Details

sample108.0ms

Algorithm

intervals

Results

32.0ms	66×	body	10240	exit
26.0ms	59×	body	1280	valid
19.0ms	327×	body	80	valid
9.0ms	35×	body	640	valid
4.0ms	22×	body	320	valid
1.0ms	8×	body	160	valid

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (36.0ms)

Iter	Nodes	Cost
0	46	16
1	122	16
2	347	16
3	1295	16
4	5001	15

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 29.7b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 eps) x)
0.0b	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
0.0b	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
2.6b	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

122×	`*-un-lft-identity`
106×	`times-frac`
96×	`add-sqr-sqrt`
36×	`add-cube-cbrt`
27×	`distribute-lft-out--`
18×	`difference-of-squares`
10×	`add-cbrt-cube` `distribute-lft-out` `associate-/l*`
8×	`add-exp-log`
6×	`pow1` `associate-/r*` `add-log-exp`
5×	`associate-l`
4×	`div-inv` `associate-/l/`
3×	`flip3--` `div-sub` `associate-r` `flip--`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `associate-*l/` `clear-num`
1×	`sub-neg` `distribute-rgt-out--` `flip3-+` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `sub-div` `associate--r-` `unswap-sqr`

Counts

4 → 138

Calls

4 calls:

6.0ms	(* (- 1.0 eps) x)
10.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
12.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
144.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series290.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (- 1.0 eps) x)
40.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
45.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
176.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify72.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	684	1993
1	2176	1881
2	5002	1880

prune385.0ms

Filtered

150 candidates to 107 candidates (71.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	149	2	151

Merged error: 0.7b

Counts

151 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.33333333333333337 (pow x 3)) 1.0)
0.0b	(* 0.5 (pow x 2))
0.1b	(* 0.33333333333333337 (pow x 3))
6.6b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`associate-r`
14×	`add-exp-log`
11×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
8×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `cube-prod` `sqr-pow`
2×	`pow-to-exp` `diff-log` `pow-exp` `sum-log` `*-commutative` `cbrt-unprod` `unpow2`
1×	`+-commutative` `cube-mult` `sub-neg` `flip3--` `flip3-+` `unpow3` `associate--l+` `flip--` `flip-+`

Counts

4 → 83

Calls

4 calls:

5.0ms	(+ (* 0.33333333333333337 (pow x 3)) 1.0)
5.0ms	(* 0.5 (pow x 2))
6.0ms	(* 0.33333333333333337 (pow x 3))
7.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series178.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(+ (* 0.33333333333333337 (pow x 3)) 1.0)
24.0ms	(* 0.5 (pow x 2))
40.0ms	(* 0.33333333333333337 (pow x 3))
39.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify51.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	325	433
1	1340	396
2	5002	383

prune174.0ms

Filtered

95 candidates to 58 candidates (61.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	92	5	97

Merged error: 0.7b

Counts

97 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

6.6b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
11.1b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
11.1b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
11.1b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`pow1/3`
2×	`diff-log`
1×	`sub-neg` `associate--l+` `sum-log`

Counts

4 → 53

Calls

4 calls:

7.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
7.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
7.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
7.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

series491.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
152.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
151.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
150.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

simplify134.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	253	983
1	904	924
2	4251	839
3	5001	839

prune252.0ms

Filtered

65 candidates to 59 candidates (90.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	66	4	70

Merged error: 0.7b

Counts

70 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

11.1b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
11.1b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
11.1b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
11.1b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3--` `pow1/3` `add-cbrt-cube` `flip--` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

7.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
7.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
7.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
7.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

series602.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
152.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
152.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
150.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

simplify127.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	229	1104
1	830	1044
2	3710	940
3	5002	940

prune321.0ms

Filtered

64 candidates to 64 candidates (100.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	64	4	68

Merged error: 0.7b

Counts

68 → 4

regimes74.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.5b

bsearch122.0ms

Steps

Iters	Range		Point
8	0.011261476250181132	4.265898263168925	0.946688725138101

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	26
1	41	26

end0.0ms

sample2.9s

Algorithm

intervals

Results

790.0ms	1905×	body	10240	exit
736.0ms	1672×	body	1280	valid
573.0ms	10060×	body	80	valid
344.0ms	1288×	body	640	valid
112.0ms	648×	body	320	valid
38.0ms	338×	body	160	valid