Details

sample118.0ms

Algorithm

intervals

Results

36.0ms	116×	body	320	valid
28.0ms	138×	body	160	valid
22.0ms	250×	body	80	nan
0.0ms	2×	body	80	valid

simplify10.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	19	645
1	44	645
2	124	645
3	287	645
4	595	645
5	984	645
6	1310	645
7	1639	645
8	2537	645
done	5000	645

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize74.0ms

Local error

Found 4 expressions with local error:

6.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
8.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
31.5b	(sqrt (- (* g g) (* h h)))
31.5b	(sqrt (- (* g g) (* h h)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-div`
8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `frac-times` `flip3--` `add-cbrt-cube` `sqrt-div` `associate-*r/` `add-exp-log` `log1p-expm1-u` `flip--` `add-log-exp`
2×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `associate-*l/` `flip-+` `difference-of-squares`

Counts

4 → 68

Calls

4 calls:

38.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
45.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
18.0ms	(sqrt (- (* g g) (* h h)))
16.0ms	(sqrt (- (* g g) (* h h)))

series1.0s

Counts

4 → 12

Calls

4 calls:

409.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
451.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
74.0ms	(sqrt (- (* g g) (* h h)))
67.0ms	(sqrt (- (* g g) (* h h)))

simplify3.7s

Counts

80 → 80

Iterations

Useful iterations: 3 (2.4s)

Iter	Nodes	Cost
0	172	33766
1	406	30254
2	1302	29284
3	4894	28454
done	5000	28454

prune927.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 32.9b

localize46.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
8.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
31.5b	(sqrt (- (* g g) (* h h)))
31.5b	(sqrt (- (* g g) (* h h)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
5×	`cbrt-div`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u`
3×	`flip3--` `flip--` `difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+`
1×	`cbrt-prod` `sub-neg` `fma-neg` `pow1/3` `diff-log` `prod-diff` `associate-*l/`

Counts

4 → 69

Calls

4 calls:

7.0ms	(- (* g g) (* h h))
35.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series602.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (* g g) (* h h))
435.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
49.0ms	(sqrt (- (* g g) (* h h)))
78.0ms	(sqrt (- (* g g) (* h h)))

simplify142.0ms

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	146	26930