Details

sample52.0ms

Algorithm

intervals

Results

13.0ms	36×	body	2560	valid
8.0ms	179×	body	80	valid
6.0ms	28×	body	1280	valid
4.0ms	79×	body	80	nan
3.0ms	15×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	2×	body	160	valid

simplify122.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	12	17
1	22	17
2	42	16
3	82	16
4	104	16
5	112	16
done	112	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.5b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.6b	(- (* b b) (* (* 3.0 a) c))
21.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`pow1` `add-sqr-sqrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `neg-log` `*-commutative` `flip-+`

Counts

4 → 80

Calls

4 calls:

17.0ms	(* (* 3.0 a) c)
22.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(- (* b b) (* (* 3.0 a) c))
17.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (* 3.0 a) c)
87.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
53.0ms	(- (* b b) (* (* 3.0 a) c))
92.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.7s

Counts

92 → 92

Iterations

Useful iterations: 3 (1.9s)

Iter	Nodes	Cost
0	135	1109
1	332	1006
2	1193	900
3	4662	889
done	5000	889

prune363.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* a c) 3.0)
0.5b	(+ (- b) (sqrt (- (* b b) (pow (* (* a c) 3.0) 1))))
0.6b	(- (* b b) (pow (* (* a c) 3.0) 1))
21.8b	(sqrt (- (* b b) (pow (* (* a c) 3.0) 1)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
5×	`prod-diff` `sqrt-prod`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u` `difference-of-squares`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `sqr-pow`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `unpow-prod-down` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-l` `neg-log` `*-commutative` `flip-+`

Counts

4 → 88

Calls

4 calls:

27.0ms	(* (* a c) 3.0)
36.0ms	(+ (- b) (sqrt (- (* b b) (pow (* (* a c) 3.0) 1))))
17.0ms	(- (* b b) (pow (* (* a c) 3.0) 1))
22.0ms	(sqrt (- (* b b) (pow (* (* a c) 3.0) 1)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (* a c) 3.0)
104.0ms	(+ (- b) (sqrt (- (* b b) (pow (* (* a c) 3.0) 1))))
78.0ms	(- (* b b) (pow (* (* a c) 3.0) 1))
92.0ms	(sqrt (- (* b b) (pow (* (* a c) 3.0) 1)))

simplify1.5s

Counts

100 → 100

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	171	1586
1	398	1162
2	1452	1027
done	5000	1017

prune378.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (* a c) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))
0.5b	(+ (- b) (sqrt (- (* b b) (pow (* (* (* a c) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)) 1))))
0.6b	(- (* b b) (pow (* (* (* a c) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)) 1))
21.8b	(sqrt (- (* b b) (pow (* (* (* a c) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)) 1)))

rewrite266.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
22×	`add-exp-log`
15×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`pow-prod-down` `prod-exp` `add-cbrt-cube` `cbrt-unprod`
11×	`add-cube-cbrt`
10×	`fma-def` `add-log-exp`
6×	`associate-r`
5×	`prod-diff` `sqrt-prod`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u` `difference-of-squares`
3×	`cbrt-prod` `distribute-lft-neg-in` `sqr-pow`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `unpow-prod-down` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-l` `neg-log` `*-commutative` `flip-+`

Counts

4 → 100

Calls

4 calls:

177.0ms	(* (* (* a c) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))
48.0ms	(+ (- b) (sqrt (- (* b b) (pow (* (* (* a c) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)) 1))))
14.0ms	(- (* b b) (pow (* (* (* a c) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)) 1))
22.0ms	(sqrt (- (* b b) (pow (* (* (* a c) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)) 1)))

series592.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (* (* a c) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))
163.0ms	(+ (- b) (sqrt (- (* b b) (pow (* (* (* a c) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)) 1))))
146.0ms	(- (* b b) (pow (* (* (* a c) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)) 1))
200.0ms	(sqrt (- (* b b) (pow (* (* (* a c) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)) 1)))

simplify1.7s

Counts

112 → 112

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	201	2692
1	488	2094
2	1960	1443
done	5000	1086

prune460.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.3b

localize23.0ms

Local error

Found 4 expressions with local error:

21.8b	(sqrt (* (* (cbrt (- (* b b) (* (* 3.0 a) c))) (cbrt (- (* b b) (* (* 3.0 a) c)))) (cbrt (- (* b b) (* (* 3.0 a) c)))))
22.6b	(cbrt (- (* b b) (* (* 3.0 a) c)))
22.6b	(cbrt (- (* b b) (* (* 3.0 a) c)))
22.6b	(cbrt (- (* b b) (* (* 3.0 a) c)))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 97

Calls

4 calls:

139.0ms	(sqrt (* (* (cbrt (- (* b b) (* (* 3.0 a) c))) (cbrt (- (* b b) (* (* 3.0 a) c)))) (cbrt (- (* b b) (* (* 3.0 a) c)))))
12.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
12.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
11.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))

series472.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(sqrt (* (* (cbrt (- (* b b) (* (* 3.0 a) c))) (cbrt (- (* b b) (* (* 3.0 a) c)))) (cbrt (- (* b b) (* (* 3.0 a) c)))))
108.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
115.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
151.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))

simplify2.3s

Counts

109 → 109

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	193	3874
1	361	3353
2	762	2692
3	2254	2632
done	5000	2554

prune414.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.3b

regimes466.0ms

Accuracy

97.6% (0.5b remaining)

Error of 12.6b against oracle of 12.1b and baseline of 34.4b

bsearch243.0ms

Steps

Iters	Range	Point
8	9.62326813722015e+150	3.6001811539733483e+155	1.3605336024717198e+154
6	1.230628501312938e-151	7.040558363340882e-151	4.3313464211392044e-151
9	-1.489991982892314e+158	-2.0545059602165346e+153	-1.3596485852230119e+154

Iters

Range

Point

9.62326813722015e+150

3.6001811539733483e+155

1.3605336024717198e+154

1.230628501312938e-151

7.040558363340882e-151

4.3313464211392044e-151

-1.489991982892314e+158

-2.0545059602165346e+153

-1.3596485852230119e+154

simplify9.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	47	88
1	58	84
done	58	84

end0.0ms

sample3.2s

Algorithm

intervals

Results

889.0ms	5914×	body	80	valid
613.0ms	1022×	body	2560	valid
605.0ms	2919×	body	80	nan
262.0ms	870×	body	1280	valid
144.0ms	469×	body	640	valid
92.0ms	125×	body	5120	valid
40.0ms	236×	body	320	valid
12.0ms	107×	body	160	valid