Details

Time bar (total: 2.1m)

sample48.0ms

Algorithm
intervals
Results
22.0ms256×body80valid
14.0ms233×body80nan

simplify7.0ms

Calls
1 calls:
Slowest
7.0ms
(/ a (- (acos a)))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 1 expressions with local error:

0.2b
(/ a (- (acos a)))

rewrite12.0ms

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
Calls
1 calls:
Slowest
11.0ms
(/ a (- (acos a)))

series69.0ms

Calls
1 calls:
Slowest
69.0ms
(/ a (- (acos a)))

simplify1.1s

Calls
77 calls:
Slowest
200.0ms
(/ (* (* a a) a) (* (* (- (acos a)) (- (acos a))) (- (acos a))))
63.0ms
(/ (* (cbrt a) (cbrt a)) (- (* (cbrt (acos a)) (cbrt (acos a)))))
43.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (- (acos a))) (cbrt (- (acos a)))))
41.0ms
(* -1 (/ a (acos a)))
40.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (acos a)) (cbrt (acos a))))

prune450.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 2 expressions with local error:

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
252×times-frac
146×*-un-lft-identity
144×add-sqr-sqrt add-cube-cbrt
52×distribute-rgt-neg-in
51×distribute-lft-neg-in
40×associate-/r*
25×associate-/l*
17×neg-mul-1
16×associate-/r/
15×add-exp-log
9×add-cbrt-cube
8×div-exp
6×div-inv
4×cbrt-undiv clear-num
3×pow1 frac-2neg remove-double-div
2×rec-exp 1-exp insert-posit16 add-log-exp
1×neg-sub0 div-sub distribute-frac-neg pow-flip inv-pow
Calls
2 calls:
Slowest
10.0ms
(/ 1 (/ (- (acos a)) a))
9.0ms
(/ (- (acos a)) a)

series111.0ms

Calls
2 calls:
Slowest
58.0ms
(/ 1 (/ (- (acos a)) a))
52.0ms
(/ (- (acos a)) a)

simplify15.8s

Calls
343 calls:
Slowest
542.0ms
(/ (sqrt 1) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
512.0ms
(/ (* (* 1 1) 1) (/ (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* a a) a)))
344.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (sqrt a)))
342.0ms
(/ (sqrt 1) (/ (* (cbrt (- (acos a))) (cbrt (- (acos a)))) (* (cbrt a) (cbrt a))))
339.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))

prune2.0s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 2 expressions with local error:

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

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
1207×times-frac
556×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
141×distribute-lft-neg-in distribute-rgt-neg-in
51×div-inv
47×neg-mul-1
46×add-exp-log
43×associate-/l*
36×associate-/r*
34×div-exp
16×add-cbrt-cube associate-/l/
9×cbrt-undiv rec-exp 1-exp associate-/r/
4×clear-num frac-2neg
3×pow1
2×insert-posit16 add-log-exp
1×pow-flip inv-pow
Calls
2 calls:
Slowest
21.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
5.0ms
(/ 1 (- (acos a)))

series68.0ms

Calls
2 calls:
Slowest
57.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
11.0ms
(/ 1 (- (acos a)))

simplify1.6m

Calls
1051 calls:
Slowest
1.2s
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
641.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (sqrt 1) (sqrt a)))
641.0ms
(/ (/ 1 (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (* (cbrt 1) (cbrt 1)) (sqrt a)))
641.0ms
(/ (/ (sqrt 1) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a))))
640.0ms
(/ (/ (sqrt 1) (- (sqrt (acos a)))) (/ (sqrt 1) (* (cbrt a) (cbrt a))))

prune4.8s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))
1.0b
(* (/ 1 (- (acos a))) (/ 1 (- (acos a))))
1.0b
(* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))
0.4b
(/ (cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))) (/ 1 a))

rewrite2.7s

Algorithm
rewrite-expression-head
Rules
27280×frac-times
26456×associate-/r*
16811×add-sqr-sqrt
14878×*-un-lft-identity
13859×add-cube-cbrt
9932×cbrt-div
8827×times-frac
8790×distribute-rgt-neg-in
8688×distribute-lft-neg-in
8201×associate-/l*
4966×associate-/l/
3120×cbrt-prod
2896×neg-mul-1
2701×clear-num
2646×frac-2neg
2562×associate-*l*
1705×associate-*l/
1305×unswap-sqr
1122×associate-*r*
880×associate-*r/
858×swap-sqr
331×div-inv
302×add-exp-log
165×un-div-inv
148×prod-exp
120×div-exp
83×*-commutative
65×add-cbrt-cube
59×pow1
58×rec-exp 1-exp
31×pow-prod-up
29×pow-flip inv-pow
23×cbrt-undiv
22×cbrt-unprod
10×pow-prod-down
9×associate-/r/ pow-sqr
7×pow-plus
4×pow3 insert-posit16 add-log-exp
3×pow2
2×rem-cbrt-cube
1×pow1/3
Calls
4 calls:
Slowest
298.0ms
(/ (cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))) (/ 1 a))
171.0ms
(cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))
156.0ms
(* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))
36.0ms
(* (/ 1 (- (acos a))) (/ 1 (- (acos a))))

series228.0ms

Calls
4 calls:
Slowest
97.0ms
(/ (cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))) (/ 1 a))
55.0ms
(* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))
46.0ms
(cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))
30.0ms
(* (/ 1 (- (acos a))) (/ 1 (- (acos a))))