Details

sample249.0ms

Algorithm

intervals

Results

205.0ms	453×	body	80	nan
11.0ms	243×	body	80	valid
9.0ms	230×	body	80	overflowed
2.0ms	19×	body	160	valid

simplify71.0ms

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: 3.2b

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 (* 2.0 x)) 1.0)
3.6b	(- (exp x) 1.0)

rewrite34.0ms

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)))
9.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series32.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
8.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
3.0ms	(- (exp (* 2.0 x)) 1.0)
10.0ms	(- (exp x) 1.0)

simplify129.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (107.0ms)

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

prune242.0ms

Filtered

92 candidates to 135 candidates (-46.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	132	3	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	133	3	136

Merged error: 0b

Counts

136 → 3

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)))
3.6b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
3.6b	(- (exp x) 1.0)

rewrite50.0ms

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:

21.0ms	(/ (* (+ (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)

series35.0ms

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)

simplify63.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (51.0ms)

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

prune287.0ms

Filtered

83 candidates to 117 candidates (-41.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	117	3	120

Merged error: 0b

Counts

120 → 3

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x (+ 1.0 (* 0.5 x))) 2.0)
0.0b	(* x (+ 1.0 (* 0.5 x)))
26.2b	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 50

Calls

3 calls:

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

series17.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(+ (* x (+ 1.0 (* 0.5 x))) 2.0)
8.0ms	(* x (+ 1.0 (* 0.5 x)))
6.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	308	385
1	1305	364
2	5001	352

prune75.0ms

Filtered

42 candidates to 59 candidates (-40.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	59	3	62

Merged error: 0b

Counts

62 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))
0.2b	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
0.3b	(/ (pow x 2) (sqrt 2.0))
0.5b	(/ x (sqrt 2.0))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac`
108×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
81×	`add-cube-cbrt`
67×	`sqrt-prod`
52×	`associate-l`
41×	`unpow-prod-down`
21×	`add-exp-log`
15×	`unpow2` `sqr-pow`
13×	`add-cbrt-cube`
12×	`associate-/r*`
11×	`associate-/l*`
9×	`unswap-sqr`
7×	`div-exp`
6×	`pow1` `associate-r` `add-log-exp`
4×	`distribute-rgt-in` `sub-neg` `associate-+r+` `distribute-lft-in` `prod-exp`
3×	`cbrt-undiv` `div-inv`
2×	`frac-times` `pow-to-exp` `flip3--` `frac-2neg` `associate-*r/` `pow-exp` `clear-num` `flip--` `cbrt-unprod` `difference-of-squares`
1×	`+-commutative` `flip3-+` `pow-prod-down` `associate-l/` `sum-log` `-commutative` `flip-+` `distribute-lft-out--`

Counts

4 → 221

Calls

4 calls:

4.0ms	(+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))
23.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
6.0ms	(/ (pow x 2) (sqrt 2.0))
4.0ms	(/ x (sqrt 2.0))

series29.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))
7.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
6.0ms	(/ (pow x 2) (sqrt 2.0))
5.0ms	(/ x (sqrt 2.0))

simplify70.0ms

Algorithm

egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	607	1757
1	2614	1546
2	5001	1528

prune452.0ms

Filtered

143 candidates to 233 candidates (-62.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	233	0	233
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	233	3	236

Merged error: 0b

Counts

236 → 3

regimes37.0ms

Accuracy

77.6% (0.7b remaining)

Error of 0.9b against oracle of 0.2b and baseline of 3.3b

bsearch15.0ms

Steps

Iters	Range		Point
7	-9.98236031775492e-06	-1.913226438347973e-07	-9.812383449396218e-06

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	20
1	30	20

end0.0ms

sample1.6s

Algorithm

intervals

Results

505.0ms	12760×	body	80	nan
321.0ms	7423×	body	80	valid
257.0ms	6720×	body	80	overflowed
72.0ms	705×	body	160	valid

Details

sample249.0ms

simplify71.0ms

prune5.0ms

localize11.0ms

rewrite34.0ms

series32.0ms

simplify129.0ms

prune242.0ms

localize13.0ms

rewrite50.0ms

series35.0ms

simplify63.0ms

prune287.0ms

localize7.0ms

rewrite16.0ms

series17.0ms

simplify42.0ms

prune75.0ms

localize13.0ms

rewrite46.0ms

series29.0ms

simplify70.0ms

prune452.0ms

regimes37.0ms

bsearch15.0ms

simplify2.0ms

end0.0ms

sample1.6s

Profiling