Details

sample320.0ms

Algorithm

intervals

Results

26.0ms	371×	body	80	nan
19.0ms	224×	body	80	valid
14.0ms	202×	body	80	overflowed
6.0ms	36×	body	160	valid

simplify69.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.1b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
6.8b	(- (exp (* 2.0 x)) 1.0)
7.0b	(- (exp x) 1.0)

rewrite53.0ms

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:

13.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
23.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
6.0ms	(- (exp x) 1.0)

series197.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
60.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
24.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp x) 1.0)

simplify121.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	387	1380
1	1054	1314
2	4287	1301
3	5003	1293

prune336.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

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)))
0.1b	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
7.0b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
7.0b	(- (exp x) 1.0)

rewrite86.0ms

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:

47.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
24.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
7.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series370.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
185.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
47.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify64.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	481	1464
1	2401	1163
2	5003	1124

prune343.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (sqrt (exp (* 2.0 x))) 3)
0.5b	(/ (* (+ (pow (sqrt (exp (* 2.0 x))) 3) (pow (sqrt 1.0) 3)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (* (- (+ (exp (* 2.0 x)) 1.0) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0)))
7.0b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
7.0b	(- (exp x) 1.0)

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
17×	`add-exp-log` `add-cbrt-cube`
15×	`*-un-lft-identity`
12×	`sqrt-prod`
11×	`flip3--` `flip--`
9×	`add-cube-cbrt` `add-log-exp`
8×	`frac-times` `associate-/r/` `associate-/l/`
6×	`pow1` `unpow-prod-down` `cube-prod`
5×	`pow-pow` `difference-of-squares`
4×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `prod-exp` `cbrt-unprod`
3×	`pow-unpow` `sqrt-pow1` `flip3-+` `flip-+` `distribute-lft-out--`
2×	`sub-neg` `diff-log`
1×	`cube-mult` `pow-to-exp` `exp-prod` `exp-to-pow` `frac-2neg` `times-frac` `pow1/2` `unpow3` `pow-exp` `clear-num` `associate-/r` `sqrt-pow2` `div-inv` `associate-/l` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 103

Calls

4 calls:

3.0ms	(pow (sqrt (exp (* 2.0 x))) 3)
67.0ms	(/ (* (+ (pow (sqrt (exp (* 2.0 x))) 3) (pow (sqrt 1.0) 3)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (* (- (+ (exp (* 2.0 x)) 1.0) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0)))
11.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series958.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(pow (sqrt (exp (* 2.0 x))) 3)
842.0ms	(/ (* (+ (pow (sqrt (exp (* 2.0 x))) 3) (pow (sqrt 1.0) 3)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (* (- (+ (exp (* 2.0 x)) 1.0) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0)))
47.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
18.0ms	(- (exp x) 1.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	982	2006
1	5001	1651

prune455.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1.0)
0.1b	(/ (+ (+ (exp (* 2.0 x)) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (+ (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1.0))) (- (exp x) 1.0))
7.0b	(- (exp x) 1.0)
7.0b	(+ (+ (exp (* 2.0 x)) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (+ (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1.0)))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

61×	`*-un-lft-identity`
48×	`add-sqr-sqrt`
30×	`times-frac`
25×	`add-log-exp`
21×	`distribute-lft-out`
17×	`add-cube-cbrt`
15×	`distribute-rgt-out`
12×	`sum-log`
11×	`flip3-+` `flip-+`
8×	`frac-add` `distribute-neg-frac` `distribute-lft-out--` `difference-of-squares`
7×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l/` `associate-/l*`
5×	`associate-/r*`
4×	`pow1` `neg-log`
3×	`div-sub`
2×	`+-commutative` `neg-sub0` `associate-+r-` `flip3--` `unsub-neg` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `associate-+l+` `associate-+r+` `distribute-neg-in` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 118

Calls

4 calls:

6.0ms	(+ (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1.0)
131.0ms	(/ (+ (+ (exp (* 2.0 x)) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (+ (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1.0))) (- (exp x) 1.0))
4.0ms	(- (exp x) 1.0)
47.0ms	(+ (+ (exp (* 2.0 x)) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (+ (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1.0)))

series163.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(+ (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1.0)
62.0ms	(/ (+ (+ (exp (* 2.0 x)) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (+ (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1.0))) (- (exp x) 1.0))
14.0ms	(- (exp x) 1.0)
27.0ms	(+ (+ (exp (* 2.0 x)) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (+ (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1.0)))

simplify78.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	559	2792
1	2423	2524
2	5003	2300

prune384.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes42.0ms

Accuracy

98.3% (0.1b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 3.3b

bsearch109.0ms

Steps

Iters	Range		Point
8	1.74439964077893e-09	1.5703764843175337e-06	3.155072360085553e-09
9	-0.09294265133275766	-5.033370145566524e-07	-1.273190028162842e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	21
1	38	21

end0.0ms

sample2.4s

Algorithm

intervals

Results

905.0ms	12775×	body	80	nan
563.0ms	7418×	body	80	valid
451.0ms	6583×	body	80	overflowed
105.0ms	714×	body	160	valid