Details

sample60.0ms

Algorithm

intervals

Results

25.0ms	83×	body	1280	valid
11.0ms	57×	body	640	valid
6.0ms	160×	body	80	valid
3.0ms	26×	body	320	valid
1.0ms	9×	body	160	valid

simplify3.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.1b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.0b	(- (exp x) 1.0)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

35.0ms	(/ (- (exp x) 1.0) x)
12.0ms	(- (exp x) 1.0)

series76.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (- (exp x) 1.0) x)
25.0ms	(- (exp x) 1.0)

simplify108.0ms

Counts: 58 → 58

prune193.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (pow x 2) (+ (* x 1/6) 1/2)) x)
0.1b	(* (pow x 2) (+ (* x 1/6) 1/2))
0.3b	(* x 1/6)
3.3b	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log`
11×	`associate-l`
10×	`add-cbrt-cube`
9×	`times-frac`
6×	`pow1` `associate-r` `add-log-exp`
5×	`unswap-sqr`
4×	`unpow-prod-down` `prod-exp`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `associate-r/` `-commutative` `cbrt-unprod` `associate-/l/` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `frac-2neg` `div-exp` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 91

Calls

4 calls:

26.0ms	(+ (* (pow x 2) (+ (* x 1/6) 1/2)) x)
52.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
12.0ms	(* x 1/6)
76.0ms	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)

series179.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* (pow x 2) (+ (* x 1/6) 1/2)) x)
70.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
15.0ms	(* x 1/6)
64.0ms	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)

simplify42.0ms

Counts: 103 → 103

prune219.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (- (exp x) 1.0) (/ 1 x))
3.0b	(- (exp x) 1.0)

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`associate-r`
11×	`add-exp-log` `times-frac`
10×	`add-cube-cbrt`
7×	`add-cbrt-cube`
5×	`associate-l`
4×	`pow1` `prod-exp` `add-log-exp`
3×	`flip3--` `flip--` `unswap-sqr`
2×	`frac-times` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

2 → 56

Calls

2 calls:

71.0ms	(* (- (exp x) 1.0) (/ 1 x))
11.0ms	(- (exp x) 1.0)

series87.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(* (- (exp x) 1.0) (/ 1 x))
23.0ms	(- (exp x) 1.0)

simplify88.0ms

Counts: 62 → 62

prune171.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (- (exp x) 1.0))
3.0b	(- (exp x) 1.0)
3.0b	(- (exp x) 1.0)
3.0b	(- (exp x) 1.0)

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-log-exp`
5×	`cbrt-prod` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 57

Calls

4 calls:

12.0ms	(cbrt (- (exp x) 1.0))
18.0ms	(- (exp x) 1.0)
11.0ms	(- (exp x) 1.0)
17.0ms	(- (exp x) 1.0)

series165.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(cbrt (- (exp x) 1.0))
22.0ms	(- (exp x) 1.0)
18.0ms	(- (exp x) 1.0)
24.0ms	(- (exp x) 1.0)

simplify55.0ms

Counts: 69 → 69

prune180.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes36.0ms

Accuracy

99% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.3b

bsearch57.0ms

Steps

Iters	Range		Point
9	-0.00024022063624403673	-1.822584514918214e-10	-0.00016968847179270482

simplify86.0ms

end0.0ms

sample1.7s

Algorithm

intervals

Results

650.0ms	2277×	body	1280	valid
393.0ms	1690×	body	640	valid
178.0ms	5489×	body	80	valid
133.0ms	807×	body	320	valid
38.0ms	412×	body	160	valid