Details

sample73.0ms

Algorithm

intervals

Results

21.0ms	47×	body	1280	valid
12.0ms	43×	body	640	valid
10.0ms	176×	body	80	valid
6.0ms	29×	body	320	valid
5.0ms	118×	body	80	nan
2.0ms	15×	body	160	valid

simplify1.2s

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (exp (* x (log (/ x (+ x y))))) x)
0.0b	(/ x (+ x y))
0.1b	(* x (log (/ x (+ x y))))
8.7b	(log (/ x (+ x y)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

261×	`times-frac`
221×	`*-un-lft-identity`
198×	`log-prod`
149×	`add-sqr-sqrt`
147×	`add-cube-cbrt`
144×	`exp-sum`
90×	`distribute-rgt-in` `distribute-lft-in`
42×	`associate-/l*`
37×	`distribute-lft-out`
24×	`associate-/r/`
13×	`div-inv`
12×	`add-exp-log` `flip3-+` `flip-+`
10×	`add-cbrt-cube`
8×	`pow1`
7×	`associate-/r*`
4×	`associate-r` `add-log-exp`
3×	`div-exp` `associate-l`
2×	`cbrt-undiv` `frac-2neg` `rem-log-exp` `clear-num` `log-pow`
1×	`log-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 288

Calls

4 calls:

54.0ms	(/ (exp (* x (log (/ x (+ x y))))) x)
12.0ms	(/ x (+ x y))
35.0ms	(* x (log (/ x (+ x y))))
7.0ms	(log (/ x (+ x y)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (exp (* x (log (/ x (+ x y))))) x)
41.0ms	(/ x (+ x y))
116.0ms	(* x (log (/ x (+ x y))))
69.0ms	(log (/ x (+ x y)))

simplify1.1s

Counts: 300 → 300

prune835.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.5b	(cbrt x)
4.3b	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-exp-log`
13×	`log-prod`
12×	`cbrt-div`
9×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `associate-/r/`
6×	`flip3-+` `flip-+`
5×	`pow1` `rem-log-exp`
4×	`frac-times` `div-exp` `prod-exp` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
2×	`associate-r/` `associate-l/`
1×	`log-div` `times-frac` `log-pow` `div-inv`

Counts

4 → 60

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
29.0ms	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

series865.0ms

Counts

4 → 12

Calls

4 calls:

257.0ms	(cbrt x)
255.0ms	(cbrt x)
244.0ms	(cbrt x)
108.0ms	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

simplify1.2s

Counts: 72 → 72

prune527.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
3.9b	(log (/ (cbrt x) (cbrt (+ x y))))
3.9b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

96×	`cbrt-prod` `log-prod`
84×	`*-un-lft-identity` `times-frac`
60×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`distribute-lft-out`
10×	`add-exp-log`
6×	`pow1`
4×	`cbrt-div` `rem-log-exp` `associate-/r/` `add-cbrt-cube` `add-log-exp`
2×	`log-div` `flip3-+` `pow1/3` `div-exp` `log-pow` `flip-+` `div-inv`

Counts

4 → 140

Calls

4 calls:

1.0ms	(cbrt x)
2.0ms	(cbrt x)
16.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
17.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series761.0ms

Counts

4 → 12

Calls

4 calls:

281.0ms	(cbrt x)
267.0ms	(cbrt x)
99.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
114.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify999.0ms

Counts: 152 → 152

prune879.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sqrt (/ x (+ x y))) x)
0.3b	(pow (sqrt (/ x (+ x y))) x)
4.8b	(sqrt (/ x (+ x y)))
4.8b	(sqrt (/ x (+ x y)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
64×	`*-un-lft-identity`
50×	`times-frac`
46×	`add-sqr-sqrt`
42×	`unpow-prod-down`
40×	`add-cube-cbrt`
12×	`distribute-lft-out`
10×	`pow1`
8×	`associate-/r/`
6×	`add-exp-log` `pow-unpow` `pow-pow`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `div-inv` `add-log-exp`
2×	`pow-to-exp` `sqrt-div` `pow-exp` `sqrt-pow2` `sqr-pow`

Counts

4 → 136

Calls

4 calls:

15.0ms	(pow (sqrt (/ x (+ x y))) x)
32.0ms	(pow (sqrt (/ x (+ x y))) x)
20.0ms	(sqrt (/ x (+ x y)))
16.0ms	(sqrt (/ x (+ x y)))

series965.0ms

Counts

4 → 12

Calls

4 calls:

416.0ms	(pow (sqrt (/ x (+ x y))) x)
376.0ms	(pow (sqrt (/ x (+ x y))) x)
79.0ms	(sqrt (/ x (+ x y)))
94.0ms	(sqrt (/ x (+ x y)))

simplify675.0ms

Counts: 148 → 148

prune580.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes82.0ms

Accuracy

94.3% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 5.8b

bsearch129.0ms

Steps

Iters	Range		Point
6	1.6549904719812824e-10	1.1362596833603348e-09	1.1158984721914147e-09
8	-1.1610098128388504e+53	-3.2818405371306287e+50	-4.12015628866316e+50

simplify660.0ms

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.2s	1484×	body	1280	valid
607.0ms	1464×	body	640	valid
552.0ms	3128×	body	80	nan
520.0ms	4912×	body	80	valid
292.0ms	798×	body	320	valid
92.0ms	507×	body	160	valid