Details

sample238.0ms

Algorithm

intervals

Results

96.0ms	95×	body	2560	valid
61.0ms	84×	body	1280	valid
32.0ms	245×	body	80	nan
22.0ms	39×	body	640	valid
8.0ms	17×	body	320	valid
4.0ms	15×	body	160	valid
1.0ms	6×	body	80	valid

simplify453.0ms

Calls

1 calls:

Slowest

453.0ms

(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize27.0ms

Local error

Found 3 expressions with local error:

0.7b	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
0.2b	(* 5 (* v v))
0.0b	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-cube-cbrt`
12×	`times-frac`
12×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
5×	`add-exp-log`
5×	`add-cbrt-cube`
4×	`difference-of-sqr-1`
4×	`associate-/r*`
3×	`add-log-exp`
3×	`associate-/l*`
3×	`pow1`
2×	`associate-/l/`
2×	`flip--`
2×	`associate-/r/`
2×	`flip3--`
1×	`div-inv`
1×	`*-commutative`
1×	`associate-r`
1×	`div-exp`
1×	`div-sub`
1×	`frac-2neg`
1×	`clear-num`
1×	`cbrt-undiv`
1×	`acos-asin`

Calls

3 calls:

Slowest

14.0ms	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
2.0ms	(* 5 (* v v))
1.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

series47.0ms

Calls

3 calls:

Slowest

23.0ms	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
16.0ms	(* 5 (* v v))
8.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

simplify4.6s

Calls

46 calls:

Slowest

831.0ms	(/ (* (* (- 1 (* 5 (* v v))) (- 1 (* 5 (* v v)))) (- 1 (* 5 (* v v)))) (* (* (- (* v v) 1) (- (* v v) 1)) (- (* v v) 1)))
340.0ms	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
314.0ms	(- (* 1 1) (* (* 5 (* v v)) (* 5 (* v v))))
210.0ms	(/ (- 1 (* 5 (* v v))) (cbrt (- (* v v) 1)))
189.0ms	(/ (- 1 (* 5 (* v v))) (sqrt (- (* v v) 1)))

prune505.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize24.0ms

Local error

Found 3 expressions with local error:

0.7b	(acos (+ -1 (* (+ (* v v) (pow v 4)) 4)))
0.0b	(* (+ (* v v) (pow v 4)) 4)
0.0b	(+ (* v v) (pow v 4))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-log-exp`
4×	`add-cube-cbrt`
4×	`*-un-lft-identity`
4×	`add-sqr-sqrt`
3×	`add-exp-log`
3×	`associate-l`
3×	`add-cbrt-cube`
3×	`pow1`
2×	`flip-+`
2×	`associate-*l/`
2×	`flip3-+`
1×	`*-commutative`
1×	`sum-log`
1×	`+-commutative`
1×	`acos-asin`

Calls

3 calls:

Slowest

9.0ms	(* (+ (* v v) (pow v 4)) 4)
2.0ms	(+ (* v v) (pow v 4))
1.0ms	(acos (+ -1 (* (+ (* v v) (pow v 4)) 4)))

series88.0ms

Calls

3 calls:

Slowest

49.0ms	(+ (* v v) (pow v 4))
35.0ms	(* (+ (* v v) (pow v 4)) 4)
4.0ms	(acos (+ -1 (* (+ (* v v) (pow v 4)) 4)))

simplify970.0ms

Calls

14 calls:

