Details

sample32.0ms

Algorithm

intervals

Results

14.0ms

276×

body

valid

simplify14.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize21.0ms

Local error

Found 2 expressions with local error:

0.3b	(fma a c (* b d))
27.2b	(/ (fma a c (* b d)) (fma d d (* c c)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 39

Calls

2 calls:

0.0ms	(fma a c (* b d))
4.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))

series226.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(fma a c (* b d))
164.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))

simplify2.0s

Counts

45 → 45

Iterations

Iter	Nodes
done	5001
3	1854
2	358
1	107
0	63

prune385.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 26.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma a c (* b d))
15.3b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
31.3b	(sqrt (fma d d (* c c)))
31.3b	(sqrt (fma d d (* c c)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 83

Calls

4 calls:

0.0ms	(fma a c (* b d))
9.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
1.0ms	(sqrt (fma d d (* c c)))
1.0ms	(sqrt (fma d d (* c c)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(fma a c (* b d))
165.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
56.0ms	(sqrt (fma d d (* c c)))
69.0ms	(sqrt (fma d d (* c c)))

simplify2.0s

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
3	2336
2	480
1	143
0	88

prune699.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 25.3b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (fma d d (* c c)))) (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))))
15.3b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
31.3b	(sqrt (fma d d (* c c)))
31.3b	(sqrt (fma d d (* c c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
28×	`add-exp-log`
22×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`associate-/r*`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `fma-udef` `hypot-def`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 158

Calls

4 calls:

31.0ms	(* (/ 1 (sqrt (fma d d (* c c)))) (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))))
5.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
1.0ms	(sqrt (fma d d (* c c)))
1.0ms	(sqrt (fma d d (* c c)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(* (/ 1 (sqrt (fma d d (* c c)))) (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))))
161.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
49.0ms	(sqrt (fma d d (* c c)))
50.0ms	(sqrt (fma d d (* c c)))

simplify2.5s

Counts

170 → 170

Iterations

Iter	Nodes
done	5000
2	2985
1	462
0	168

prune936.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 25.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma a c (* b d))
15.3b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
31.3b	(sqrt (fma d d (* c c)))
31.3b	(sqrt (fma d d (* c c)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 83

Calls

4 calls:

1.0ms	(fma a c (* b d))
5.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
2.0ms	(sqrt (fma d d (* c c)))
6.0ms	(sqrt (fma d d (* c c)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(fma a c (* b d))
138.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
63.0ms	(sqrt (fma d d (* c c)))
58.0ms	(sqrt (fma d d (* c c)))

simplify1.8s

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
3	2336
2	480
1	143
0	88

prune664.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 25.3b

regimes338.0ms

Accuracy

-14.4% (3.3b remaining)

Error of 26.2b against oracle of 22.9b and baseline of 25.8b

bsearch27.0ms

Steps

Iters	Range		Point
5	1.34232255763024e+37	2.8506796103821506e+37	2.814854621501251e+37

simplify3.0ms

Iterations

Iter	Nodes
done	22
2	22
1	21
0	17

end0.0ms

sample1.1s

Algorithm

intervals

Results

814.0ms

8473×

body

valid