Details

Time bar (total: 1.8m)

sample27.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
8.0ms241×body80nan

simplify3.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
3.0ms
(/ a (- (acos a)))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize7.0ms

Local error

Found 1 expressions with local error:

0.3b
(/ a (- (acos a)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
30×times-frac
24×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
12×distribute-lft-neg-in distribute-rgt-neg-in
10×associate-/r*
4×neg-mul-1
3×add-cbrt-cube add-exp-log associate-/l*
1×pow1 cbrt-undiv clear-num frac-2neg div-exp insert-posit16 div-inv add-log-exp
Counts
1 → 56
Calls
1 calls:
Slowest
5.0ms
(/ a (- (acos a)))

series35.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
35.0ms
(/ a (- (acos a)))

simplify1.1s

Counts
77 → 59
Calls
77 calls:
Slowest
252.0ms
(/ (* (* a a) a) (* (* (- (acos a)) (- (acos a))) (- (acos a))))
101.0ms
(/ (* (cbrt a) (cbrt a)) (- (* (cbrt (acos a)) (cbrt (acos a)))))
41.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (acos a)) (cbrt (acos a))))
34.0ms
(/ 1 (- (* (cbrt (acos a)) (cbrt (acos a)))))
31.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (- (acos a))) (cbrt (- (acos a)))))

prune380.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ 1 (/ (- (acos a)) a))
0.3b
(/ (- (acos a)) a)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
252×times-frac
140×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
48×distribute-lft-neg-in distribute-rgt-neg-in
37×associate-/r*
16×neg-mul-1
15×add-exp-log
13×associate-/l*
9×add-cbrt-cube
8×div-exp
6×div-inv
4×cbrt-undiv
3×pow1
2×rec-exp clear-num frac-2neg 1-exp insert-posit16 add-log-exp
1×neg-sub0 div-sub distribute-frac-neg associate-/r/ pow-flip inv-pow
Counts
2 → 219
Calls
2 calls:
Slowest
7.0ms
(/ 1 (/ (- (acos a)) a))
5.0ms
(/ (- (acos a)) a)

series107.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
66.0ms
(/ (- (acos a)) a)
41.0ms
(/ 1 (/ (- (acos a)) a))

simplify13.6s

Counts
326 → 225
Calls
326 calls:
Slowest
502.0ms
(/ (* (* 1 1) 1) (/ (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* a a) a)))
433.0ms
(/ (sqrt 1) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
336.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (- (acos a))) (cbrt (- (acos a)))) (* (cbrt a) (cbrt a))))
318.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (acos a)) (cbrt (acos a))) (* (cbrt a) (cbrt a))))
317.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))

prune1.5s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ (/ 1 (- (acos a))) (/ 1 a))
0.0b
(/ 1 (- (acos a)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
1207×times-frac
550×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
138×distribute-lft-neg-in distribute-rgt-neg-in
51×div-inv
46×neg-mul-1 add-exp-log
37×associate-/l*
34×div-exp
23×associate-/r*
16×add-cbrt-cube
9×cbrt-undiv rec-exp 1-exp
3×pow1
2×clear-num frac-2neg insert-posit16 add-log-exp
1×associate-/r/ pow-flip inv-pow associate-/l/
Counts
2 → 582
Calls
2 calls:
Slowest
11.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
7.0ms
(/ 1 (- (acos a)))

series40.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
30.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
10.0ms
(/ 1 (- (acos a)))

simplify1.4m

Counts
1031 → 588
Calls
1031 calls:
Slowest
1.1s
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
771.0ms
(/ (/ (sqrt 1) (- (sqrt (acos a)))) (/ 1 (* (cbrt a) (cbrt a))))
769.0ms
(/ (/ (* (* 1 1) 1) (* (* (- (acos a)) (- (acos a))) (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
605.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (sqrt 1) (sqrt a)))
585.0ms
(/ (/ 1 (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (sqrt 1) (* (cbrt a) (cbrt a))))

prune2.7s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ 1 (* (/ 1 a) (- (acos a))))
0.3b
(* (/ 1 a) (- (acos a)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
46×add-exp-log
21×add-sqr-sqrt
18×div-exp
16×add-cbrt-cube prod-exp
15×*-un-lft-identity
14×times-frac add-cube-cbrt
13×associate-*l*
10×associate-*r*
9×rec-exp 1-exp
7×pow1
5×cbrt-undiv
4×cbrt-unprod
3×distribute-lft-neg-in distribute-rgt-neg-in associate-/l* unswap-sqr
2×pow-prod-down associate-*l/ insert-posit16 div-inv pow-flip add-log-exp
1×clear-num associate-/r* neg-mul-1 frac-2neg associate-/r/ *-commutative distribute-rgt-neg-out inv-pow
Counts
2 → 84
Calls
2 calls:
Slowest
17.0ms
(/ 1 (* (/ 1 a) (- (acos a))))
12.0ms
(* (/ 1 a) (- (acos a)))

series63.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
37.0ms
(* (/ 1 a) (- (acos a)))
26.0ms
(/ 1 (* (/ 1 a) (- (acos a))))

simplify2.3s

Counts
65 → 90
Calls
65 calls:
Slowest
368.0ms
(/ (* (* 1 1) 1) (* (* (* (/ 1 a) (/ 1 a)) (/ 1 a)) (* (* (- (acos a)) (- (acos a))) (- (acos a)))))
254.0ms
(* (* (* (/ 1 a) (/ 1 a)) (/ 1 a)) (* (* (- (acos a)) (- (acos a))) (- (acos a))))
134.0ms
(- 0 (log (* (/ 1 a) (- (acos a)))))
119.0ms
(/ (* (* 1 1) 1) (* (/ (* (* 1 1) 1) (* (* a a) a)) (* (* (- (acos a)) (- (acos a))) (- (acos a)))))
119.0ms
(- (log 1) (log (* (/ 1 a) (- (acos a)))))

prune373.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0b

regimes81.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch1.0ms

end0.0ms

sample1.2s

Algorithm
intervals
Results
608.0ms7866×body80nan
397.0ms8000×body80valid