Details

sample228.0ms

Algorithm

intervals

Results

75.0ms	83×	body	2560	valid
53.0ms	80×	body	1280	valid
50.0ms	233×	body	80	nan
20.0ms	39×	body	640	valid
10.0ms	28×	body	320	valid
6.0ms	22×	body	160	valid
0.0ms	4×	body	80	valid

simplify175.0ms

Calls

1 calls:

Slowest

175.0ms

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.1b

localize31.0ms

Local error

Found 4 expressions with local error:

1.1b	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
0.2b	(* 5 (* v v))
0.0b	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
0.0b	(- 1 (* 5 (* v v)))

rewrite333.0ms

Algorithm

rewrite-expression-head

Rules

1037×	`add-sqr-sqrt`
444×	`difference-of-squares`
431×	`*-un-lft-identity`
340×	`times-frac`
325×	`unswap-sqr`
102×	`swap-sqr`
101×	`*-commutative`
90×	`difference-of-sqr-1`
80×	`distribute-lft-out--`
49×	`add-cube-cbrt`
46×	`associate-l`
20×	`associate-/r*`
18×	`associate-r`
17×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`pow1`
6×	`add-log-exp`
4×	`insert-posit16`
3×	`flip3--` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`associate-/r/` `associate-/l/`
1×	`acos-asin` `cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Calls

4 calls:

Slowest

219.0ms	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
55.0ms	(- 1 (* 5 (* v v)))
37.0ms	(* 5 (* v v))
2.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

series239.0ms

Calls

4 calls:

Slowest

106.0ms	(- 1 (* 5 (* v v)))
91.0ms	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
38.0ms	(* 5 (* v v))
4.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

simplify1.1m

Calls

790 calls:

Slowest

643.0ms	(/ (- 1 (* 5 (* v v))) (- (* (sqrt v) (sqrt v)) 1))
418.0ms	(- (* 1 1) (* (* 5 (* v v)) (* 5 (* v v))))
393.0ms	(- (pow 1 3) (pow (* 5 (* v v)) 3))
289.0ms	(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
280.0ms	(/ (- 1 (* 5 (* v v))) (cbrt (- (* v v) 1)))

prune4.9s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.1b

localize19.0ms

Local error

Found 4 expressions with local error:

1.9b	(acos (/ (/ (- 1 (* 5 (* v v))) (+ v 1)) (- v 1)))
0.2b	(* 5 (* v v))
0.0b	(/ (- 1 (* 5 (* v v))) (+ v 1))
0.0b	(- 1 (* 5 (* v v)))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

213×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
79×	`unswap-sqr`
72×	`difference-of-squares`
68×	`times-frac`
33×	`add-cube-cbrt`
18×	`associate-r` `distribute-lft-out`
17×	`associate-/l*`
16×	`swap-sqr`
15×	`*-commutative`
12×	`associate-l` `distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
9×	`pow1`
6×	`add-log-exp`
4×	`associate-/r*` `insert-posit16`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`acos-asin` `cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `flip-+` `div-inv`

Calls

4 calls:

Slowest

135.0ms	(/ (- 1 (* 5 (* v v))) (+ v 1))
26.0ms	(- 1 (* 5 (* v v)))
19.0ms	(* 5 (* v v))
1.0ms	(acos (/ (/ (- 1 (* 5 (* v v))) (+ v 1)) (- v 1)))

series171.0ms

Calls

4 calls:

Slowest

69.0ms	(- 1 (* 5 (* v v)))
52.0ms	(/ (- 1 (* 5 (* v v))) (+ v 1))
47.0ms	(* 5 (* v v))
3.0ms	(acos (/ (/ (- 1 (* 5 (* v v))) (+ v 1)) (- v 1)))

simplify13.3s

Calls

230 calls:

Slowest

609.0ms	(/ (* (* (- 1 (* 5 (* v v))) (- 1 (* 5 (* v v)))) (- 1 (* 5 (* v v)))) (* (* (+ v 1) (+ v 1)) (+ v 1)))
454.0ms	(- (pow 1 3) (pow (* 5 (* v v)) 3))
410.0ms	(- (* 1 1) (* (* 5 (* v v)) (* 5 (* v v))))
372.0ms	(acos (* -1 (/ (- 1 (* 5 (pow v 2))) (* (- 1 v) (+ v 1)))))
279.0ms	(/ (exp 1) (exp (* 5 (* v v))))

prune1.9s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.1b

localize57.0ms

Local error

Found 4 expressions with local error:

1.9b	(acos (/ (* (+ (* (sqrt 5) v) 1) (/ (- 1 (* (sqrt 5) v)) (+ 1 v))) (- v 1)))
0.3b	(* (sqrt 5) v)
0.3b	(* (sqrt 5) v)
0.0b	(* (+ (* (sqrt 5) v) 1) (/ (- 1 (* (sqrt 5) v)) (+ 1 v)))

rewrite325.0ms

Algorithm

rewrite-expression-head

Rules

146×	`add-sqr-sqrt`
130×	`*-un-lft-identity`
60×	`associate-r`
49×	`times-frac`
42×	`frac-times` `difference-of-squares`
39×	`associate-/l*`
35×	`associate-l`
34×	`add-cube-cbrt` `unswap-sqr`
30×	`sqrt-prod`
23×	`flip3-+` `flip-+` `distribute-lft-out--`
21×	`associate-*r/`
18×	`distribute-lft-out`
13×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/r*`
10×	`pow1`
6×	`associate-/l/`
4×	`clear-num` `prod-exp` `un-div-inv` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`frac-2neg` `flip3--` `pow-prod-down` `*-commutative` `flip--`
2×	`associate-*l/` `associate-/r/`
1×	`acos-asin` `cbrt-undiv` `div-exp` `div-inv`

