Details

Time bar (total: 26.0s)

sample228.0ms

Algorithm
intervals
Results
72.0ms54×body640valid
69.0ms81×body1280valid
13.0ms28×body320valid
11.0ms83×body80valid
3.0ms10×body160valid

simplify60.0ms

Calls
1 calls:
Slowest
59.0ms
(* r (/ (sin b) (cos (+ a b))))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize18.0ms

Local error

Found 3 expressions with local error:

2.5b
(cos (+ a b))
0.2b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
13×associate-*r*
5×add-cbrt-cube add-exp-log
3×expm1-log1p-u pow1 associate-/r* insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×div-inv
1×cbrt-undiv cos-sum clear-num frac-2neg div-exp associate-*r/ *-commutative
Calls
3 calls:
Slowest
5.0ms
(* r (/ (sin b) (cos (+ a b))))
4.0ms
(/ (sin b) (cos (+ a b)))
3.0ms
(cos (+ a b))

series192.0ms

Calls
3 calls:
Slowest
112.0ms
(* r (/ (sin b) (cos (+ a b))))
44.0ms
(cos (+ a b))
35.0ms
(/ (sin b) (cos (+ a b)))

simplify1.2s

Calls
49 calls:
Slowest
203.0ms
(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
196.0ms
(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))
168.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
151.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
59.0ms
(/ (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b)))))

prune826.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u
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 fma-neg diff-log div-exp prod-diff pow-prod-down prod-exp associate-*r/ cbrt-unprod
Calls
4 calls:
Slowest
26.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
24.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
9.0ms
(* (sin a) (sin b))
8.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))

series582.0ms

Calls
4 calls:
Slowest
289.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
139.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
97.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
57.0ms
(* (sin a) (sin b))

simplify4.4s

Calls
73 calls:
Slowest
450.0ms
(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
383.0ms
(/ (* (* (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)))))
363.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
358.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
232.0ms
(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

2.7b
(log (exp (* (sin a) (sin b))))
0.2b
(* (sin a) (sin b))
0.2b
(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
0.1b
(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×times-frac associate-*r*
8×add-cbrt-cube add-exp-log
7×pow1
5×add-log-exp
4×expm1-log1p-u associate-/r/ insert-posit16 log1p-expm1-u
3×log-prod associate-/r* associate-*l* log-pow associate-/l*
2×flip3-- *-commutative div-inv flip--
1×cbrt-undiv exp-prod clear-num frac-2neg exp-to-pow div-exp rem-log-exp pow-prod-down prod-exp associate-*r/ cbrt-unprod sin-mult
Calls
4 calls:
Slowest
31.0ms
(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
24.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
9.0ms
(* (sin a) (sin b))
6.0ms
(log (exp (* (sin a) (sin b))))

series496.0ms

Calls
4 calls:
Slowest
265.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
120.0ms
(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
56.0ms
(log (exp (* (sin a) (sin b))))
54.0ms
(* (sin a) (sin b))

simplify3.7s

Calls
70 calls:
Slowest
392.0ms
(/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
390.0ms
(/ (cbrt (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
328.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (log (exp (* (sin a) (sin b)))) (log (exp (* (sin a) (sin b))))) (* (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
276.0ms
(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (log (exp (* (sin a) (sin b)))) (log (exp (* (sin a) (sin b))))) (* (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
208.0ms
(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (sin b))
0.7b
(cbrt (sin b))
0.7b
(cbrt (sin b))
0.5b
(* (cbrt (sin b)) (cbrt (sin b)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×pow1
7×pow1/3
6×associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
6.0ms
(* (cbrt (sin b)) (cbrt (sin b)))
1.0ms
(cbrt (sin b))
1.0ms
(cbrt (sin b))
1.0ms
(cbrt (sin b))

series662.0ms

Calls
4 calls:
Slowest
173.0ms
(cbrt (sin b))
163.0ms
(* (cbrt (sin b)) (cbrt (sin b)))
163.0ms
(cbrt (sin b))
162.0ms
(cbrt (sin b))

simplify817.0ms

Calls
41 calls:
Slowest
211.0ms
(- (pow b 1/3) (+ (* 1/3240 (pow (pow b 13) 1/3)) (* 1/18 (pow (pow b 7) 1/3))))
183.0ms
(- (pow b 1/3) (+ (* 1/3240 (pow (pow b 13) 1/3)) (* 1/18 (pow (pow b 7) 1/3))))
130.0ms
(- (pow b 1/3) (+ (* 1/3240 (pow (pow b 13) 1/3)) (* 1/18 (pow (pow b 7) 1/3))))
98.0ms
(- (+ (pow b 2/3) (* 1/405 (pow (pow b 14) 1/3))) (* 1/9 (pow (pow b 8) 1/3)))
8.0ms
(cbrt (* (cbrt (sin b)) (cbrt (sin b))))

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes307.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch6.0ms

end0.0ms

sample7.7s

Algorithm
intervals
Results
4.1s2908×body1280valid
2.4s1801×body640valid
430.0ms760×body320valid
373.0ms2176×body80valid
133.0ms355×body160valid