ms
(* (* (sin b) (sin a)) (* (sin b) (sin a)))
11.0ms
(* (sin b) (sin a))

series328.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
144.0ms
(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))))
64.0ms
(cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))
61.0ms
(* (* (sin b) (sin a)) (* (sin b) (sin a)))
60.0ms
(* (sin b) (sin a))

simplify24.1s

Counts
149 → 133
Calls
149 calls:
Slowest
834.0ms
(* (* (* (* (sin b) (sin b)) (sin b)) (* (* (sin a) (sin a)) (sin a))) (* (* (* (sin b) (sin b)) (sin b)) (* (* (sin a) (sin a)) (sin a))))
760.0ms
(* (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))) (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))
472.0ms
(/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a)))) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a)))))))
469.0ms
(/ (sin b) (- (* (+ (cos (+ a b)) (cos (- a b))) (cbrt 2)) (* 2 (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (- (cos (- b a)) (cos (+ b a))))))))
448.0ms
(/ (sin b) (- (* (+ (cos (+ a b)) (cos (- a b))) (cbrt (* 2 2))) (* 2 (cbrt (* (* (* (sin b) (sin a)) (- (cos (- b a)) (cos (+ b a)))) (- (cos (- b a)) (cos (+ b a))))))))

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize99.0ms

Local error

Found 4 expressions with local error:

25.3b
(cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (sin b)) (sin a)))))
0.6b
(cbrt (sin b))
0.6b
(cbrt (sin b))
0.6b
(cbrt (sin b))

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
10×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube pow1/3 associate-*l/ add-exp-log insert-posit16 log1p-expm1-u sin-mult add-log-exp
3×cbrt-div
1×frac-times associate-*r/
Counts
4 → 57
Calls
4 calls:
Slowest
236.0ms
(cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (sin b)) (sin a)))))
1.0ms
(cbrt (sin b))
1.0ms
(cbrt (sin b))
1.0ms
(cbrt (sin b))

series870.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
451.0ms
(cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (sin b)) (sin a)))))
161.0ms
(cbrt (sin b))
145.0ms
(cbrt (sin b))
112.0ms
(cbrt (sin b))

simplify7.3s

Counts
78 → 69
Calls
78 calls:
Slowest
578.0ms
(log1p (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (sin b)) (sin a))))))
559.0ms
(sqrt (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (sin b)) (sin a))))))
557.0ms
(* (* (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (sin b)) (sin a))))) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (sin b)) (sin a)))))) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (sin b)) (sin a))))))
529.0ms
(expm1 (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (sin b)) (sin a))))))
519.0ms
(exp (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (sin b)) (sin a))))))

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes252.0ms

Accuracy

0% (0.3b remaining)

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

bsearch9.0ms

end0.0ms

sample7.4s

Algorithm
intervals
Results
3.6s2873×body1280valid
1.6s1833×body640valid
1.3s743×body320valid
423.0ms2218×body80valid
192.0ms337×body160valid