Details

Time bar (total: 48.9s)

sample500.0ms

Algorithm
intervals
Results
195.0ms91×body1280valid
100.0ms59×body640valid
21.0ms26×body320valid
13.0ms63×body80valid
9.0ms17×body160valid

simplify59.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
58.0ms
(/ (* r (sin b)) (cos (+ a b)))

prune49.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize82.0ms

Local error

Found 3 expressions with local error:

2.4b
(cos (+ a b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
0.1b
(* r (sin b))

rewrite207.0ms

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
113.0ms
(cos (+ a b))
57.0ms
(* r (sin b))
31.0ms
(/ (* r (sin b)) (cos (+ a b)))

series504.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
327.0ms
(/ (* r (sin b)) (cos (+ a b)))
90.0ms
(* r (sin b))
88.0ms
(cos (+ a b))

simplify3.6s

Counts
70 → 65
Calls
70 calls:
Slowest
801.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
336.0ms
(* (* (/ (* r (sin b)) (cos (+ a b))) (/ (* r (sin b)) (cos (+ a b)))) (/ (* r (sin b)) (cos (+ a b))))
250.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
219.0ms
(/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
215.0ms
(* (* (* r (sin b)) (* r (sin b))) (* r (sin b)))

prune780.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize30.0ms

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))

rewrite94.0ms

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
47.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
17.0ms
(* (cos a) (cos b))
17.0ms
(* r (sin b))
12.0ms
(* (sin a) (sin b))

series476.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
292.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
71.0ms
(* (cos a) (cos b))
64.0ms
(* (sin a) (sin b))
49.0ms
(* r (sin b))

simplify7.8s

Counts
109 → 105
Calls
109 calls:
Slowest
437.0ms
(* (* (/ (* 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)))))
402.0ms
(/ (* r (sin b)) (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b)))))
373.0ms
(* (* (* r r) r) (* (* (sin b) (sin b)) (sin b)))
364.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
336.0ms
(* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b)))

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

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))

rewrite170.0ms

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
92.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
44.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
20.0ms
(* (cos a) (cos b))
12.0ms
(* (sin a) (sin b))

series573.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
286.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
164.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
68.0ms
(* (sin a) (sin b))
54.0ms
(* (cos a) (cos b))

simplify11.9s

Counts
140 → 129
Calls
140 calls:
Slowest
456.0ms
(/ (sin b) (- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b))))))
425.0ms
(* (* (* 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))))))
420.0ms
(* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b)))
405.0ms
(* (* (* (cos a) (cos a)) (cos a)) (* (* (cos b) (cos b)) (cos b)))
388.0ms
(/ (sin b) (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b)))))

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
29×*-un-lft-identity add-cube-cbrt
28×times-frac
13×add-cbrt-cube associate-*l* add-exp-log
6×pow1 associate-/r* associate-/l* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv div-exp associate-*r* prod-diff div-inv
2×clear-num frac-2neg flip3-- prod-exp associate-/r/ cbrt-unprod flip-- unswap-sqr
1×sub-neg fma-neg diff-log pow-prod-down associate-*l/ *-commutative
Counts
4 → 116
Calls
4 calls:
Slowest
29.0ms
(/ r (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))
25.0ms
(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
19.0ms
(/ (cos a) (sin b))
16.0ms
(* (/ (cos a) (sin b)) (cos b))

series569.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
256.0ms
(/ r (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))
154.0ms
(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
106.0ms
(* (/ (cos a) (sin b)) (cos b))
53.0ms
(/ (cos a) (sin b))

simplify9.4s

Counts
154 → 128
Calls
154 calls:
Slowest
516.0ms
(/ (* (* (cos a) (cos a)) (cos a)) (* (* (sin b) (sin b)) (sin b)))
423.0ms
(/ r (- (pow (* (/ (cos a) (sin b)) (cos b)) 3) (pow (sin a) 3)))
401.0ms
(- (pow (* (/ (cos a) (sin b)) (cos b)) 3) (pow (sin a) 3))
367.0ms
(+ (* (* (/ (cos a) (sin b)) (cos b)) (* (/ (cos a) (sin b)) (cos b))) (+ (* (sin a) (sin a)) (* (* (/ (cos a) (sin b)) (cos b)) (sin a))))
316.0ms
(/ r (- (* (* (/ (cos a) (sin b)) (cos b)) (* (/ (cos a) (sin b)) (cos b))) (* (sin a) (sin a))))

prune1.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes236.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch6.0ms

end0.0ms

sample7.0s

Algorithm
intervals
Results
3.9s2873×body1280valid
1.8s1833×body640valid
502.0ms743×body320valid
436.0ms2218×body80valid
123.0ms337×body160valid