Details

sample1.2s

Algorithm

intervals

Results

137.0ms	22×	body	1280	valid
90.0ms	338×	body	80	nan
67.0ms	34×	body	640	valid
56.0ms	24×	body	320	valid
49.0ms	159×	body	80	valid
30.0ms	27×	body	640	nan
24.0ms	17×	body	1280	nan
9.0ms	17×	body	160	valid
7.0ms	10×	body	320	nan
5.0ms	9×	body	160	nan

simplify1.1s

Counts: 1 → 1

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.0b

localize52.0ms

Local error

Found 4 expressions with local error:

22.4b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
14.9b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
0.4b	(* (sqrt 2) t)
0.0b	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-/r` `times-frac` `associate-l*` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 94

Calls

4 calls:

Slowest

50.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
50.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
27.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
13.0ms	(* (sqrt 2) t)

series2.3s

Counts

4 → 12

Calls

4 calls:

Slowest

1.4s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
502.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
253.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
80.0ms	(* (sqrt 2) t)

simplify576.0ms

Counts: 106 → 106

prune1.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 7.7b

localize54.0ms

Local error

Found 4 expressions with local error:

30.4b	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (/ x (* l l))))))
9.5b	(/ (* t t) x)
5.5b	(/ x (* l l))
4.6b	(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (/ x (* l l)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`times-frac`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `associate-/r` `div-exp` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`sqrt-prod`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 75

Calls

4 calls:

Slowest

19.0ms	(/ (* t t) x)
13.0ms	(/ x (* l l))
3.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (/ x (* l l))))))
1.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (/ x (* l l)))))

series344.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

205.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (/ x (* l l))))))
85.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (/ x (* l l)))))
27.0ms	(/ (* t t) x)
25.0ms	(/ x (* l l))

simplify1.1s

Counts: 87 → 87

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.5b

localize44.0ms

Local error

Found 4 expressions with local error:

30.4b	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (/ (/ x l) l)))))
9.5b	(/ (* t t) x)
4.6b	(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (/ (/ x l) l))))
0.4b	(* (sqrt 2) t)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1` `sqrt-prod`
6×	`associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `times-frac` `associate-r*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `-commutative` `fma-udef` `div-inv` `associate-/l`

Counts

4 → 76

Calls

4 calls:

Slowest

10.0ms	(/ (* t t) x)
7.0ms	(* (sqrt 2) t)
3.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (/ (/ x l) l)))))
0.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (/ (/ x l) l))))

series345.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

207.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (/ (/ x l) l)))))
70.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (/ (/ x l) l))))
44.0ms	(* (sqrt 2) t)
23.0ms	(/ (* t t) x)

simplify1.2s

Counts: 88 → 88

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.5b

localize72.0ms

Local error

Found 4 expressions with local error:

30.4b	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (* (/ (* (cbrt x) (cbrt x)) l) (/ (cbrt x) l))))))
9.5b	(/ (* t t) x)
4.6b	(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (* (/ (* (cbrt x) (cbrt x)) l) (/ (cbrt x) l)))))
0.5b	(cbrt x)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `associate-/r*` `times-frac` `sqrt-prod`
2×	`cbrt-undiv` `div-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow1/3` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv` `associate-/l*`

Counts

4 → 65

Calls

4 calls:

Slowest

12.0ms	(/ (* t t) x)
1.0ms	(cbrt x)
1.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (* (/ (* (cbrt x) (cbrt x)) l) (/ (cbrt x) l))))))
0.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (* (/ (* (cbrt x) (cbrt x)) l) (/ (cbrt x) l)))))

series659.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

257.0ms	(cbrt x)
234.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (* (/ (* (cbrt x) (cbrt x)) l) (/ (cbrt x) l))))))
135.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ 2 (* (/ (* (cbrt x) (cbrt x)) l) (/ (cbrt x) l)))))
34.0ms	(/ (* t t) x)

simplify881.0ms

Counts: 77 → 77

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.5b

regimes707.0ms

Accuracy

76.1% (5.6b remaining)

Error of 9.1b against oracle of 3.5b and baseline of 27.0b

bsearch1.0s

end0.0ms

sample9.4s

Algorithm

intervals

Results

3.0s	9927×	body	80	nan
1.4s	1007×	body	640	valid
1.2s	5129×	body	80	valid
997.0ms	866×	body	1280	valid
842.0ms	564×	body	1280	nan
556.0ms	642×	body	640	nan
470.0ms	643×	body	320	valid
203.0ms	345×	body	320	nan
189.0ms	355×	body	160	valid
80.0ms	200×	body	160	nan