Details

sample32.0ms

Algorithm

intervals

Results

11.0ms	68×	body	1280	valid
7.0ms	60×	body	640	valid
3.0ms	161×	body	80	valid
2.0ms	31×	body	320	valid
1.0ms	19×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	3
1	13	3
2	15	3
3	15	3

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 42.9b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

5.7b	(- (exp x) 1.0)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 14

Calls

1 calls:

4.0ms

(- (exp x) 1.0)

series15.0ms

Counts

1 → 3

Calls

1 calls:

15.0ms

(- (exp x) 1.0)

simplify63.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	78	72
1	175	67
2	471	66
3	1353	66
4	5002	66

prune36.0ms

Filtered

17 candidates to 12 candidates (29.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	13	4	17
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	14	4	18

Merged error: 0.1b

Counts

18 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

19.0ms	(+ (* (pow x 2) (+ (* x 1/6) 1/2)) x)
16.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
3.0ms	(* x 1/6)
23.0ms	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)

series162.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* (pow x 2) (+ (* x 1/6) 1/2)) x)
68.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
17.0ms	(* x 1/6)
47.0ms	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)

simplify77.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	388	781
1	2002	720
2	5001	720

prune176.0ms

Filtered

120 candidates to 75 candidates (37.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	120	4	124

Merged error: 0.1b

Counts

124 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

5.7b	(log (exp (- (exp x) 1.0)))
5.7b	(- (exp x) 1.0)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 35

Calls

2 calls:

5.0ms	(log (exp (- (exp x) 1.0)))
4.0ms	(- (exp x) 1.0)

series32.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(log (exp (- (exp x) 1.0)))
16.0ms	(- (exp x) 1.0)

simplify78.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	117	161
1	261	146
2	620	144
3	1809	144
4	5002	144

prune55.0ms

Filtered

41 candidates to 26 candidates (36.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	41	4	45

Merged error: 0.1b

Counts

45 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x)))
0.0b	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
0.0b	(pow (exp x) 3)
5.6b	(- (pow (exp x) 3) (pow 1.0 3))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

168×	`*-un-lft-identity`
116×	`add-sqr-sqrt`
90×	`times-frac`
63×	`difference-of-squares`
59×	`unpow-prod-down`
43×	`sqr-pow`
40×	`distribute-lft-out`
32×	`add-cube-cbrt`
31×	`pow-unpow`
28×	`difference-cubes`
20×	`associate-l`
18×	`associate-/l*`
14×	`distribute-lft-out--`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r*`
4×	`associate-+l+` `pow-pow`
3×	`+-commutative` `exp-prod`
2×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `flip3-+` `pow-exp` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `frac-2neg` `diff-log` `unpow3` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv` `rem-cube-cbrt`

Counts

4 → 197

Calls

4 calls:

15.0ms	(+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x)))
28.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
3.0ms	(pow (exp x) 3)
12.0ms	(- (pow (exp x) 3) (pow 1.0 3))

series220.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x)))
105.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
26.0ms	(pow (exp x) 3)
48.0ms	(- (pow (exp x) 3) (pow 1.0 3))

simplify111.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	670	2950
1	2513	2865
2	5002	2779

prune338.0ms

Filtered

209 candidates to 106 candidates (49.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	207	2	209
Fresh	1	0	1
Picked	1	0	1
Done	1	1	2
Total	210	3	213

Merged error: 0.0b

Counts

213 → 3

regimes24.0ms

Accuracy

98.9% (0.2b remaining)

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

bsearch42.0ms

Steps

Iters	Range		Point
10	-0.010589856477353462	-1.985499863706084e-13	-0.00010989487787053815

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	19
1	40	19

end0.0ms

sample920.0ms

Algorithm

intervals

Results

397.0ms	2239×	body	1280	valid
181.0ms	1623×	body	640	valid
107.0ms	5457×	body	80	valid
64.0ms	869×	body	320	valid
24.0ms	435×	body	160	valid