Details

sample199.0ms

Algorithm

intervals

Results

81.0ms	107×	body	320	valid
52.0ms	144×	body	160	valid
41.0ms	246×	body	80	nan
1.0ms	5×	body	80	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
6	3542
5	1922
4	928
3	370
2	119
1	47
0	19

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.9b

localize79.0ms

Local error

Found 4 expressions with local error:

10.0b	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
11.6b	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
31.3b	(sqrt (- (* g g) (* h h)))
31.3b	(sqrt (- (* g g) (* h h)))

rewrite107.0ms

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` `insert-posit16` `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 → 72

Calls

4 calls:

54.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
33.0ms	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series1.0s

Counts

4 → 12

Calls

4 calls:

424.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
443.0ms	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
65.0ms	(sqrt (- (* g g) (* h h)))
76.0ms	(sqrt (- (* g g) (* h h)))

simplify3.7s

Counts

84 → 84

Iterations

Iter	Nodes
3	4881
2	1255
1	408
0	171

prune1.7s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 31.9b

localize75.0ms

Local error

Found 4 expressions with local error:

4.6b	(- (* g g) (* h h))
11.6b	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
31.3b	(sqrt (- (* g g) (* h h)))
31.3b	(sqrt (- (* g g) (* h h)))

rewrite106.0ms

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` `insert-posit16` `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 → 73

Calls

4 calls:

8.0ms	(- (* g g) (* h h))
52.0ms	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
26.0ms	(sqrt (- (* g g) (* h h)))
19.0ms	(sqrt (- (* g g) (* h h)))

series562.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* g g) (* h h))
400.0ms	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
60.0ms	(sqrt (- (* g g) (* h h)))
53.0ms	(sqrt (- (* g g) (* h h)))

simplify2.5s

Counts

85 → 85

Iterations

Iter	Nodes
3	4244
2	1083
1	342
0	146

prune1.4s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 30.9b

localize54.0ms

Local error

Found 4 expressions with local error:

4.6b	(- (* g g) (* h h))
4.6b	(- (* g g) (* h h))
31.3b	(sqrt (- (* g g) (* h h)))
31.3b	(sqrt (- (* g g) (* h h)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 74

Calls

4 calls:

14.0ms	(- (* g g) (* h h))
12.0ms	(- (* g g) (* h h))
9.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* g g) (* h h))
58.0ms	(- (* g g) (* h h))
72.0ms	(sqrt (- (* g g) (* h h)))
60.0ms	(sqrt (- (* g g) (* h h)))

simplify4.3s

Counts

86 → 86

Iterations

Iter	Nodes
4	8808
3	1764
2	399
1	138
0	64

prune1.8s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 30.9b

localize50.0ms

Local error

Found 4 expressions with local error:

4.6b	(- (* g g) (* h h))
4.6b	(- (* g g) (* h h))
31.3b	(sqrt (- (* g g) (* h h)))
31.3b	(sqrt (- (* g g) (* h h)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 74

Calls

4 calls:

15.0ms	(- (* g g) (* h h))
12.0ms	(- (* g g) (* h h))
9.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series216.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* g g) (* h h))
43.0ms	(- (* g g) (* h h))
69.0ms	(sqrt (- (* g g) (* h h)))
66.0ms	(sqrt (- (* g g) (* h h)))

simplify4.5s

Counts

86 → 86

Iterations

Iter	Nodes
4	8808
3	1764
2	399
1	138
0	64

prune1.7s

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 30.9b

regimes1.4s

Accuracy

26.6% (1.6b remaining)

Error of 30.9b against oracle of 29.3b and baseline of 31.4b

bsearch572.0ms

Steps

Iters	Range		Point
7	2.289376578376978e-40	1.3632368677943003e-38	6.420654691865451e-40
8	-5.21537847731065e-199	-6.855465369280799e-203	-5.110014296461794e-199

simplify16.0ms

Iterations

Iter	Nodes
2	56
1	56
0	44

end0.0ms

sample7.6s

Algorithm

intervals

Results

2.5s	3687×	body	320	valid
2.3s	4171×	body	160	valid
2.3s	7844×	body	80	nan
28.0ms	142×	body	80	valid