Details

sample1.1s

Algorithm

intervals

Results

27.0ms	71×	body	1280	valid
10.0ms	43×	body	640	valid
5.0ms	32×	body	320	valid
5.0ms	100×	body	80	valid
3.0ms	76×	body	80	overflowed
1.0ms	12×	body	160	valid

simplify429.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune5.0ms

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: 38.6b

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))
3.5b	(- (exp x) 1.0)
3.7b	(- (exp (* 2.0 x)) 1.0)

rewrite44.0ms

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)))
19.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp x) 1.0)
6.0ms	(- (exp (* 2.0 x)) 1.0)

series32.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
8.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
2.0ms	(- (exp x) 1.0)
11.0ms	(- (exp (* 2.0 x)) 1.0)

simplify122.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	387	1380
1	1054	1314
2	4265	1301
3	5002	1293

prune271.0ms

Filtered

92 candidates to 135 candidates (-46.7%)

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: 0.0b

Counts

136 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (+ 1.0 (* 0.5 x)))
11.5b	(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))

series11.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(* 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 (32.0ms)

Iter	Nodes	Cost
0	279	280
1	1132	268
2	5002	256

prune70.0ms

Filtered

31 candidates to 43 candidates (-38.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	42	1	43
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	43	4	47

Merged error: 0.0b

Counts

47 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0)))
0.8b	(* (sqrt (sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))) (sqrt (sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))))
11.5b	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))
11.5b	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod`
54×	`add-sqr-sqrt`
38×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
20×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
2×	`associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 134

Calls

4 calls:

6.0ms	(sqrt (sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0)))
20.0ms	(* (sqrt (sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))) (sqrt (sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))))
5.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))
5.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

series25.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0)))
5.0ms	(* (sqrt (sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))) (sqrt (sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))))
5.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))
5.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

simplify63.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	427	1491
1	1763	1403
2	5002	1383

prune255.0ms

Filtered

80 candidates to 146 candidates (-82.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	146	4	150

Merged error: 0.0b

Counts

150 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (* (+ (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))) (- (exp x) 1.0))
3.5b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
3.5b	(- (exp x) 1.0)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
17×	`sqrt-prod`
10×	`times-frac`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-cube-cbrt` `associate-/l/` `add-log-exp` `difference-of-squares`
7×	`flip3--` `flip--`
6×	`distribute-lft-out--`
5×	`pow1` `associate-/r*`
4×	`frac-times` `associate-/r/`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `sub-neg` `diff-log` `associate-r/` `div-exp` `associate-l/` `div-inv`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l*`

Counts

4 → 89

Calls

4 calls:

15.0ms	(sqrt (/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0)))
18.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
6.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series57.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(sqrt (/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0)))
18.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
5.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
2.0ms	(- (exp x) 1.0)

simplify71.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	607	1410
1	2846	1184
2	5001	1166

prune288.0ms

Filtered

77 candidates to 101 candidates (-31.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	100	5	105

Merged error: 0b

Counts

105 → 5

regimes138.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 20.9b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	26
1	32	26

end0.0ms

sample2.5s

Algorithm

intervals

Results

820.0ms	2280×	body	1280	valid
370.0ms	1676×	body	640	valid
127.0ms	2872×	body	80	valid
122.0ms	843×	body	320	valid
96.0ms	2492×	body	80	overflowed
37.0ms	388×	body	160	valid

Details

sample1.1s

simplify429.0ms

prune5.0ms

localize11.0ms

rewrite44.0ms

series32.0ms

simplify122.0ms

prune271.0ms

localize7.0ms

rewrite11.0ms

series11.0ms

simplify37.0ms

prune70.0ms

localize9.0ms

rewrite42.0ms

series25.0ms

simplify63.0ms

prune255.0ms

localize15.0ms

rewrite46.0ms

series57.0ms

simplify71.0ms

prune288.0ms

regimes138.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample2.5s

Profiling