Calls

4 calls:

Slowest

280.0ms	(* (+ (* (sqrt 5) v) 1) (/ (- 1 (* (sqrt 5) v)) (+ 1 v)))
15.0ms	(* (sqrt 5) v)
14.0ms	(* (sqrt 5) v)
11.0ms	(acos (/ (* (+ (* (sqrt 5) v) 1) (/ (- 1 (* (sqrt 5) v)) (+ 1 v))) (- v 1)))

series309.0ms

Calls

4 calls:

Slowest

139.0ms	(* (+ (* (sqrt 5) v) 1) (/ (- 1 (* (sqrt 5) v)) (+ 1 v)))
86.0ms	(* (sqrt 5) v)
65.0ms	(* (sqrt 5) v)
19.0ms	(acos (/ (* (+ (* (sqrt 5) v) 1) (/ (- 1 (* (sqrt 5) v)) (+ 1 v))) (- v 1)))

simplify36.3s

Calls

217 calls:

Slowest

877.0ms	(* (- (* (sqrt 5) v) 1) (/ (+ 1 v) (sqrt (- 1 (* (sqrt 5) v)))))
640.0ms	(* (+ (pow (* (sqrt 5) v) 3) (pow 1 3)) (- (pow 1 3) (pow (* (sqrt 5) v) 3)))
606.0ms	(* (- (* (* (sqrt 5) v) (* (sqrt 5) v)) (* 1 1)) (- 1 (* (sqrt 5) v)))
585.0ms	(* (- (* (* (sqrt 5) v) (* (sqrt 5) v)) (* 1 1)) (- (pow 1 3) (pow (* (sqrt 5) v) 3)))
573.0ms	(* (+ (* (sqrt 5) v) 1) (/ (- 1 (* (sqrt 5) v)) (+ 1 v)))

prune2.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.1b

localize36.0ms

Local error

Found 4 expressions with local error:

1.4b	(acos (/ (/ (* (+ (* (sqrt 5) v) 1) (sqrt (- 1 (* (sqrt 5) v)))) (/ (+ 1 v) (sqrt (- 1 (* (sqrt 5) v))))) (- v 1)))
0.3b	(* (sqrt 5) v)
0.3b	(* (sqrt 5) v)
0.3b	(* (sqrt 5) v)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
18×	`associate-l`
13×	`*-un-lft-identity` `add-cube-cbrt`
12×	`sqrt-prod`
10×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`associate-r`
6×	`unswap-sqr`
4×	`insert-posit16` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`acos-asin`

Calls

4 calls:

Slowest

8.0ms	(* (sqrt 5) v)
7.0ms	(* (sqrt 5) v)
7.0ms	(* (sqrt 5) v)
5.0ms	(acos (/ (/ (* (+ (* (sqrt 5) v) 1) (sqrt (- 1 (* (sqrt 5) v)))) (/ (+ 1 v) (sqrt (- 1 (* (sqrt 5) v))))) (- v 1)))

series190.0ms

Calls

4 calls:

Slowest

66.0ms	(* (sqrt 5) v)
55.0ms	(* (sqrt 5) v)
50.0ms	(* (sqrt 5) v)
20.0ms	(acos (/ (/ (* (+ (* (sqrt 5) v) 1) (sqrt (- 1 (* (sqrt 5) v)))) (/ (+ 1 v) (sqrt (- 1 (* (sqrt 5) v))))) (- v 1)))

simplify2.0s

Calls

54 calls:

Slowest

495.0ms	(acos (/ (* (- 1 (* v (sqrt 5))) (+ (* v (sqrt 5)) 1)) (* (- v 1) (+ v 1))))
480.0ms	(acos (/ (* (- 1 (* v (sqrt 5))) (+ (* v (sqrt 5)) 1)) (* (- v 1) (+ v 1))))
208.0ms	(* (* (* (sqrt 5) (sqrt 5)) (sqrt 5)) (* (* v v) v))
193.0ms	(acos (* -1 (/ (* (- 1 (* v (sqrt 5))) (+ (* v (sqrt 5)) 1)) (* (- 1 v) (+ v 1)))))
163.0ms	(* (* (* (sqrt 5) (sqrt 5)) (sqrt 5)) (* (* v v) v))

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.1b

regimes140.0ms

Accuracy

97.8% (0.0b remaining)

Error of 0.6b against oracle of 0.6b and baseline of 1.2b

bsearch6.0ms

end0.0ms

sample7.6s

Algorithm

intervals

Results

2.9s	2984×	body	2560	valid
1.8s	2530×	body	1280	valid
1.5s	8259×	body	80	nan
732.0ms	1173×	body	640	valid
246.0ms	609×	body	320	valid
117.0ms	471×	body	160	valid
30.0ms	233×	body	80	valid