Details

sample111.0ms

Algorithm

intervals

Results

51.0ms	364×	body	80	valid
38.0ms	365×	body	80	nan

simplify3.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	2899
5	1666
4	719
3	264
2	92
1	40
0	20

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.8b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.2b	(* (- x 0.5) (log x))
0.2b	(- (* (- x 0.5) (log x)) x)
6.7b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity`
23×	`add-cube-cbrt`
18×	`log-prod`
12×	`associate--l+`
11×	`associate-+l+` `add-log-exp`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac`
8×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`prod-diff`
5×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `fma-def` `associate-/l`
2×	`sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `associate-*l/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `frac-2neg` `fma-neg` `div-exp` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `associate-+l-` `cbrt-unprod` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 120

Calls

4 calls:

87.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
17.0ms	(* (- x 0.5) (log x))
20.0ms	(- (* (- x 0.5) (log x)) x)
55.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.8s

Counts

4 → 12

Calls

4 calls:

714.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
373.0ms	(* (- x 0.5) (log x))
606.0ms	(- (* (- x 0.5) (log x)) x)
106.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.4s

Counts

132 → 132

Iterations

Iter	Nodes
done	5003
2	1931
1	632
0	245

prune881.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 1.1b

localize62.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
6.7b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`cbrt-prod` `times-frac`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `pow1/3` `associate-/l`
2×	`associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `div-inv`

Counts

4 → 74

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
49.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series813.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(cbrt x)
255.0ms	(cbrt x)
199.0ms	(cbrt x)
124.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify2.6s

Counts

86 → 86

Iterations

Iter	Nodes
done	5001
3	2513
2	667
1	234
0	103

prune728.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize77.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (sqrt x)) (- x 0.5))
0.2b	(- (* (log (sqrt x)) (- x 0.5)) x)
0.3b	(+ (* (log (sqrt x)) (- x 0.5)) (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467))
6.7b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite250.0ms

Algorithm

rewrite-expression-head

Rules

57×	`prod-diff`
55×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
51×	`add-cube-cbrt`
33×	`distribute-rgt-in` `distribute-lft-in`
22×	`associate-+l+` `associate--l+`
15×	`add-log-exp`
9×	`times-frac`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
7×	`sub-neg`
6×	`associate-l` `associate-*r/`
5×	`sum-log` `associate-r`
4×	`expm1-log1p-u` `flip3-+` `flip3--` `frac-add` `flip-+` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/r` `log-pow` `associate-/l`
2×	`diff-log` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r+` `clear-num` `associate-+r-` `fma-def` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `associate-+l-` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 168

Calls

4 calls:

17.0ms	(* (log (sqrt x)) (- x 0.5))
18.0ms	(- (* (log (sqrt x)) (- x 0.5)) x)
152.0ms	(+ (* (log (sqrt x)) (- x 0.5)) (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467))
60.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series636.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* (log (sqrt x)) (- x 0.5))
187.0ms	(- (* (log (sqrt x)) (- x 0.5)) x)
207.0ms	(+ (* (log (sqrt x)) (- x 0.5)) (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467))
113.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.8s

Counts

180 → 180

Iterations

Iter	Nodes
done	5000
2	3355
1	938
0	324

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (sqrt x)) (- x 0.5))
0.2b	(- (* (log (sqrt x)) (- x 0.5)) x)
0.2b	(fma (log (sqrt x)) (- x 0.5) (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467))
6.7b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
39×	`prod-diff` `add-cube-cbrt`
22×	`distribute-rgt-in` `distribute-lft-in` `associate--l+`
9×	`times-frac`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-l` `add-log-exp`
5×	`sub-neg` `associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `log-pow` `associate-/l`
2×	`flip3--` `associate-*r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 134

Calls

4 calls:

35.0ms	(* (log (sqrt x)) (- x 0.5))
26.0ms	(- (* (log (sqrt x)) (- x 0.5)) x)
0.0ms	(fma (log (sqrt x)) (- x 0.5) (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467))
49.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series841.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(* (log (sqrt x)) (- x 0.5))
216.0ms	(- (* (log (sqrt x)) (- x 0.5)) x)
337.0ms	(fma (log (sqrt x)) (- x 0.5) (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467))
147.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.9s

Counts

146 → 146

Iterations

Iter	Nodes
done	5001
2	1966
1	683
0	270

prune961.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes998.0ms

Accuracy

96.9% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 5.7b

bsearch129.0ms

Steps

Iters	Range		Point
7	170178.13541022167	3402034.979919666	3366613.9142424935

simplify19.0ms

Iterations

Iter	Nodes
done	68
2	68
1	63
0	44

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.9s	11666×	body	80	valid
2.7s	11724×	body	80	nan