Details

sample23.0ms

Algorithm

intervals

Results

13.0ms

273×

body

valid

simplify47.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	80
5	80
4	76
3	56
2	40
1	21
0	11

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize20.0ms

Local error

Found 2 expressions with local error:

0.2b	(- (* b c) (* a d))
24.9b	(/ (- (* b c) (* a d)) (fma d d (* c c)))

rewrite349.0ms

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` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`expm1-log1p-u` `pow1` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

2 → 50

Calls

2 calls:

326.0ms	(- (* b c) (* a d))
21.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

series196.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(- (* b c) (* a d))
151.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

simplify3.1s

Counts

56 → 56

Iterations

Iter	Nodes
done	5002
3	2547
2	717
1	220
0	88

prune366.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 24.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b c) (* a d))
15.0b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
29.3b	(sqrt (fma d d (* c c)))
29.3b	(sqrt (fma d d (* c c)))

rewrite37.0ms

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` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `fma-udef` `hypot-def` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

4 → 96

Calls

4 calls:

10.0ms	(- (* b c) (* a d))
22.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
2.0ms	(sqrt (fma d d (* c c)))
2.0ms	(sqrt (fma d d (* c c)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* b c) (* a d))
167.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
61.0ms	(sqrt (fma d d (* c c)))
57.0ms	(sqrt (fma d d (* c c)))

simplify1.8s

Counts

108 → 108

Iterations

Iter	Nodes
done	5000
3	2196
2	778
1	266
0	115

prune584.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.6b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (hypot d c))
0.2b	(- (* b c) (* a d))
15.0b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
29.3b	(sqrt (fma d d (* c c)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
96×	`add-sqr-sqrt`
95×	`*-un-lft-identity` `add-cube-cbrt`
51×	`sqrt-prod`
25×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `fma-udef` `hypot-def`

Counts

4 → 189

Calls

4 calls:

34.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (hypot d c))
9.0ms	(- (* b c) (* a d))
26.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
3.0ms	(sqrt (fma d d (* c c)))

series559.0ms

Counts

4 → 12

Calls

4 calls:

251.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (hypot d c))
50.0ms	(- (* b c) (* a d))
187.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
70.0ms	(sqrt (fma d d (* c c)))

simplify1.5s

Counts

201 → 201

Iterations

Iter	Nodes
done	5001
2	1660
1	619
0	257

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.6b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
0.2b	(- (* b c) (* a d))
15.0b	(/ (- (* b c) (* a d)) (hypot d c))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/l*`
10×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `div-sub` `insert-posit16` `log1p-expm1-u` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

3 → 124

Calls

3 calls:

29.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
18.0ms	(- (* b c) (* a d))
22.0ms	(/ (- (* b c) (* a d)) (hypot d c))

series402.0ms

Counts

3 → 9

Calls

3 calls:

196.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
58.0ms	(- (* b c) (* a d))
148.0ms	(/ (- (* b c) (* a d)) (hypot d c))

simplify1.6s

Counts

133 → 133

Iterations

Iter	Nodes
done	5000
2	1468
1	461
0	188

prune677.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.6b

regimes311.0ms

Accuracy

35.9% (7.6b remaining)

Error of 12.3b against oracle of 4.7b and baseline of 16.5b

bsearch87.0ms

Steps

Iters	Range		Point
6	2.8364102844858466e+132	3.3182823546818055e+133	7.209078410675665e+132
9	-5.99730792027498e+155	-1.8300824072553637e+149	-4.78970221325173e+151

simplify4.0ms

Iterations

Iter	Nodes
done	24
1	24
0	21

end0.0ms

sample926.0ms

Algorithm

intervals

Results

693.0ms

8506×

body

valid