Details

sample64.0ms

Algorithm

intervals

Results

48.0ms

268×

body

valid

simplify118.0ms

Calls

1 calls:

Slowest

118.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.9b

localize19.0ms

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))

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

340×	`*-un-lft-identity`
276×	`add-sqr-sqrt`
170×	`associate-l`
144×	`prod-diff`
104×	`add-cube-cbrt`
88×	`times-frac`
78×	`associate-r`
66×	`unswap-sqr`
65×	`distribute-lft-out`
40×	`distribute-lft-out--` `difference-of-squares`
29×	`swap-sqr`
26×	`*-commutative`
15×	`fma-def`
12×	`fma-neg`
11×	`associate-/l*`
8×	`associate-/r*`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
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

153.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
45.0ms	(+ (* c c) (* d d))
32.0ms	(- (* b c) (* a d))

series198.0ms

Calls

3 calls:

Slowest

113.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
53.0ms	(- (* b c) (* a d))
32.0ms	(+ (* c c) (* d d))

simplify36.1s

Calls

533 calls:

Slowest

465.0ms	(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
385.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
329.0ms	(fma (* (sqrt b) (sqrt c)) (* (sqrt b) (sqrt c)) (- (* (cbrt (* a d)) (* (cbrt (* a d)) (cbrt (* a d))))))
262.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
224.0ms	(fma (sqrt (* b c)) (sqrt (* b c)) (- (* (cbrt (* a d)) (* (cbrt (* a d)) (cbrt (* a d))))))

prune3.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 25.5b

localize39.0ms

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))

rewrite251.0ms

Algorithm

rewrite-expression-head

Rules

425×	`add-sqr-sqrt`
389×	`*-un-lft-identity`
183×	`associate-l`
144×	`prod-diff`
121×	`times-frac`
117×	`add-cube-cbrt`
112×	`sqrt-prod`
97×	`unswap-sqr`
75×	`associate-r`
70×	`distribute-lft-out`
52×	`hypot-def` `distribute-lft-out--` `difference-of-squares`
48×	`swap-sqr`
45×	`*-commutative`
12×	`fma-neg`
11×	`associate-/r` `associate-/l`
6×	`pow1` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`flip3-+` `flip-+`
2×	`+-commutative` `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

133.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
39.0ms	(sqrt (+ (* c c) (* d d)))
35.0ms	(sqrt (+ (* c c) (* d d)))
35.0ms	(- (* b c) (* a d))

series333.0ms

Calls

4 calls:

Slowest

168.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
62.0ms	(- (* b c) (* a d))
51.0ms	(sqrt (+ (* c c) (* d d)))
51.0ms	(sqrt (+ (* c c) (* d d)))

simplify40.8s

Calls

641 calls:

Slowest

486.0ms	(/ (sqrt (- (* b c) (* a d))) (sqrt (+ (* c c) (* d d))))
437.0ms	(/ (* (* (- (* 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)))))
354.0ms	(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))
347.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
315.0ms	(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))

prune4.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 23.6b

localize31.0ms

Local error

Found 4 expressions with local error:

30.7b	(sqrt (+ (* c c) (* d d)))
15.5b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
1.1b	(- (* b c) (* a d))
0.1b	(/ (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) (hypot c d))

rewrite327.0ms

Algorithm

rewrite-expression-head

Rules

1543×	`*-un-lft-identity`
1180×	`add-sqr-sqrt`
986×	`times-frac`
539×	`associate-l`
464×	`sqrt-prod`
383×	`add-cube-cbrt`
290×	`distribute-lft-out`
267×	`unswap-sqr`
232×	`distribute-lft-out--` `difference-of-squares`
149×	`associate-/l*`
144×	`prod-diff`
126×	`swap-sqr`
75×	`associate-r`
35×	`*-commutative`
31×	`associate-/l/`
26×	`hypot-def`
25×	`associate-/r*`
12×	`fma-neg` `sqrt-div`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
6×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`clear-num` `frac-2neg` `flip3--` `div-sub` `flip--`
1×	`+-commutative` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Calls

4 calls:

Slowest

128.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) (hypot c d))
94.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
38.0ms	(sqrt (+ (* c c) (* d d)))
36.0ms	(- (* b c) (* a d))

series441.0ms

Calls

4 calls:

Slowest

200.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) (hypot c d))
131.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
56.0ms	(sqrt (+ (* c c) (* d d)))
53.0ms	(- (* b c) (* a d))

simplify1.7m

Calls

1531 calls:

Slowest

520.0ms	(/ (/ (- (* b c) (* a d)) (cbrt (sqrt (+ (* c c) (* d d))))) (hypot c d))
505.0ms	(/ (/ (- (sqrt (* b c)) (* (sqrt a) (sqrt d))) (sqrt (+ (* c c) (* d d)))) (cbrt (hypot c d)))
448.0ms	(fma b c (- (* (cbrt (* a d)) (* (cbrt (* a d)) (cbrt (* a d))))))
427.0ms	(/ (* (* (- (* 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)))))
381.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))) 1)

prune8.7s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.9b

localize20.0ms

Local error

Found 3 expressions with local error:

15.5b	(/ (- (* b c) (* a d)) (hypot c d))
1.1b	(- (* b c) (* a d))
0.1b	(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

460×	`add-sqr-sqrt`
338×	`*-un-lft-identity`
276×	`times-frac`
194×	`add-cube-cbrt`
147×	`associate-l`
144×	`prod-diff`
97×	`unswap-sqr`
75×	`associate-r`
72×	`distribute-lft-out--` `difference-of-squares`
59×	`associate-/l*`
25×	`*-commutative`
23×	`associate-/l/`
12×	`fma-neg`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*`
6×	`div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `flip3--` `div-sub` `insert-posit16` `log1p-expm1-u` `flip--`
1×	`sub-neg` `diff-log`

Calls

3 calls:

Slowest

63.0ms	(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
61.0ms	(/ (- (* b c) (* a d)) (hypot c d))
26.0ms	(- (* b c) (* a d))

series282.0ms

Calls

3 calls:

Slowest

122.0ms	(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
117.0ms	(/ (- (* b c) (* a d)) (hypot c d))
43.0ms	(- (* b c) (* a d))

simplify37.1s

Calls

677 calls:

Slowest

603.0ms	(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (hypot c d) (hypot c d)) (hypot c d)))
581.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
258.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
177.0ms	(/ (/ (- (* (sqrt b) (sqrt c)) (* (sqrt a) (sqrt d))) (cbrt (hypot c d))) (sqrt (hypot c d)))
175.0ms	(/ (/ (- (* (sqrt b) (sqrt c)) (* (sqrt a) (sqrt d))) (sqrt (hypot c d))) (cbrt (hypot c d)))

prune3.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.9b

regimes316.0ms

Accuracy

31% (7.8b remaining)

Error of 13.6b against oracle of 5.8b and baseline of 17.2b

bsearch86.0ms

end0.0ms

sample1.0s

Algorithm

intervals

Results

865.0ms

8414×

body

valid