Details

sample43.0ms

Algorithm

intervals

Results

27.0ms

268×

body

valid

simplify31.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

31.0ms

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

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.5b

localize42.0ms

Local error

Found 3 expressions with local error:

27.5b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
1.0b	(+ (* a c) (* b d))
0.0b	(+ (* c c) (* d d))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
4×	`flip3-+` `flip-+`
3×	`expm1-log1p-u` `pow1` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l`
2×	`+-commutative` `sum-log` `fma-def` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 64

Calls

3 calls:

Slowest

47.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
15.0ms	(+ (* c c) (* d d))
15.0ms	(+ (* a c) (* b d))

series204.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

99.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
54.0ms	(+ (* a c) (* b d))
51.0ms	(+ (* c c) (* d d))

simplify6.4s

Counts

83 → 73

Calls

83 calls:

Slowest

629.0ms	(* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d)))
500.0ms	(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
397.0ms	(* (+ (* c c) (* d d)) (- (* a c) (* b d)))
359.0ms	(/ (+ (* a c) (* b d)) (- (* (* c c) (* c c)) (* (* d d) (* d d))))
330.0ms	(/ (+ (* a c) (* b d)) (+ (pow (* c c) 3) (pow (* d d) 3)))

prune852.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 27.1b

localize25.0ms

Local error

Found 4 expressions with local error:

27.6b	(sqrt (+ (* c c) (* d d)))
27.6b	(sqrt (+ (* c c) (* d d)))
17.5b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
1.0b	(+ (* a c) (* b d))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `hypot-def` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `fma-def` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 99

Calls

4 calls:

Slowest

42.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
13.0ms	(sqrt (+ (* c c) (* d d)))
9.0ms	(+ (* a c) (* b d))
6.0ms	(sqrt (+ (* c c) (* d d)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

161.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
65.0ms	(sqrt (+ (* c c) (* d d)))
65.0ms	(sqrt (+ (* c c) (* d d)))
54.0ms	(+ (* a c) (* b d))

simplify7.1s

Counts

134 → 111

Calls

134 calls:

Slowest

358.0ms	(+ (* (* a c) (* a c)) (- (* (* b d) (* b d)) (* (* a c) (* b d))))
335.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
332.0ms	(/ (+ (* a c) (* b d)) (sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d)))))
320.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (pow (* c c) 3) (pow (* d d) 3))))
279.0ms	(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.6b

localize28.0ms

Local error

Found 4 expressions with local error:

27.6b	(sqrt (+ (* c c) (* d d)))
17.5b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
1.0b	(+ (* a c) (* b d))
0.1b	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (hypot c d))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
98×	`add-sqr-sqrt`
97×	`*-un-lft-identity` `add-cube-cbrt`
51×	`sqrt-prod`
27×	`associate-/l*`
12×	`sqrt-div`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
9×	`associate-/r*`
8×	`flip3-+` `flip-+`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `fma-def` `sqrt-pow1` `pow1/2` `hypot-def`

Counts

4 → 197

Calls

4 calls:

Slowest

42.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (hypot c d))
42.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
7.0ms	(+ (* a c) (* b d))
6.0ms	(sqrt (+ (* c c) (* d d)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

183.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (hypot c d))
142.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
51.0ms	(+ (* a c) (* b d))
46.0ms	(sqrt (+ (* c c) (* d d)))

simplify17.7s

Counts

303 → 209

Calls

303 calls:

Slowest

500.0ms	(/ (hypot c d) (sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))))
380.0ms	(/ (* (* (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))) (* (* (hypot c d) (hypot c d)) (hypot c d)))
324.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))) (sqrt (hypot c d)))
319.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))) (sqrt (hypot c d)))
301.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))) 1)

prune2.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.0b

localize20.0ms

Local error

Found 4 expressions with local error:

17.6b	(/ (hypot c d) (fma c a (* d b)))
0.3b	(fma c a (* d b))
0.2b	(/ 1 (/ (hypot c d) (fma c a (* d b))))
0.1b	(/ (/ 1 (/ (hypot c d) (fma c a (* d b)))) (hypot c d))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
239×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
50×	`associate-/l*`
36×	`add-exp-log`
23×	`div-inv`
22×	`div-exp`
20×	`add-cbrt-cube`
19×	`associate-/r*`
10×	`cbrt-undiv`
5×	`pow1` `associate-/r/`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`fma-udef` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 323

Calls

4 calls:

Slowest

19.0ms	(/ (/ 1 (/ (hypot c d) (fma c a (* d b)))) (hypot c d))
6.0ms	(/ 1 (/ (hypot c d) (fma c a (* d b))))
5.0ms	(/ (hypot c d) (fma c a (* d b)))
0.0ms	(fma c a (* d b))

series500.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

208.0ms	(/ (/ 1 (/ (hypot c d) (fma c a (* d b)))) (hypot c d))
142.0ms	(/ 1 (/ (hypot c d) (fma c a (* d b))))
109.0ms	(/ (hypot c d) (fma c a (* d b)))
42.0ms	(fma c a (* d b))

simplify56.0s

Counts

517 → 335

Calls

517 calls:

Slowest

622.0ms	(* (* (/ (/ 1 (/ (hypot c d) (fma c a (* d b)))) (hypot c d)) (/ (/ 1 (/ (hypot c d) (fma c a (* d b)))) (hypot c d))) (/ (/ 1 (/ (hypot c d) (fma c a (* d b)))) (hypot c d)))
587.0ms	(/ (/ (* (* 1 1) 1) (* (* (/ (hypot c d) (fma c a (* d b))) (/ (hypot c d) (fma c a (* d b)))) (/ (hypot c d) (fma c a (* d b))))) (* (* (hypot c d) (hypot c d)) (hypot c d)))
542.0ms	(/ (* (* 1 1) 1) (/ (* (* (hypot c d) (hypot c d)) (hypot c d)) (* (* (fma c a (* d b)) (fma c a (* d b))) (fma c a (* d b)))))
505.0ms	(/ (/ (cbrt 1) (/ (hypot c d) (fma c a (* d b)))) (cbrt (hypot c d)))
416.0ms	(/ (/ (cbrt 1) (/ (hypot c d) (fma c a (* d b)))) (hypot c d))

prune2.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.0b

regimes222.0ms

Accuracy

33.7% (7.2b remaining)

Error of 13.1b against oracle of 5.9b and baseline of 16.8b

bsearch82.0ms

end0.0ms

sample986.0ms

Algorithm

intervals

Results

765.0ms

8453×

body

valid