Details

sample53.0ms

Algorithm

intervals

Results

9.0ms	184×	body	80	valid
9.0ms	32×	body	2560	valid
7.0ms	31×	body	1280	valid
4.0ms	84×	body	80	nan
3.0ms	17×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify88.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	120
5	120
4	112
3	83
2	42
1	22
0	12

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.4b	(- (* b b) (* (* 3.0 a) c))
24.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`fma-def` `add-cube-cbrt` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`neg-sub0` `cbrt-undiv` `sum-log` `flip3-+` `flip3--` `sqrt-div` `div-exp` `associate-+l-` `flip-+` `flip--` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `neg-mul-1` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

29.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
83.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
6.0ms	(- (* b b) (* (* 3.0 a) c))
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
137.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
54.0ms	(- (* b b) (* (* 3.0 a) c))
114.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.9s

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
2	2084
1	446
0	167

prune699.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* c a) 3.0)
0.2b	(- (sqrt (- (* b b) (* (* c a) 3.0))) b)
1.4b	(- (* b b) (* (* c a) 3.0))
24.6b	(sqrt (- (* b b) (* (* c a) 3.0)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`prod-diff`
16×	`sqrt-prod`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`fma-neg`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 94

Calls

4 calls:

25.0ms	(* (* c a) 3.0)
82.0ms	(- (sqrt (- (* b b) (* (* c a) 3.0))) b)
7.0ms	(- (* b b) (* (* c a) 3.0))
9.0ms	(sqrt (- (* b b) (* (* c a) 3.0)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (* c a) 3.0)
105.0ms	(- (sqrt (- (* b b) (* (* c a) 3.0))) b)
81.0ms	(- (* b b) (* (* c a) 3.0))
107.0ms	(sqrt (- (* b b) (* (* c a) 3.0)))

simplify2.3s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1997
1	411
0	162

prune626.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.8b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* c a) (* (cbrt 3.0) (cbrt 3.0)))
0.3b	(* (* (* c a) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))
1.4b	(- (* b b) (* (* (* c a) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)))
24.6b	(sqrt (- (* b b) (* (* (* c a) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

35×	`pow1`
34×	`add-exp-log`
21×	`add-cbrt-cube` `pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
7×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
6×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-prod` `sqrt-prod`
2×	`flip3--` `sqrt-div` `associate-l` `*-commutative` `flip--`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 89

Calls

4 calls:

48.0ms	(* (* c a) (* (cbrt 3.0) (cbrt 3.0)))
122.0ms	(* (* (* c a) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))
7.0ms	(- (* b b) (* (* (* c a) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)))
17.0ms	(sqrt (- (* b b) (* (* (* c a) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))))

series598.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (* c a) (* (cbrt 3.0) (cbrt 3.0)))
124.0ms	(* (* (* c a) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))
169.0ms	(- (* b b) (* (* (* c a) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)))
185.0ms	(sqrt (- (* b b) (* (* (* c a) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))))

simplify1.8s

Counts

101 → 101

Iterations

Iter	Nodes
done	5000
2	2330
1	392
0	144

prune606.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.8b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.2b	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
1.4b	(- (* b b) (* (* 3.0 a) c))
24.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`fma-def` `add-cube-cbrt` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `associate-/r*` `times-frac`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `sum-log` `flip3-+` `flip3--` `sqrt-div` `div-exp` `associate-/r/` `flip-+` `flip--`
1×	`neg-sub0` `+-commutative` `rem-sqrt-square` `clear-num` `neg-mul-1` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `neg-log` `prod-exp` `associate-+l-` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 89

Calls

4 calls:

27.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
54.0ms	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
13.0ms	(- (* b b) (* (* 3.0 a) c))
18.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series614.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
297.0ms	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
83.0ms	(- (* b b) (* (* 3.0 a) c))
106.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.8s

Counts

101 → 101

Iterations

Iter	Nodes
done	5004
2	2052
1	434
0	159

prune685.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.8b

regimes905.0ms

Accuracy

83.8% (4.6b remaining)

Error of 10.7b against oracle of 6.1b and baseline of 34.5b

bsearch162.0ms

Steps

Iters	Range		Point
8	2.8373581988670566e-35	2.2677514638291856e-31	2.8983489306952693e-35
8	-2.748004767191833e+152	-7.260401024913698e+147	-2.221067196710922e+149

simplify26.0ms

Iterations

Iter	Nodes
done	37
1	37
0	32

end0.0ms

sample2.6s

Algorithm

intervals

Results

837.0ms	5834×	body	80	valid
561.0ms	1040×	body	2560	valid
344.0ms	910×	body	1280	valid
215.0ms	2881×	body	80	nan
111.0ms	453×	body	640	valid
87.0ms	101×	body	5120	valid
81.0ms	232×	body	320	valid
14.0ms	116×	body	160	valid