Details

sample1.1s

Algorithm

intervals

Results

8.0ms	29×	body	1280	valid
8.0ms	178×	body	80	valid
6.0ms	32×	body	640	valid
3.0ms	19×	body	320	valid
3.0ms	75×	body	80	overflowed

simplify317.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	19	7
1	28	7
2	40	7
3	73	7
4	176	7
5	559	7
6	2626	7
7	5001	7

prune4.0ms

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: 20.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.7b	(- (exp (* 2.0 x)) 1.0)
0.7b	(- (exp x) 1.0)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
51×	`times-frac`
31×	`sqrt-prod`
27×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`associate-/r/`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 123

Calls

4 calls:

9.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
8.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
6.0ms	(- (exp x) 1.0)

series45.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
21.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
3.0ms	(- (exp (* 2.0 x)) 1.0)
10.0ms	(- (exp x) 1.0)

simplify125.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	387	1380
1	1054	1314
2	4265	1301
3	5001	1293

prune244.0ms

Filtered

135 candidates to 92 candidates (31.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	131	4	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	4	136

Merged error: 0b

Counts

136 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
0.0b	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
0.7b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
0.7b	(- (exp x) 1.0)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
14×	`sqrt-prod`
11×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
9×	`flip3--` `associate-r` `flip--`
8×	`frac-times` `add-cube-cbrt` `associate-/l/` `add-log-exp`
7×	`distribute-lft-out--`
6×	`pow1` `flip3-+` `flip-+`
5×	`times-frac` `associate-l` `associate-/r*`
4×	`sub-neg` `associate-r/` `associate-l/`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `diff-log` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

20.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
15.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
6.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series36.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
10.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
5.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
2.0ms	(- (exp x) 1.0)

simplify66.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	481	1464
1	2403	1163
2	5002	1124

prune290.0ms

Filtered

117 candidates to 82 candidates (29.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	117	4	121

Merged error: 0b

Counts

121 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0))
0.0b	(* (exp x) (exp x))
0.7b	(- (* (exp x) (exp x)) (* 1.0 1.0))
0.7b	(- (exp (* 2.0 x)) 1.0)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
18×	`exp-prod`
16×	`times-frac`
11×	`pow1`
8×	`add-cbrt-cube` `add-log-exp`
7×	`difference-of-squares`
6×	`add-exp-log`
5×	`distribute-lft-out`
4×	`pow-prod-down` `associate-/r` `pow-sqr` `pow-prod-up` `associate-/l`
3×	`flip3--` `swap-sqr` `associate-r` `associate-l` `flip--`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `flip3-+` `pow-plus` `div-sub` `div-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

11.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0))
8.0ms	(* (exp x) (exp x))
6.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)

series19.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0))
3.0ms	(* (exp x) (exp x))
4.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))
2.0ms	(- (exp (* 2.0 x)) 1.0)

simplify57.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	415	860
1	1790	771
2	5001	753

prune177.0ms

Filtered

114 candidates to 79 candidates (30.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	114	4	118

Merged error: 0b

Counts

118 → 4

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (+ 1.0 (* 0.5 x)))
16.6b	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sqrt-prod`
2×	`flip3-+` `sqrt-div` `associate-*r/` `flip-+` `add-log-exp`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 37

Calls

2 calls:

5.0ms	(* x (+ 1.0 (* 0.5 x)))
5.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

series13.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(* x (+ 1.0 (* 0.5 x)))
5.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

simplify37.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	279	281
1	1132	268
2	5002	256

prune55.0ms

Filtered

43 candidates to 31 candidates (27.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	43	4	47

Merged error: 0b

Counts

47 → 4

regimes42.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 20.7b

bsearch43.0ms

Steps

Iters	Range		Point
15	-5.198581744599781	1.0450147493914085e-304	-1.0650974381070239e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	20
1	30	20

end0.0ms

sample1.9s

Algorithm

intervals

Results

297.0ms	1152×	body	1280	valid
242.0ms	5400×	body	80	valid
155.0ms	862×	body	640	valid
93.0ms	2453×	body	80	overflowed
51.0ms	400×	body	320	valid
23.0ms	237×	body	160	valid

Details

sample1.1s

simplify317.0ms

prune4.0ms

localize11.0ms

rewrite33.0ms

series45.0ms

simplify125.0ms

prune244.0ms

localize13.0ms

rewrite48.0ms

series36.0ms

simplify66.0ms

prune290.0ms

localize12.0ms

rewrite32.0ms

series19.0ms

simplify57.0ms

prune177.0ms

localize6.0ms

rewrite11.0ms

series13.0ms

simplify37.0ms

prune55.0ms

regimes42.0ms

bsearch43.0ms

simplify2.0ms

end0.0ms

sample1.9s

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