Details

sample34.0ms

Algorithm

intervals

Results

24.0ms

268×

body

valid

simplify104.0ms

Calls

1 calls:

Slowest

104.0ms

(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.9b

localize26.0ms

Local error

Found 3 expressions with local error:

25.9b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
1.1b	(- (* b c) (* a d))
0.0b	(+ (* c c) (* d d))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

260×	`*-un-lft-identity`
144×	`add-sqr-sqrt`
92×	`associate-l`
88×	`times-frac`
65×	`distribute-lft-out`
40×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
26×	`swap-sqr`
24×	`add-cube-cbrt`
11×	`associate-/l*`
8×	`associate-/r*`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
3×	`pow1` `insert-posit16`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Calls

3 calls:

Slowest

121.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
35.0ms	(+ (* c c) (* d d))
22.0ms	(- (* b c) (* a d))

series195.0ms

Calls

3 calls:

Slowest

110.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
54.0ms	(- (* b c) (* a d))
31.0ms	(+ (* c c) (* d d))

simplify11.3s

Calls

226 calls:

Slowest

419.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
336.0ms	(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
328.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
165.0ms	(* (exp (* c c)) (exp (* d d)))
158.0ms	(/ (- (* (sqrt b) (sqrt c)) (* (sqrt a) (sqrt d))) (+ (* c c) (* d d)))

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 25.5b

localize51.0ms

Local error

Found 4 expressions with local error:

30.7b	(sqrt (+ (* c c) (* d d)))
30.7b	(sqrt (+ (* c c) (* d d)))
15.5b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
1.1b	(- (* b c) (* a d))

rewrite266.0ms

Algorithm

rewrite-expression-head

Rules

314×	`*-un-lft-identity`
200×	`add-sqr-sqrt`
121×	`times-frac`
112×	`sqrt-prod`
108×	`associate-l`
70×	`distribute-lft-out`
52×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
42×	`add-cube-cbrt`
28×	`swap-sqr`
11×	`associate-/r` `associate-/l`
6×	`pow1` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
4×	`insert-posit16`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Calls

4 calls:

Slowest

155.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
44.0ms	(- (* b c) (* a d))
38.0ms	(sqrt (+ (* c c) (* d d)))
23.0ms	(sqrt (+ (* c c) (* d d)))

series320.0ms

Calls

4 calls:

Slowest

142.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
65.0ms	(sqrt (+ (* c c) (* d d)))
59.0ms	(sqrt (+ (* c c) (* d d)))
54.0ms	(- (* b c) (* a d))

simplify17.2s

Calls

315 calls:

Slowest

868.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
459.0ms	(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))))
329.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
299.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
294.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))

prune2.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 23.6b

localize20.0ms

Local error

Found 3 expressions with local error:

25.9b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
1.1b	(- (* b c) (* a d))
0.0b	(+ (* c c) (* d d))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

260×	`*-un-lft-identity`
144×	`add-sqr-sqrt`
92×	`associate-l`
88×	`times-frac`
65×	`distribute-lft-out`
40×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
26×	`swap-sqr`
24×	`add-cube-cbrt`
11×	`associate-/l*`
8×	`associate-/r*`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
3×	`pow1` `insert-posit16`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Calls

3 calls:

Slowest

80.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
24.0ms	(- (* b c) (* a d))
19.0ms	(+ (* c c) (* d d))

series173.0ms

Calls

3 calls:

Slowest

95.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
46.0ms	(- (* b c) (* a d))
32.0ms	(+ (* c c) (* d d))

simplify7.5s

Calls

226 calls:

Slowest

252.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
240.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
205.0ms	(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
124.0ms	(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
111.0ms	(/ (exp (* b c)) (exp (* a d)))

prune1.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 23.6b

localize27.0ms

Local error

Found 4 expressions with local error:

30.7b	(sqrt (+ (* c c) (* d d)))
30.7b	(sqrt (+ (* c c) (* d d)))
15.5b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
1.1b	(- (* b c) (* a d))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

314×	`*-un-lft-identity`
200×	`add-sqr-sqrt`
121×	`times-frac`
112×	`sqrt-prod`
108×	`associate-l`
70×	`distribute-lft-out`
52×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
42×	`add-cube-cbrt`
28×	`swap-sqr`
11×	`associate-/r` `associate-/l`
6×	`pow1` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
4×	`insert-posit16`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Calls

4 calls:

Slowest

76.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
28.0ms	(sqrt (+ (* c c) (* d d)))
23.0ms	(- (* b c) (* a d))
22.0ms	(sqrt (+ (* c c) (* d d)))

series245.0ms

Calls

4 calls:

Slowest

116.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
45.0ms	(- (* b c) (* a d))
44.0ms	(sqrt (+ (* c c) (* d d)))
39.0ms	(sqrt (+ (* c c) (* d d)))

simplify11.2s

Calls

315 calls:

Slowest

272.0ms	(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))))
250.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
239.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
211.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
211.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))

prune2.1s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 23.6b

regimes349.0ms

Accuracy

0% (2.6b remaining)

Error of 26.4b against oracle of 23.8b and baseline of 26.4b

bsearch2.0ms

end0.0ms

sample1.1s

Algorithm

intervals

Results

916.0ms

8414×

body

valid