Details

sample35.0ms

Algorithm

intervals

Results

13.0ms	127×	pre	10240	exit
6.0ms	256×	body	80	valid
3.0ms	129×	pre	80	true

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	12	7
done	12	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.9b

localize15.0ms

Local error

Found 2 expressions with local error:

0.8b	(/ x0 (- 1.0 x1))
7.5b	(- (/ x0 (- 1.0 x1)) x0)

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

106×	`add-sqr-sqrt`
103×	`*-un-lft-identity`
76×	`times-frac`
69×	`add-cube-cbrt`
63×	`prod-diff`
21×	`fma-neg`
18×	`difference-of-squares`
17×	`distribute-lft-out--`
10×	`associate-/r/`
6×	`flip3--` `flip--`
5×	`associate-/r*` `div-inv`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num`

Counts

2 → 140

Calls

2 calls:

11.0ms	(/ x0 (- 1.0 x1))
118.0ms	(- (/ x0 (- 1.0 x1)) x0)

series106.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(/ x0 (- 1.0 x1))
51.0ms	(- (/ x0 (- 1.0 x1)) x0)

simplify3.2s

Counts

146 → 146

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	190	2805
1	4667	1870
done	5000	1869

prune480.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (cbrt x0) (- 1.0 x1))
6.3b	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 67

Calls

2 calls:

13.0ms	(/ (cbrt x0) (- 1.0 x1))
0.0ms	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

series201.0ms

Counts

2 → 6

Calls

2 calls:

93.0ms	(/ (cbrt x0) (- 1.0 x1))
108.0ms	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

simplify1.6s

Counts

73 → 73

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	151	1049
1	1261	962
done	5001	900

prune183.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.0b

localize35.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (cbrt x0) (- 1.0 x1))
0.8b	(exp (log (fma (* (cbrt x0) (cbrt x0)) (/ (cbrt x0) (- 1.0 x1)) (- x0))))
6.3b	(fma (* (cbrt x0) (cbrt x0)) (/ (cbrt x0) (- 1.0 x1)) (- x0))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`times-frac`
24×	`add-cube-cbrt`
18×	`cbrt-prod`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/l*`
5×	`add-exp-log` `associate-/r*`
4×	`pow1` `exp-prod` `add-cbrt-cube`
3×	`expm1-log1p-u` `log-prod` `exp-sum` `log1p-expm1-u` `add-log-exp`
2×	`associate-/r/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `log-pow` `flip--` `fma-udef` `div-inv` `rem-exp-log`

Counts

3 → 84

Calls

3 calls:

13.0ms	(/ (cbrt x0) (- 1.0 x1))
5.0ms	(exp (log (fma (* (cbrt x0) (cbrt x0)) (/ (cbrt x0) (- 1.0 x1)) (- x0))))
1.0ms	(fma (* (cbrt x0) (cbrt x0)) (/ (cbrt x0) (- 1.0 x1)) (- x0))

series333.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(/ (cbrt x0) (- 1.0 x1))
128.0ms	(exp (log (fma (* (cbrt x0) (cbrt x0)) (/ (cbrt x0) (- 1.0 x1)) (- x0))))
111.0ms	(fma (* (cbrt x0) (cbrt x0)) (/ (cbrt x0) (- 1.0 x1)) (- x0))

simplify1.6s

Counts

93 → 93

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	174	1418
1	1305	1281
done	5000	1183

prune222.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (cbrt x0) (- 1.0 x1))
1.5b	(pow E (log (fma (* (cbrt x0) (cbrt x0)) (/ (cbrt x0) (- 1.0 x1)) (- x0))))
6.3b	(fma (* (cbrt x0) (cbrt x0)) (/ (cbrt x0) (- 1.0 x1)) (- x0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`times-frac`
25×	`add-cube-cbrt`
18×	`cbrt-prod`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`add-exp-log` `associate-/l*`
5×	`pow1` `associate-/r*`
4×	`pow-unpow` `add-cbrt-cube`
3×	`unpow-prod-up` `expm1-log1p-u` `unpow-prod-down` `log-prod` `log1p-expm1-u` `add-log-exp`
2×	`pow-exp` `associate-/r/`
1×	`cbrt-undiv` `pow-to-exp` `e-exp-1` `flip3--` `pow-pow` `frac-2neg` `div-exp` `clear-num` `log-pow` `flip--` `fma-udef` `div-inv` `sqr-pow`

Counts

3 → 91

Calls

3 calls:

13.0ms	(/ (cbrt x0) (- 1.0 x1))
3.0ms	(pow E (log (fma (* (cbrt x0) (cbrt x0)) (/ (cbrt x0) (- 1.0 x1)) (- x0))))
0.0ms	(fma (* (cbrt x0) (cbrt x0)) (/ (cbrt x0) (- 1.0 x1)) (- x0))

series359.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(/ (cbrt x0) (- 1.0 x1))
166.0ms	(pow E (log (fma (* (cbrt x0) (cbrt x0)) (/ (cbrt x0) (- 1.0 x1)) (- x0))))
99.0ms	(fma (* (cbrt x0) (cbrt x0)) (/ (cbrt x0) (- 1.0 x1)) (- x0))

simplify3.8s

Counts

100 → 100

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	197	1677
1	1894	1546
done	5000	1453

prune243.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.0b

regimes70.0ms

Accuracy

47.8% (1.2b remaining)

Error of 6.1b against oracle of 4.9b and baseline of 7.2b

bsearch35.0ms

Steps

Iters	Range		Point
7	0.000209	0.0186	0.00021208908081054686

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	75
1	29	75
2	31	75
done	31	75

end0.0ms

sample966.0ms

Algorithm

intervals

Results

433.0ms	3989×	pre	10240	exit
216.0ms	8000×	body	80	valid
103.0ms	4011×	pre	80	true