Details

sample95.0ms

Algorithm

intervals

Results

48.0ms

287×

body

valid

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5005
5	3129
4	1167
3	380
2	130
1	62
0	30

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
0.0b	(fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a)
0.1b	(fma y (/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)) x)
25.3b	(/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `fma-udef` `associate-/l`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 59

Calls

4 calls:

0.0ms	(fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
0.0ms	(fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a)
0.0ms	(fma y (/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)) x)
4.0ms	(/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))

series1.5s

Counts

4 → 12

Calls

4 calls:

56.0ms	(fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
87.0ms	(fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a)
1.0s	(fma y (/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)) x)
381.0ms	(/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))

simplify2.4s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
3	1972
2	660
1	262
0	138

prune906.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.6b

localize75.0ms

Local error

Found 4 expressions with local error:

4.9b	(sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
4.9b	(sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
19.0b	(/ (/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))) (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))
21.7b	(/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

276×	`times-frac`
160×	`add-sqr-sqrt`
158×	`*-un-lft-identity` `add-cube-cbrt`
150×	`sqrt-prod`
25×	`associate-/l*`
12×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`associate-/l/`

Counts

4 → 248

Calls

4 calls:

2.0ms	(sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
2.0ms	(sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
20.0ms	(/ (/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))) (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))
5.0ms	(/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))

series1.2s

Counts

4 → 12

Calls

4 calls:

155.0ms	(sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
197.0ms	(sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
345.0ms	(/ (/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))) (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))
517.0ms	(/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))

simplify2.1s

Counts

260 → 260

Iterations

Iter	Nodes
done	5000
2	1677
1	690
0	314

prune2.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.6b

localize100.0ms

Local error

Found 4 expressions with local error:

4.9b	(sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
17.8b	(sqrt (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))
17.8b	(sqrt (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))
19.0b	(/ (* (/ 1 (sqrt (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))) (/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (sqrt (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))))) (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-exp-log`
29×	`sqrt-prod`
22×	`add-cbrt-cube`
18×	`add-sqr-sqrt`
17×	`div-exp`
13×	`*-un-lft-identity` `add-cube-cbrt`
9×	`pow1` `cbrt-undiv` `sqrt-pow1`
8×	`prod-exp`
6×	`associate-/r*` `times-frac`
5×	`rem-sqrt-square` `pow1/2`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l/`
2×	`rec-exp` `1-exp`
1×	`frac-times` `clear-num` `frac-2neg` `associate-l/` `associate-r/` `div-inv` `associate-/l*`

Counts

4 → 99

Calls

4 calls:

1.0ms	(sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
2.0ms	(sqrt (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))
2.0ms	(sqrt (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))
37.0ms	(/ (* (/ 1 (sqrt (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))) (/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (sqrt (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))))) (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))

series769.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
163.0ms	(sqrt (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))
148.0ms	(sqrt (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))
335.0ms	(/ (* (/ 1 (sqrt (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))) (/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (sqrt (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))))) (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))

simplify2.2s

Counts

111 → 111

Iterations

Iter	Nodes
done	5000
2	1583
1	508
0	199

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.6b

localize173.0ms

Local error

Found 4 expressions with local error:

13.2b	(cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
17.8b	(sqrt (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))
17.8b	(sqrt (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))
18.6b	(/ (* (/ 1 (sqrt (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))) (/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (sqrt (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))))) (sqrt (* (cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)) (cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-exp-log`
22×	`add-cbrt-cube` `sqrt-prod`
17×	`div-exp`
15×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cube-cbrt`
9×	`cbrt-undiv`
8×	`pow1` `sqrt-pow1` `prod-exp`
4×	`expm1-log1p-u` `rem-sqrt-square` `associate-/r*` `times-frac` `pow1/2` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `associate-/l/`
2×	`rec-exp` `1-exp`
1×	`frac-times` `clear-num` `frac-2neg` `pow1/3` `associate-l/` `associate-r/` `div-inv` `associate-/l*`

Counts

4 → 93

Calls

4 calls:

1.0ms	(cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
2.0ms	(sqrt (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))
2.0ms	(sqrt (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))
27.0ms	(/ (* (/ 1 (sqrt (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))) (/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (sqrt (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))))) (sqrt (* (cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)) (cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))))

series1.9s

Counts

4 → 12

Calls

4 calls:

169.0ms	(cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))
180.0ms	(sqrt (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))
178.0ms	(sqrt (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))
1.4s	(/ (* (/ 1 (sqrt (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))) (/ (fma (fma z (fma (fma 3.13060547623 z 11.1667541262) z t) a) z b) (sqrt (sqrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771))))) (sqrt (* (cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)) (cbrt (fma z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721) 0.607771387771)))))

simplify2.1s

Counts

105 → 105

Iterations

Iter	Nodes
done	5001
2	1894
1	570
0	228

prune1.1s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.6b

regimes1.7s

Accuracy

95.5% (1.2b remaining)

Error of 1.7b against oracle of 0.4b and baseline of 28.0b

bsearch446.0ms

Steps

Iters	Range		Point
9	0.0009624679332913742	80.54988193836768	79.53191583974852
8	-1.3541555744178473e+45	-3.1905416021720325e+41	-9.828139804829426e+41

simplify13.0ms

Iterations

Iter	Nodes
done	46
1	46
0	38

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.8s

8844×

body

valid