Details

sample149.0ms

Algorithm

intervals

Results

121.0ms

710×

body

valid

simplify156.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

156.0ms

(- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1)

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (+ (* a a) (* b b)) (+ (* a a) (* b b)))
0.0b	(* (* b b) 4)
0.0b	(+ (* (* b b) 4) (* (+ (* a a) (* b b)) (+ (* a a) (* b b))))
0.0b	(+ (* a a) (* b b))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
12×	`add-sqr-sqrt`
11×	`add-cbrt-cube` `add-exp-log`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`flip3-+` `flip-+` `add-log-exp`
6×	`associate-r`
4×	`frac-times` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16`
3×	`swap-sqr`
2×	`distribute-rgt-in` `+-commutative` `associate-+r+` `sum-log` `distribute-lft-in` `associate-l/` `associate-r/` `*-commutative` `unswap-sqr`
1×	`pow2` `pow-plus` `pow-sqr` `pow-prod-up`

Counts

4 → 82

Calls

4 calls:

Slowest

31.0ms	(* (+ (* a a) (* b b)) (+ (* a a) (* b b)))
18.0ms	(* (* b b) 4)
16.0ms	(+ (* (* b b) 4) (* (+ (* a a) (* b b)) (+ (* a a) (* b b))))
7.0ms	(+ (* a a) (* b b))

series216.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

94.0ms	(+ (* (* b b) 4) (* (+ (* a a) (* b b)) (+ (* a a) (* b b))))
44.0ms	(* (+ (* a a) (* b b)) (+ (* a a) (* b b)))
41.0ms	(+ (* a a) (* b b))
37.0ms	(* (* b b) 4)

simplify7.6s

Counts

61 → 94

Calls

61 calls:

Slowest

682.0ms	(* (+ (pow (* a a) 3) (pow (* b b) 3)) (- (* (* a a) (* a a)) (* (* b b) (* b b))))
547.0ms	(* (+ (* (* a a) (* a a)) (- (* (* b b) (* b b)) (* (* a a) (* b b)))) (- (* a a) (* b b)))
470.0ms	(* (- (* (* a a) (* a a)) (* (* b b) (* b b))) (+ (* a a) (* b b)))
435.0ms	(* (+ (pow (* a a) 3) (pow (* b b) 3)) (+ (* a a) (* b b)))
385.0ms	(* (- (* (* a a) (* a a)) (* (* b b) (* b b))) (- (* (* a a) (* a a)) (* (* b b) (* b b))))

prune875.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

7.2b	(sqrt (+ (* a a) (* b b)))
7.2b	(sqrt (+ (* a a) (* b b)))
0.2b	(* (sqrt (+ (* a a) (* b b))) (+ (* a a) (* b b)))
0.1b	(* (sqrt (+ (* a a) (* b b))) (* (sqrt (+ (* a a) (* b b))) (+ (* a a) (* b b))))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

46×	`sqrt-div`
35×	`flip3-+` `flip-+`
32×	`frac-times`
30×	`pow1`
19×	`add-sqr-sqrt`
16×	`associate-*r/`
15×	`pow-prod-up`
13×	`sqrt-prod`
12×	`sqrt-pow1` `pow1/2` `associate-l`
11×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
10×	`associate-*l/`
6×	`pow-plus`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `cube-unmult` `*-commutative` `unswap-sqr`

Counts

4 → 131

Calls

4 calls:

Slowest

100.0ms	(* (sqrt (+ (* a a) (* b b))) (* (sqrt (+ (* a a) (* b b))) (+ (* a a) (* b b))))
44.0ms	(* (sqrt (+ (* a a) (* b b))) (+ (* a a) (* b b)))
6.0ms	(sqrt (+ (* a a) (* b b)))
6.0ms	(sqrt (+ (* a a) (* b b)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

143.0ms	(* (sqrt (+ (* a a) (* b b))) (+ (* a a) (* b b)))
67.0ms	(* (sqrt (+ (* a a) (* b b))) (* (sqrt (+ (* a a) (* b b))) (+ (* a a) (* b b))))
49.0ms	(sqrt (+ (* a a) (* b b)))
45.0ms	(sqrt (+ (* a a) (* b b)))

simplify20.7s

Counts

137 → 143

Calls

137 calls:

