Details

analyze664.0ms

Algorithm: search

sample57.0ms

Algorithm

intervals

Results

24.0ms	63×	body	1280	valid
14.0ms	55×	body	640	valid
4.0ms	102×	body	80	valid
3.0ms	23×	body	320	valid
1.0ms	13×	body	160	valid

simplify431.0ms

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: 37.8b

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)

rewrite54.0ms

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)
6.0ms	(- (exp x) 1.0)

series33.0ms

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)

simplify120.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (106.0ms)

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

prune264.0ms

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

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (+ 1.0 (* 0.5 x)))
12.2b	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

rewrite14.0ms

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))

series12.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(* x (+ 1.0 (* 0.5 x)))
6.0ms	(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

prune68.0ms

Filtered

31 candidates to 43 candidates (-38.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	42	1	43
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	44	2	46

Merged error: 0b

Counts

46 → 2

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* x (+ 1.0 (* 0.5 x)))
0.0b	(sqrt (+ (log (exp (* x (+ 1.0 (* 0.5 x))))) 2.0))
3.8b	(log (exp (* x (+ 1.0 (* 0.5 x)))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 55

Calls

3 calls:

5.0ms	(* x (+ 1.0 (* 0.5 x)))
4.0ms	(sqrt (+ (log (exp (* x (+ 1.0 (* 0.5 x))))) 2.0))
3.0ms	(log (exp (* x (+ 1.0 (* 0.5 x)))))

series17.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify40.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	307	427
1	1184	403
2	5001	389

prune106.0ms

Filtered

44 candidates to 64 candidates (-45.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	64	2	66

Merged error: 0b

Counts

66 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
0.0b	(sqrt (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))))
3.6b	(- (exp x) 1.0)
3.6b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-log-exp`
9×	`sqrt-prod`
7×	`pow1`
5×	`sqrt-div` `difference-of-squares`
4×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`flip3-+` `flip-+` `distribute-lft-out--`
2×	`frac-times` `sub-neg` `flip3--` `sqrt-pow1` `diff-log` `associate-*l/` `flip--` `distribute-lft-out`
1×	`+-commutative` `pow1/2` `associate-*r/` `pow-prod-down` `sum-log`

Counts

4 → 61

Calls

4 calls:

6.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
20.0ms	(sqrt (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))))
4.0ms	(- (exp x) 1.0)
7.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

series41.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
28.0ms	(sqrt (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))))
2.0ms	(- (exp x) 1.0)
5.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

simplify47.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	423	784
1	1662	727
2	5001	716

prune210.0ms

Filtered

53 candidates to 73 candidates (-37.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	73	2	75

Merged error: 0b

Counts

75 → 2

regimes35.0ms

Accuracy

99.1% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.9b

bsearch27.0ms

Steps

Iters	Range		Point
9	-0.7070315175924097	-1.249707567782931e-06	-1.617814403009848e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	22
1	32	22

end0.0ms

analyze460.0ms

Algorithm: search

sample1.6s

Algorithm

intervals

Results

805.0ms	2225×	body	1280	valid
380.0ms	1650×	body	640	valid
134.0ms	865×	body	320	valid
125.0ms	2837×	body	80	valid
43.0ms	423×	body	160	valid
0.0ms	1×	body	80	invalid

Details

analyze664.0ms

sample57.0ms

simplify431.0ms

prune5.0ms

localize11.0ms

rewrite54.0ms

series33.0ms

simplify120.0ms

prune264.0ms

localize7.0ms

rewrite14.0ms

series12.0ms

simplify37.0ms

prune68.0ms

localize9.0ms

rewrite13.0ms

series17.0ms

simplify40.0ms

prune106.0ms

localize13.0ms

rewrite39.0ms

series41.0ms

simplify47.0ms

prune210.0ms

regimes35.0ms

bsearch27.0ms

simplify2.0ms

end0.0ms

analyze460.0ms

sample1.6s

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