Details

sample104.0ms

Algorithm

intervals

Results

25.0ms	198×	body	80	valid
24.0ms	34×	body	2560	valid
17.0ms	29×	body	1280	valid
11.0ms	91×	body	80	nan
5.0ms	8×	body	640	valid
2.0ms	7×	body	320	valid
2.0ms	2×	body	5120	valid
1.0ms	6×	body	160	valid

simplify124.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	102
7	102
6	101
5	99
4	91
3	73
2	41
1	22
0	12

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 37.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
1.2b	(- (* b b) (* (* 3 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
27.8b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite137.0ms

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` `insert-posit16` `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 → 94

Calls

4 calls:

85.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
17.0ms	(- (* b b) (* (* 3 a) c))
24.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
10.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series469.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
78.0ms	(- (* b b) (* (* 3 a) c))
140.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
96.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify3.2s

Counts

106 → 106

Iterations

Iter	Nodes
3	4550
2	1336
1	439
0	170

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* a c) -3)
1.4b	(- (sqrt (fma b b (* (* a c) -3))) b)
1.5b	(fma b b (* (* a c) -3))
27.8b	(sqrt (fma b b (* (* a c) -3)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
16×	`sqrt-prod`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
6×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `associate-l` `*-commutative` `fma-udef` `flip--` `distribute-lft-out--`

Counts

4 → 90

Calls

4 calls:

21.0ms	(* (* a c) -3)
8.0ms	(- (sqrt (fma b b (* (* a c) -3))) b)
0.0ms	(fma b b (* (* a c) -3))
1.0ms	(sqrt (fma b b (* (* a c) -3)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (* a c) -3)
131.0ms	(- (sqrt (fma b b (* (* a c) -3))) b)
74.0ms	(fma b b (* (* a c) -3))
126.0ms	(sqrt (fma b b (* (* a c) -3)))

simplify1.6s

Counts

102 → 102

Iterations

Iter	Nodes
3	2698
2	841
1	316
0	145

prune855.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.7b

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* 3 a))
1.2b	(- (* b b) (* (* 3 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
27.8b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-exp-log`
14×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`fma-def` `add-cube-cbrt` `add-log-exp`
9×	`add-cbrt-cube`
8×	`pow1`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `times-frac` `prod-exp` `sqrt-prod` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `sum-log` `flip3--` `sqrt-div` `1-exp` `pow-flip` `flip--` `distribute-lft-out`
1×	`neg-sub0` `+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `neg-mul-1` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `neg-log` `associate-+l-` `cbrt-unprod` `flip-+` `div-inv` `inv-pow`

Counts

4 → 94

Calls

4 calls:

17.0ms	(/ 1 (* 3 a))
16.0ms	(- (* b b) (* (* 3 a) c))
31.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
19.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ 1 (* 3 a))
68.0ms	(- (* b b) (* (* 3 a) c))
93.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
99.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify2.4s

Counts

106 → 106

Iterations

Iter	Nodes
3	3480
2	1069
1	379
0	155

prune1.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.7b

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1/3 a)
1.2b	(- (* b b) (* (* 3 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
27.8b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite456.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
10×	`fma-def` `add-log-exp`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r` `sqrt-prod` `associate-/l`
2×	`sum-log` `flip3--` `sqrt-div` `flip--` `distribute-lft-out`
1×	`neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `neg-mul-1` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `div-exp` `prod-diff` `neg-log` `associate-+l-` `flip-+` `div-inv`

Counts

4 → 93

Calls

4 calls:

4.0ms	(/ 1/3 a)
9.0ms	(- (* b b) (* (* 3 a) c))
17.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
425.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ 1/3 a)
46.0ms	(- (* b b) (* (* 3 a) c))
90.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
83.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.6s

Counts

105 → 105

Iterations

Iter	Nodes
3	2933
2	1022
1	352
0	156

prune941.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 7.7b

regimes556.0ms

Accuracy

83% (4.8b remaining)

Error of 10.4b against oracle of 5.6b and baseline of 33.5b

bsearch150.0ms

Steps

Iters	Range		Point
8	2.764110880089542e-64	2.3245141193625934e-60	2.854741727591693e-61
6	-1.4884796866541563e+36	-1.9318991936063168e+35	-1.4577715279110013e+36

simplify11.0ms

Iterations

Iter	Nodes
2	34
1	34
0	29

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.3s	1057×	body	2560	valid
960.0ms	5887×	body	80	valid
695.0ms	908×	body	1280	valid
384.0ms	2991×	body	80	nan
268.0ms	444×	body	640	valid
163.0ms	109×	body	5120	valid
85.0ms	233×	body	320	valid
25.0ms	110×	body	160	valid