Slowest

662.0ms	(* (sqrt (+ (pow (* a a) 3) (pow (* b b) 3))) (* (sqrt (- (* (* a a) (* a a)) (* (* b b) (* b b)))) (- (* (* a a) (* a a)) (* (* b b) (* b b)))))
624.0ms	(* (sqrt (+ (pow (* a a) 3) (pow (* b b) 3))) (* (sqrt (+ (* a a) (* b b))) (- (* (* a a) (* a a)) (* (* b b) (* b b)))))
593.0ms	(* (sqrt (- (* (* a a) (* a a)) (* (* b b) (* b b)))) (* (sqrt (+ (pow (* a a) 3) (pow (* b b) 3))) (- (* (* a a) (* a a)) (* (* b b) (* b b)))))
589.0ms	(* (sqrt (+ (pow (* a a) 3) (pow (* b b) 3))) (* (sqrt (+ (pow (* a a) 3) (pow (* b b) 3))) (- (* (* a a) (* a a)) (* (* b b) (* b b)))))
553.0ms	(* (sqrt (+ (* (* a a) (* a a)) (- (* (* b b) (* b b)) (* (* a a) (* b b))))) (* (sqrt (+ (* (* a a) (* a a)) (- (* (* b b) (* b b)) (* (* a a) (* b b))))) (- (* a a) (* b b))))

prune2.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

7.2b	(sqrt (+ (* a a) (* b b)))
0.0b	(* (* b b) 4)
0.0b	(+ (* (* b b) 4) (pow (sqrt (+ (* a a) (* b b))) 4))
0.0b	(+ (* a a) (* b b))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `add-log-exp`
6×	`*-un-lft-identity` `add-cube-cbrt`
4×	`insert-posit16`
3×	`flip3-+` `associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod` `flip-+`
2×	`+-commutative` `sum-log` `sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

Slowest

37.0ms	(+ (* (* b b) 4) (pow (sqrt (+ (* a a) (* b b))) 4))
19.0ms	(* (* b b) 4)
7.0ms	(+ (* a a) (* b b))
6.0ms	(sqrt (+ (* a a) (* b b)))

series219.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

90.0ms	(+ (* (* b b) 4) (pow (sqrt (+ (* a a) (* b b))) 4))
49.0ms	(sqrt (+ (* a a) (* b b)))
47.0ms	(* (* b b) 4)
33.0ms	(+ (* a a) (* b b))

simplify2.3s

Counts

31 → 72

Calls

31 calls:

Slowest

283.0ms	(sqrt (- (* (* a a) (* a a)) (* (* b b) (* b b))))
274.0ms	(sqrt (+ (pow (* a a) 3) (pow (* b b) 3)))
273.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (* 4 (pow b 2))))
243.0ms	(* (* (* (* b b) b) (* (* b b) b)) (* (* 4 4) 4))
239.0ms	(* (* (* (* b b) (* b b)) (* b b)) (* (* 4 4) 4))

prune781.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize72.0ms

Local error

Found 4 expressions with local error:

21.4b	(log (* b b))
7.2b	(sqrt (+ (* a a) (* b b)))
3.5b	(exp (+ (log (* b b)) (log 4)))
0.2b	(+ (log (* b b)) (log 4))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

31×	`pow1`
20×	`log-pow`
17×	`*-un-lft-identity`
12×	`distribute-lft-out`
9×	`exp-prod`
8×	`add-sqr-sqrt`
7×	`add-exp-log` `add-cube-cbrt`
5×	`log-prod` `pow-prod-down` `add-log-exp`
4×	`add-cbrt-cube` `insert-posit16`
3×	`associate-+r+` `sqrt-prod`
2×	`sum-log` `flip3-+` `sqrt-div` `rem-log-exp` `flip-+` `rem-exp-log`
1×	`pow2` `+-commutative` `rem-sqrt-square` `associate-+l+` `sqrt-pow1` `pow-plus` `pow1/2` `exp-sum` `prod-exp` `pow-sqr` `pow-prod-up`

Counts

4 → 75

Calls

4 calls:

Slowest

84.0ms	(exp (+ (log (* b b)) (log 4)))
17.0ms	(+ (log (* b b)) (log 4))
12.0ms	(sqrt (+ (* a a) (* b b)))
9.0ms	(log (* b b))

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

429.0ms	(exp (+ (log (* b b)) (log 4)))
399.0ms	(+ (log (* b b)) (log 4))
262.0ms	(log (* b b))
52.0ms	(sqrt (+ (* a a) (* b b)))

simplify1.9s

Counts

48 → 87

Calls

48 calls:

Slowest

334.0ms	(sqrt (+ (pow (* a a) 3) (pow (* b b) 3)))
253.0ms	(sqrt (- (* (* a a) (* a a)) (* (* b b) (* b b))))
244.0ms	(exp (- (log 4) (* 2 (log (/ 1 b)))))
211.0ms	(exp (- (log 4) (* 2 (log (/ -1 b)))))
120.0ms	(exp (* (cbrt (+ (log (* b b)) (log 4))) (cbrt (+ (log (* b b)) (log 4)))))

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes131.0ms

Accuracy

0% (0.0b remaining)

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

bsearch4.0ms

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.8s

20415×

body

valid