Details

sample335.0ms

Algorithm

intervals

Results

29.0ms	407×	body	80	nan
21.0ms	240×	body	80	valid
15.0ms	220×	body	80	overflowed
3.0ms	19×	body	160	valid

simplify70.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize18.0ms

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))
4.0b	(- (exp (* 2.0 x)) 1.0)
4.0b	(- (exp x) 1.0)

rewrite45.0ms

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:

14.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
15.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series201.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
55.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
33.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp 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	4287	1301
3	5003	1293

prune358.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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))
4.0b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0b	(- (exp x) 1.0)

rewrite89.0ms

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:

48.0ms	(* (+ (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))
8.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series360.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
180.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
51.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
14.0ms	(- (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

prune349.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (sqrt (exp (* 2.0 x))) 3)
4.0b	(- (* (sqrt 1.0) (sqrt 1.0)) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
4.0b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0b	(- (exp x) 1.0)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
12×	`sqrt-prod`
11×	`add-log-exp`
9×	`add-cube-cbrt`
6×	`pow1` `unpow-prod-down` `cube-prod`
5×	`add-exp-log` `pow-pow` `add-cbrt-cube` `difference-of-squares`
3×	`sub-neg` `pow-unpow` `flip3--` `sqrt-pow1` `diff-log` `flip--` `distribute-lft-out--`
1×	`cube-mult` `pow-to-exp` `exp-prod` `exp-to-pow` `distribute-rgt-out--` `pow1/2` `unpow3` `pow-exp` `sqrt-pow2` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 79

Calls

4 calls:

3.0ms	(pow (sqrt (exp (* 2.0 x))) 3)
5.0ms	(- (* (sqrt 1.0) (sqrt 1.0)) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
8.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series212.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(pow (sqrt (exp (* 2.0 x))) 3)
102.0ms	(- (* (sqrt 1.0) (sqrt 1.0)) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
51.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
14.0ms	(- (exp x) 1.0)

simplify47.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	360	621
1	1438	550
2	5002	540

prune332.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

4.0b	(- (exp x) 1.0)
4.0b	(- (exp x) 1.0)
4.0b	(- (exp x) 1.0)
4.0b	(- (* (sqrt 1.0) (sqrt 1.0)) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-log-exp`
10×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--`
3×	`distribute-lft-out--` `difference-of-squares`
1×	`distribute-rgt-out--`

Counts

4 → 55

Calls

4 calls:

4.0ms	(- (exp x) 1.0)
4.0ms	(- (exp x) 1.0)
4.0ms	(- (exp x) 1.0)
5.0ms	(- (* (sqrt 1.0) (sqrt 1.0)) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)))

series149.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (exp x) 1.0)
14.0ms	(- (exp x) 1.0)
14.0ms	(- (exp x) 1.0)
107.0ms	(- (* (sqrt 1.0) (sqrt 1.0)) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)))

simplify66.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	195	408
1	665	348
2	2377	343
3	5002	343

prune337.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes27.0ms

Accuracy

80.3% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 3.4b

bsearch53.0ms

Steps

Iters	Range		Point
7	-5.023588783947765e-05	-7.23934040408857e-07	-1.1563998871691034e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	40
1	41	40

end0.0ms

sample2.4s

Algorithm

intervals

Results

908.0ms	12822×	body	80	nan
561.0ms	7450×	body	80	valid
466.0ms	6743×	body	80	overflowed
102.0ms	691×	body	160	valid