Details

sample90.0ms

Algorithm

intervals

Results

19.0ms	37×	body	2560	valid
16.0ms	192×	body	80	valid
12.0ms	30×	body	1280	valid
6.0ms	81×	body	80	nan
4.0ms	12×	body	640	valid
3.0ms	13×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify114.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	120
5	120
4	112
3	83
2	42
1	22
0	12

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* 3.0 a) (- c) (* b b))
0.2b	(/ (- (sqrt (fma (* 3.0 a) (- c) (* b b))) b) (* 3.0 a))
1.2b	(- (sqrt (fma (* 3.0 a) (- c) (* b b))) b)
22.3b	(sqrt (fma (* 3.0 a) (- c) (* b b)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`prod-diff` `sqrt-prod`
9×	`add-cbrt-cube` `add-exp-log`
6×	`times-frac` `fma-neg` `associate-/l*` `add-log-exp` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 98

Calls

4 calls:

0.0ms	(fma (* 3.0 a) (- c) (* b b))
35.0ms	(/ (- (sqrt (fma (* 3.0 a) (- c) (* b b))) b) (* 3.0 a))
18.0ms	(- (sqrt (fma (* 3.0 a) (- c) (* b b))) b)
2.0ms	(sqrt (fma (* 3.0 a) (- c) (* b b)))

series514.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(fma (* 3.0 a) (- c) (* b b))
183.0ms	(/ (- (sqrt (fma (* 3.0 a) (- c) (* b b))) b) (* 3.0 a))
128.0ms	(- (sqrt (fma (* 3.0 a) (- c) (* b b))) b)
115.0ms	(sqrt (fma (* 3.0 a) (- c) (* b b)))

simplify955.0ms

Counts

110 → 110

Iterations

Iter	Nodes
done	5001
2	1258
1	342
0	148

prune655.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ b (sqrt (fma b b (* (- 3.0) (* c a)))))
4.2b	(/ (/ (fma (* c a) (- 3.0) 0) (+ b (sqrt (fma b b (* (- 3.0) (* c a)))))) (* 3.0 a))
9.8b	(/ (fma (* c a) (- 3.0) 0) (+ b (sqrt (fma b b (* (- 3.0) (* c a))))))
22.3b	(sqrt (fma b b (* (- 3.0) (* c a))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
53×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
21×	`associate-/l*`
18×	`add-cbrt-cube` `add-exp-log`
11×	`distribute-lft-out`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `div-inv`
3×	`fma-def` `sqrt-prod`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 125

Calls

4 calls:

7.0ms	(+ b (sqrt (fma b b (* (- 3.0) (* c a)))))
25.0ms	(/ (/ (fma (* c a) (- 3.0) 0) (+ b (sqrt (fma b b (* (- 3.0) (* c a)))))) (* 3.0 a))
24.0ms	(/ (fma (* c a) (- 3.0) 0) (+ b (sqrt (fma b b (* (- 3.0) (* c a))))))
2.0ms	(sqrt (fma b b (* (- 3.0) (* c a))))

series862.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(+ b (sqrt (fma b b (* (- 3.0) (* c a)))))
282.0ms	(/ (/ (fma (* c a) (- 3.0) 0) (+ b (sqrt (fma b b (* (- 3.0) (* c a)))))) (* 3.0 a))
321.0ms	(/ (fma (* c a) (- 3.0) 0) (+ b (sqrt (fma b b (* (- 3.0) (* c a))))))
121.0ms	(sqrt (fma b b (* (- 3.0) (* c a))))

simplify1.2s

Counts

137 → 137

Iterations

Iter	Nodes
done	5002
2	2307
1	519
0	212

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ b (sqrt (fma (* a c) (- 3.0) (* b b))))
4.1b	(/ (/ (/ (- (* 3.0 (* a c))) (+ b (sqrt (fma (* a c) (- 3.0) (* b b))))) 3.0) a)
9.8b	(/ (- (* 3.0 (* a c))) (+ b (sqrt (fma (* a c) (- 3.0) (* b b)))))
22.3b	(sqrt (fma (* a c) (- 3.0) (* b b)))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

954×	`times-frac`
529×	`*-un-lft-identity`
370×	`add-sqr-sqrt`
369×	`add-cube-cbrt`
100×	`associate-/l*`
80×	`distribute-lft-out`
53×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in`
26×	`associate-/r/`
18×	`div-inv`
15×	`add-cbrt-cube` `add-exp-log`
14×	`flip3-+` `flip-+`
7×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `div-sub` `distribute-frac-neg` `log1p-expm1-u`
3×	`fma-def` `sqrt-prod`
2×	`neg-sub0` `clear-num` `frac-2neg`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 484

