Details

Time bar (total: 21.8s)

sample23.0ms

Algorithm
intervals
Results
8.0ms256×body80valid
5.0ms276×body80nan

simplify1.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045
done45

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize4.0ms

Local error

Found 1 expressions with local error:

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

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
30×times-frac
24×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×distribute-lft-neg-in distribute-rgt-neg-in
10×associate-/r*
4×neg-mul-1
3×add-exp-log add-cbrt-cube associate-/l*
1×pow1 cbrt-undiv expm1-log1p-u frac-2neg div-exp clear-num log1p-expm1-u div-inv add-log-exp
Counts
1 → 57
Calls
1 calls:
18.0ms
(/ a (- (acos a)))

series28.0ms

Counts
1 → 3
Calls
1 calls:
28.0ms
(/ a (- (acos a)))

simplify4.8s

Counts
60 → 60
Iterations

Useful iterations: 5 (1.9s)

IterNodesCost
096613
1166581
2333563
3587563
41105563
52150558
done5001558

prune167.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ -1 (acos a))
0.3b
(* a (/ -1 (acos a)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×times-frac
18×add-cube-cbrt *-un-lft-identity
13×associate-*r*
9×add-exp-log add-cbrt-cube
4×pow1
3×associate-*l* associate-/r* associate-/l*
2×cbrt-undiv expm1-log1p-u div-exp prod-exp cbrt-unprod log1p-expm1-u div-inv add-log-exp unswap-sqr
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative
Counts
2 → 63
Calls
2 calls:
9.0ms
(/ -1 (acos a))
14.0ms
(* a (/ -1 (acos a)))

series41.0ms

Counts
2 → 6
Calls
2 calls:
13.0ms
(/ -1 (acos a))
28.0ms
(* a (/ -1 (acos a)))

simplify6.3s

Counts
69 → 69
Iterations

Useful iterations: 3 (560.0ms)

IterNodesCost
090582
1184532
2512482
31392480
43526480
done5000480

prune212.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
171×times-frac
101×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
52×distribute-lft-neg-in distribute-rgt-neg-in
33×associate-/r*
10×div-inv
8×add-exp-log
6×add-cbrt-cube associate-/l*
4×neg-mul-1
3×pow1 div-exp
2×cbrt-undiv expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
1×acos-asin rec-exp pow-flip 1-exp div-sub associate-/r/ distribute-neg-frac inv-pow
Counts
2 → 172
Calls
2 calls:
14.0ms
(/ (acos a) a)
30.0ms
(/ 1 (- (/ (acos a) a)))

series64.0ms

Counts
2 → 6
Calls
2 calls:
32.0ms
(/ (acos a) a)
33.0ms
(/ 1 (- (/ (acos a) a)))

simplify6.5s

Counts
178 → 178
Iterations

Useful iterations: 3 (812.0ms)

IterNodesCost
02652409
14722004
27741861
315101711
427551711
done50001711

prune350.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 1 (acos a))
0.6b
(/ (/ 1 (acos a)) (- (/ 1 a)))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
930×times-frac
437×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
182×distribute-lft-neg-in distribute-rgt-neg-in
61×div-inv
33×associate-/r*
16×associate-/l*
15×add-exp-log
14×neg-mul-1
9×add-cbrt-cube
8×div-exp
4×cbrt-undiv
3×pow1
2×expm1-log1p-u rec-exp frac-2neg 1-exp clear-num log1p-expm1-u add-log-exp
1×pow-flip associate-/r/ associate-/l/ distribute-neg-frac inv-pow
Counts
2 → 486
Calls
2 calls:
6.0ms
(/ 1 (acos a))
42.0ms
(/ (/ 1 (acos a)) (- (/ 1 a)))

series53.0ms

Counts
2 → 6
Calls
2 calls:
11.0ms
(/ 1 (acos a))
42.0ms
(/ (/ 1 (acos a)) (- (/ 1 a)))

simplify2.5s

Counts
492 → 492
Iterations

Useful iterations: done (2.5s)

IterNodesCost
071310319
117377603
226406678
done50006309

prune394.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes1.0ms