Slowest

452.0ms	(* (- (* (* v v) (* v v)) (* (pow v 4) (pow v 4))) 4)
279.0ms	(* (+ (pow (* v v) 3) (pow (pow v 4) 3)) 4)
58.0ms	(acos (- (+ (* 4 (pow v 4)) (* 4 (pow v 2))) 1))
56.0ms	(acos (- (+ (* 4 (pow v 4)) (* 4 (pow v 2))) 1))
51.0ms	(acos (- (+ (* 4 (pow v 4)) (* 4 (pow v 2))) 1))

prune357.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(asin (+ -1 (* (+ (* v v) (pow v 4)) 4)))
0.0b	(- (/ PI 2) (asin (+ -1 (* (+ (* v v) (pow v 4)) 4))))
0.0b	(* (+ (* v v) (pow v 4)) 4)
0.0b	(+ (* v v) (pow v 4))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-log-exp`
7×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
5×	`add-cube-cbrt`
4×	`add-exp-log`
4×	`add-cbrt-cube`
4×	`pow1`
3×	`associate-l`
2×	`flip-+`
2×	`associate-*l/`
2×	`flip3-+`
2×	`asin-acos`
1×	`difference-of-squares`
1×	`associate--r-`
1×	`distribute-lft-out--`
1×	`flip--`
1×	`*-commutative`
1×	`diff-log`
1×	`flip3--`
1×	`sub-neg`
1×	`sum-log`
1×	`+-commutative`

Calls

4 calls:

Slowest

9.0ms	(* (+ (* v v) (pow v 4)) 4)
7.0ms	(- (/ PI 2) (asin (+ -1 (* (+ (* v v) (pow v 4)) 4))))
5.0ms	(+ (* v v) (pow v 4))
1.0ms	(asin (+ -1 (* (+ (* v v) (pow v 4)) 4)))

series172.0ms

Calls

4 calls:

Slowest

64.0ms	(* (+ (* v v) (pow v 4)) 4)
53.0ms	(- (/ PI 2) (asin (+ -1 (* (+ (* v v) (pow v 4)) 4))))
48.0ms	(+ (* v v) (pow v 4))
7.0ms	(asin (+ -1 (* (+ (* v v) (pow v 4)) 4)))

simplify1.2s

Calls

22 calls:

Slowest

518.0ms	(* (- (* (* v v) (* v v)) (* (pow v 4) (pow v 4))) 4)
241.0ms	(* (+ (pow (* v v) 3) (pow (pow v 4) 3)) 4)
66.0ms	(- (* 1/2 PI) (asin (- (+ (* 4 (pow v 4)) (* 4 (pow v 2))) 1)))
55.0ms	(asin (- (+ (* 4 (pow v 4)) (* 4 (pow v 2))) 1))
53.0ms	(- (* 1/2 PI) (asin (- (+ (* 4 (pow v 4)) (* 4 (pow v 2))) 1)))

prune569.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* (acos (+ -1 (* (+ (* v v) (pow v 4)) 4))) (acos (+ -1 (* (+ (* v v) (pow v 4)) 4)))) (acos (+ -1 (* (+ (* v v) (pow v 4)) 4))))
1.0b	(cbrt (* (* (acos (+ -1 (* (+ (* v v) (pow v 4)) 4))) (acos (+ -1 (* (+ (* v v) (pow v 4)) 4)))) (acos (+ -1 (* (+ (* v v) (pow v 4)) 4)))))
0.7b	(acos (+ -1 (* (+ (* v v) (pow v 4)) 4)))
0.7b	(acos (+ -1 (* (+ (* v v) (pow v 4)) 4)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1`
9×	`add-exp-log`
9×	`add-cbrt-cube`
5×	`add-cube-cbrt`
5×	`pow-prod-up`
5×	`pow-plus`
5×	`*-un-lft-identity`
5×	`add-sqr-sqrt`
4×	`add-log-exp`
3×	`cbrt-unprod`
3×	`prod-exp`
3×	`pow-prod-down`
3×	`associate-r`
2×	`pow3`
2×	`acos-asin`
2×	`pow2`
1×	`rem-cbrt-cube`
1×	`*-commutative`
1×	`associate-l`
1×	`pow1/3`
1×	`cbrt-prod`

Calls

4 calls:

Slowest

20.0ms	(* (* (acos (+ -1 (* (+ (* v v) (pow v 4)) 4))) (acos (+ -1 (* (+ (* v v) (pow v 4)) 4)))) (acos (+ -1 (* (+ (* v v) (pow v 4)) 4))))
11.0ms	(cbrt (* (* (acos (+ -1 (* (+ (* v v) (pow v 4)) 4))) (acos (+ -1 (* (+ (* v v) (pow v 4)) 4)))) (acos (+ -1 (* (+ (* v v) (pow v 4)) 4)))))
1.0ms	(acos (+ -1 (* (+ (* v v) (pow v 4)) 4)))
1.0ms	(acos (+ -1 (* (+ (* v v) (pow v 4)) 4)))

series72.0ms

Calls

4 calls:

Slowest

50.0ms	(* (* (acos (+ -1 (* (+ (* v v) (pow v 4)) 4))) (acos (+ -1 (* (+ (* v v) (pow v 4)) 4)))) (acos (+ -1 (* (+ (* v v) (pow v 4)) 4))))
8.0ms	(cbrt (* (* (acos (+ -1 (* (+ (* v v) (pow v 4)) 4))) (acos (+ -1 (* (+ (* v v) (pow v 4)) 4)))) (acos (+ -1 (* (+ (* v v) (pow v 4)) 4)))))
6.0ms	(acos (+ -1 (* (+ (* v v) (pow v 4)) 4)))
6.0ms	(acos (+ -1 (* (+ (* v v) (pow v 4)) 4)))

simplify1.1s

Calls

34 calls:

Slowest

106.0ms	(* (* (* (* (acos (+ -1 (* (+ (* v v) (pow v 4)) 4))) (acos (+ -1 (* (+ (* v v) (pow v 4)) 4)))) (* (acos (+ -1 (* (+ (* v v) (pow v 4)) 4))) (acos (+ -1 (* (+ (* v v) (pow v 4)) 4))))) (* (acos (+ -1 (* (+ (* v v) (pow v 4)) 4))) (acos (+ -1 (* (+ (* v v) (pow v 4)) 4))))) (* (* (acos (+ -1 (* (+ (* v v) (pow v 4)) 4))) (acos (+ -1 (* (+ (* v v) (pow v 4)) 4)))) (acos (+ -1 (* (+ (* v v) (pow v 4)) 4)))))
66.0ms	(* (* (* (* (acos (+ -1 (* (+ (* v v) (pow v 4)) 4))) (acos (+ -1 (* (+ (* v v) (pow v 4)) 4)))) (acos (+ -1 (* (+ (* v v) (pow v 4)) 4)))) (* (* (acos (+ -1 (* (+ (* v v) (pow v 4)) 4))) (acos (+ -1 (* (+ (* v v) (pow v 4)) 4)))) (acos (+ -1 (* (+ (* v v) (pow v 4)) 4))))) (* (* (acos (+ -1 (* (+ (* v v) (pow v 4)) 4))) (acos (+ -1 (* (+ (* v v) (pow v 4)) 4)))) (acos (+ -1 (* (+ (* v v) (pow v 4)) 4)))))
61.0ms	(acos (- (+ (* 4 (pow v 4)) (* 4 (pow v 2))) 1))
51.0ms	(acos (- (+ (* 4 (pow v 4)) (* 4 (pow v 2))) 1))
49.0ms	(acos (- (+ (* 4 (pow v 4)) (* 4 (pow v 2))) 1))

prune439.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

regimes50.0ms

Accuracy

0% (0.0b remaining)

Error of 0.8b against oracle of 0.8b and baseline of 0.8b

bsearch2.0ms

end0.0ms

sample7.9s

Algorithm

intervals

Results

3.5s	3049×	body	2560	valid
1.8s	2499×	body	1280	valid
948.0ms	7885×	body	80	nan
608.0ms	1190×	body	640	valid
563.0ms	416×	body	160	valid
245.0ms	633×	body	320	valid
27.0ms	213×	body	80	valid