Details

sample105.0ms

Algorithm

intervals

Results

29.0ms	30×	body	2560	valid
20.0ms	182×	body	80	valid
19.0ms	32×	body	1280	valid
9.0ms	86×	body	80	nan
4.0ms	9×	body	640	valid
4.0ms	5×	body	5120	valid
3.0ms	9×	body	320	valid
1.0ms	7×	body	160	valid

simplify111.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	93
7	93
6	92
5	90
4	82
3	66
2	40
1	21
0	12

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `sqrt-prod` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 76

Calls

4 calls:

117.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
13.0ms	(- (* b b) (* (* 3 a) c))
64.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
55.0ms	(- (* b b) (* (* 3 a) c))
120.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
105.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify2.9s

Counts

88 → 88

Iterations

Iter	Nodes
3	4888
2	1249
1	396
0	157

prune850.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* 3 a))
1.4b	(- (* b b) (* (* 3 a) c))
2.3b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
21.8b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-exp-log`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cbrt-cube`
8×	`pow1` `add-log-exp`
7×	`add-cube-cbrt`
4×	`div-exp` `sqrt-prod` `insert-posit16`
3×	`times-frac` `flip3--` `prod-exp` `flip--` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `sub-neg` `sqrt-div` `diff-log` `1-exp` `pow-flip` `difference-of-squares`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `cbrt-unprod` `div-inv` `distribute-lft-out--` `inv-pow`

Counts

4 → 74

Calls

4 calls:

12.0ms	(/ 1 (* 3 a))
12.0ms	(- (* b b) (* (* 3 a) c))
49.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
9.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ 1 (* 3 a))
49.0ms	(- (* b b) (* (* 3 a) c))
91.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
103.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify2.1s

Counts

86 → 86

Iterations

Iter	Nodes
3	3356
2	933
1	326
0	140

prune967.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod` `insert-posit16`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3-+` `sqrt-div` `flip-+` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `associate-l` `*-commutative` `flip--` `distribute-lft-out--`

Counts

4 → 63

Calls

4 calls:

21.0ms	(* (* a c) -3)
24.0ms	(+ (* (* a c) -3) (* b b))
130.0ms	(- (sqrt (+ (* (* a c) -3) (* b b))) b)
19.0ms	(sqrt (+ (* (* a c) -3) (* b b)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (* a c) -3)
86.0ms	(+ (* (* a c) -3) (* b b))
120.0ms	(- (sqrt (+ (* (* a c) -3) (* b b))) b)
93.0ms	(sqrt (+ (* (* a c) -3) (* b b)))

simplify1.8s

Counts

75 → 75

Iterations

Iter	Nodes
3	3388
2	873
1	273
0	112

prune860.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1/3 a)
1.4b	(- (* b b) (* (* 3 a) c))
2.3b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
21.8b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`sqrt-prod` `insert-posit16`
3×	`associate-/r` `flip3--` `flip--` `associate-/l`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv` `distribute-lft-out--`

Counts

4 → 73

Calls

4 calls:

3.0ms	(/ 1/3 a)
7.0ms	(- (* b b) (* (* 3 a) c))
58.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ 1/3 a)
53.0ms	(- (* b b) (* (* 3 a) c))
117.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
107.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.4s

Counts

85 → 85

Iterations

Iter	Nodes
3	2863
2	862
1	301
0	141

prune914.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 6.0b

regimes571.0ms

Accuracy

83.5% (4.6b remaining)

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

bsearch133.0ms

Steps

Iters	Range		Point
7	6.1141969789339016e-111	5.505912162480727e-109	1.7070929733814247e-109
8	-3.470087527686165e+109	-1.3123866845995092e+107	-7.645130993934684e+108

simplify4.0ms

Iterations

Iter	Nodes
2	32
1	32
0	27

end0.0ms

sample4.2s

Algorithm

intervals

Results

878.0ms	1109×	body	2560	valid
827.0ms	5850×	body	80	valid
757.0ms	883×	body	1280	valid
566.0ms	228×	body	320	valid
416.0ms	2882×	body	80	nan
260.0ms	422×	body	640	valid
148.0ms	114×	body	5120	valid
29.0ms	125×	body	160	valid