Details

sample146.0ms

Algorithm

intervals

Results

33.0ms	196×	body	80	valid
26.0ms	26×	body	2560	valid
22.0ms	26×	body	1280	valid
18.0ms	96×	body	80	nan
11.0ms	16×	body	640	valid
7.0ms	6×	body	5120	valid
3.0ms	5×	body	320	valid
1.0ms	4×	body	160	valid

simplify183.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	142
7	142
6	140
5	135
4	130
3	110
2	63
1	29
0	14

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
1.2b	(- (* b b) (* 4 (* a c)))
1.4b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
19.8b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 157

Calls

4 calls:

71.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
7.0ms	(- (* b b) (* 4 (* a c)))
24.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
16.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series434.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
77.0ms	(- (* b b) (* 4 (* a c)))
129.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
86.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify4.6s

Counts

169 → 169

Iterations

Iter	Nodes
3	6436
2	1646
1	590
0	235

prune2.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.6b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
1.2b	(- (* b b) (* 4 (* a c)))
1.4b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
19.8b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
61×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`associate-r`
11×	`fma-neg`
10×	`times-frac` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`pow1` `neg-mul-1` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log`
2×	`frac-times` `sub-neg` `sqrt-div` `associate-*l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `neg-log` `associate-r/` `-commutative` `div-inv`

Counts

4 → 165

Calls

4 calls:

73.0ms	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
16.0ms	(- (* b b) (* 4 (* a c)))
26.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
8.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series399.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
55.0ms	(- (* b b) (* 4 (* a c)))
118.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
88.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify3.6s

Counts

177 → 177

Iterations

Iter	Nodes
3	5805
2	1778
1	639
0	258

prune2.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (fma b b (* a (* c -4))))) (/ 1/2 a))
1.4b	(- (- b) (sqrt (fma b b (* a (* c -4)))))
1.5b	(fma b b (* a (* c -4)))
19.8b	(sqrt (fma b b (* a (* c -4))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
60×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`associate-r`
10×	`times-frac` `fma-neg`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`pow1` `neg-mul-1` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `flip--`
2×	`frac-times` `diff-log` `associate-*l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `neg-log` `associate-r/` `-commutative` `fma-udef` `div-inv`

Counts

4 → 157

Calls

4 calls:

36.0ms	(* (- (- b) (sqrt (fma b b (* a (* c -4))))) (/ 1/2 a))
25.0ms	(- (- b) (sqrt (fma b b (* a (* c -4)))))
0.0ms	(fma b b (* a (* c -4)))
1.0ms	(sqrt (fma b b (* a (* c -4))))

series394.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (- (- b) (sqrt (fma b b (* a (* c -4))))) (/ 1/2 a))
114.0ms	(- (- b) (sqrt (fma b b (* a (* c -4)))))
65.0ms	(fma b b (* a (* c -4)))
83.0ms	(sqrt (fma b b (* a (* c -4))))

simplify3.0s

Counts

169 → 169

Iterations

Iter	Nodes
3	4337
2	1520
1	560
0	238

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.6b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (/ 2 (- (+ b (sqrt (fma b b (* -4 (* a c))))))) a))
1.4b	(+ b (sqrt (fma b b (* -4 (* a c)))))
1.5b	(fma b b (* -4 (* a c)))
19.8b	(sqrt (fma b b (* -4 (* a c))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
13×	`add-cbrt-cube`
10×	`*-un-lft-identity`
9×	`add-sqr-sqrt` `div-exp`
8×	`pow1` `add-cube-cbrt`
6×	`prod-exp` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `log1p-expm1-u`
3×	`rec-exp` `fma-def` `times-frac` `1-exp` `sqrt-prod` `associate-/l*`
2×	`cbrt-unprod` `pow-flip`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r` `sum-log` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `associate-l/` `associate-/r/` `flip-+` `fma-udef` `div-inv` `distribute-lft-out` `inv-pow`

Counts

4 → 77

Calls

4 calls:

21.0ms	(/ 1 (* (/ 2 (- (+ b (sqrt (fma b b (* -4 (* a c))))))) a))
4.0ms	(+ b (sqrt (fma b b (* -4 (* a c)))))
0.0ms	(fma b b (* -4 (* a c)))
2.0ms	(sqrt (fma b b (* -4 (* a c))))

series467.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ 1 (* (/ 2 (- (+ b (sqrt (fma b b (* -4 (* a c))))))) a))
97.0ms	(+ b (sqrt (fma b b (* -4 (* a c)))))
88.0ms	(fma b b (* -4 (* a c)))
109.0ms	(sqrt (fma b b (* -4 (* a c))))

simplify2.0s

Counts

89 → 89

Iterations

Iter	Nodes
3	4127
2	1138
1	360
0	148

prune830.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.6b

regimes325.0ms

Accuracy

84.8% (4.3b remaining)

Error of 9.8b against oracle of 5.5b and baseline of 33.5b

bsearch188.0ms

Steps

Iters	Range		Point
9	1.5347927881719531e+137	5.414027326126016e+143	6.359263193477048e+137
7	-3.433369562555282e-53	-1.9970851824949347e-54	-2.852138444177435e-54

simplify6.0ms

Iterations

Iter	Nodes
3	35
2	35
1	34
0	25

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.3s	5848×	body	80	valid
898.0ms	1055×	body	2560	valid
810.0ms	960×	body	1280	valid
444.0ms	2886×	body	80	nan
292.0ms	461×	body	640	valid
89.0ms	107×	body	5120	valid
70.0ms	197×	body	320	valid
27.0ms	110×	body	160	valid