Details

sample125.0ms

Algorithm

intervals

Results

30.0ms	30×	body	2560	valid
26.0ms	182×	body	80	valid
23.0ms	32×	body	1280	valid
12.0ms	86×	body	80	nan
5.0ms	9×	body	640	valid
5.0ms	5×	body	5120	valid
3.0ms	9×	body	320	valid
2.0ms	7×	body	160	valid

simplify100.0ms

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.9b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
1.4b	(- (* b b) (* (* 3 a) c))
2.3b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
21.8b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite101.0ms

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:

55.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
16.0ms	(- (* b b) (* (* 3 a) c))
20.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
56.0ms	(- (* b b) (* (* 3 a) c))
113.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
78.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify2.6s

Counts

106 → 106

Iterations

Iter	Nodes
3	4498
2	1340
1	440
0	170

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* -3 (* a c))
1.8b	(fma b b (* -3 (* a c)))
2.3b	(- (sqrt (fma b b (* -3 (* a c)))) b)
21.8b	(sqrt (fma b b (* -3 (* a c))))

rewrite48.0ms

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-l` `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-r` `*-commutative` `fma-udef` `flip--` `distribute-lft-out--`

Counts

4 → 90

Calls

4 calls:

31.0ms	(* -3 (* a c))
0.0ms	(fma b b (* -3 (* a c)))
13.0ms	(- (sqrt (fma b b (* -3 (* a c)))) b)
2.0ms	(sqrt (fma b b (* -3 (* a c))))

series345.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* -3 (* a c))
57.0ms	(fma b b (* -3 (* a c)))
131.0ms	(- (sqrt (fma b b (* -3 (* a c)))) b)
120.0ms	(sqrt (fma b b (* -3 (* a c))))

simplify999.0ms

Counts

102 → 102

Iterations

Iter	Nodes
3	2470
2	762
1	302
0	142

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* -3 (* a c))
1.8b	(fma b b (* -3 (* a c)))
2.3b	(+ (- b) (sqrt (fma b b (* -3 (* a c)))))
21.8b	(sqrt (fma b b (* -3 (* a c))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `pow1` `fma-def`
9×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
8×	`add-log-exp`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-l` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`sum-log` `distribute-lft-out`
1×	`neg-sub0` `+-commutative` `rem-sqrt-square` `neg-mul-1` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r` `neg-log` `*-commutative` `associate-+l-` `flip-+` `fma-udef`

Counts

4 → 76

Calls

4 calls:

18.0ms	(* -3 (* a c))
0.0ms	(fma b b (* -3 (* a c)))
16.0ms	(+ (- b) (sqrt (fma b b (* -3 (* a c)))))
2.0ms	(sqrt (fma b b (* -3 (* a c))))

series358.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* -3 (* a c))
91.0ms	(fma b b (* -3 (* a c)))
135.0ms	(+ (- b) (sqrt (fma b b (* -3 (* a c)))))
94.0ms	(sqrt (fma b b (* -3 (* a c))))

simplify796.0ms

Counts

88 → 88

Iterations

Iter	Nodes
3	2337
2	748
1	271
0	116

prune908.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.0b

localize40.0ms

Local error

Found 4 expressions with local error:

2.3b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
2.3b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
21.8b	(sqrt (- (* b b) (* (* 3 a) c)))
21.8b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

20×	`fma-def` `*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `add-log-exp`
8×	`distribute-rgt-neg-in`
6×	`distribute-lft-neg-in` `pow1` `sqrt-prod`
4×	`expm1-log1p-u` `sum-log` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
2×	`neg-sub0` `+-commutative` `rem-sqrt-square` `neg-mul-1` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `neg-log` `associate-+l-` `flip-+` `flip--`

Counts

4 → 92

Calls

4 calls:

28.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
23.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
122.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
138.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
109.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.5s

Counts

104 → 104

Iterations

Iter	Nodes
3	2514
2	738
1	233
0	88

prune1.4s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 6.0b

regimes891.0ms

Accuracy

83.5% (4.6b remaining)

Error of 10.1b against oracle of 5.5b and baseline of 33.2b

bsearch169.0ms

Steps

Iters	Range		Point
7	6.1141969789339016e-111	5.505912162480727e-109	4.7587539095277834e-110
10	-7.890092876878924e+158	-3.245965949054454e+146	-6.4670828746192654e+153

simplify9.0ms

Iterations

Iter	Nodes
2	36
1	36
0	29

end0.0ms

sample4.1s

Algorithm

intervals

Results

905.0ms	1109×	body	2560	valid
830.0ms	5850×	body	80	valid
569.0ms	883×	body	1280	valid
533.0ms	114×	body	5120	valid
481.0ms	2882×	body	80	nan
255.0ms	422×	body	640	valid
113.0ms	125×	body	160	valid
78.0ms	228×	body	320	valid