Calls

4 calls:

6.0ms	(+ b (sqrt (fma (* a c) (- 3.0) (* b b))))
68.0ms	(/ (/ (/ (- (* 3.0 (* a c))) (+ b (sqrt (fma (* a c) (- 3.0) (* b b))))) 3.0) a)
23.0ms	(/ (- (* 3.0 (* a c))) (+ b (sqrt (fma (* a c) (- 3.0) (* b b)))))
2.0ms	(sqrt (fma (* a c) (- 3.0) (* b b)))

series920.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(+ b (sqrt (fma (* a c) (- 3.0) (* b b))))
286.0ms	(/ (/ (/ (- (* 3.0 (* a c))) (+ b (sqrt (fma (* a c) (- 3.0) (* b b))))) 3.0) a)
333.0ms	(/ (- (* 3.0 (* a c))) (+ b (sqrt (fma (* a c) (- 3.0) (* b b)))))
142.0ms	(sqrt (fma (* a c) (- 3.0) (* b b)))

simplify1.1s

Counts

496 → 496

Iterations

Iter	Nodes
done	5001
1	2130
0	849

prune3.9s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ b (sqrt (fma (* a c) (- 3.0) (pow b 2))))
2.0b	(/ a (/ (+ b (sqrt (fma (* a c) (- 3.0) (pow b 2)))) c))
4.1b	(/ (/ (* (- 3.0) (/ a (/ (+ b (sqrt (fma (* a c) (- 3.0) (pow b 2)))) c))) 3.0) a)
22.3b	(sqrt (fma (* a c) (- 3.0) (pow b 2)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

129×	`times-frac`
97×	`*-un-lft-identity`
72×	`add-sqr-sqrt`
71×	`add-cube-cbrt`
29×	`add-cbrt-cube` `add-exp-log`
19×	`associate-/r*`
15×	`cbrt-undiv` `div-exp`
13×	`distribute-lft-out`
10×	`div-inv` `associate-/l*`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `distribute-frac-neg`
1×	`distribute-lft-neg-out` `+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `flip-+` `associate-/l/`

Counts

4 → 171

Calls

4 calls:

6.0ms	(+ b (sqrt (fma (* a c) (- 3.0) (pow b 2))))
23.0ms	(/ a (/ (+ b (sqrt (fma (* a c) (- 3.0) (pow b 2)))) c))
44.0ms	(/ (/ (* (- 3.0) (/ a (/ (+ b (sqrt (fma (* a c) (- 3.0) (pow b 2)))) c))) 3.0) a)
3.0ms	(sqrt (fma (* a c) (- 3.0) (pow b 2)))

series907.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(+ b (sqrt (fma (* a c) (- 3.0) (pow b 2))))
358.0ms	(/ a (/ (+ b (sqrt (fma (* a c) (- 3.0) (pow b 2)))) c))
308.0ms	(/ (/ (* (- 3.0) (/ a (/ (+ b (sqrt (fma (* a c) (- 3.0) (pow b 2)))) c))) 3.0) a)
128.0ms	(sqrt (fma (* a c) (- 3.0) (pow b 2)))

simplify555.0ms

Counts

183 → 183

Iterations

Iter	Nodes
done	5000
1	910
0	335

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.8b

regimes567.0ms

Accuracy

85.9% (3.2b remaining)

Error of 12.5b against oracle of 9.3b and baseline of 31.8b

bsearch371.0ms

Steps

Iters	Range		Point
9	3.768382185355077e+69	1.107955803311012e+78	8.314142307267397e+76
6	7.749510238072602e-284	9.91186464917741e-283	9.662302160771727e-283
10	-1.201051446166949e+166	-1.848574411380385e+148	-1.3539912349407793e+154

simplify49.0ms

Iterations

Iter	Nodes
done	114
4	114
3	113
2	95
1	75
0	56

end0.0ms

sample3.9s

Algorithm

intervals

Results

990.0ms	5831×	body	80	valid
855.0ms	936×	body	1280	valid
853.0ms	1070×	body	2560	valid
306.0ms	2812×	body	80	nan
135.0ms	451×	body	640	valid
55.0ms	94×	body	5120	valid
50.0ms	224×	body	320	valid
17.0ms	115×	body	160	valid