Details

sample362.0ms

Algorithm

intervals

Results

60.0ms	217×	body	10240	exit
25.0ms	401×	body	80	nan
15.0ms	246×	body	80	valid
2.0ms	15×	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.5b

localize12.0ms

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))
2.8b	(- (exp (* 2.0 x)) 1.0)
2.9b	(- (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:

15.0ms	(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)

series205.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
62.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
26.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

simplify122.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (109.0ms)

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

prune329.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1))
0.0b	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
2.9b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
2.9b	(- (exp x) 1.0)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
33×	`sqrt-prod`
27×	`add-sqr-sqrt`
17×	`times-frac`
13×	`add-cube-cbrt`
10×	`add-log-exp`
8×	`distribute-lft-out`
5×	`pow1` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube`
3×	`rem-sqrt-square` `distribute-lft-out--`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`+-commutative` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `sum-log` `flip-+` `div-inv`

Counts

4 → 77

Calls

4 calls:

13.0ms	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1))
9.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
8.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series193.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1))
46.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
47.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify93.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	309	746
1	946	698
2	3752	656
3	5002	628

prune255.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3))
0.1b	(pow (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3)
2.9b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
2.9b	(- (exp x) 1.0)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
16×	`cbrt-prod`
14×	`sqrt-prod`
10×	`add-cube-cbrt` `unpow-prod-down` `cube-prod`
8×	`distribute-lft-out` `add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `difference-of-squares`
4×	`cube-div`
3×	`pow-unpow` `distribute-lft-out--`
2×	`cube-mult` `sub-neg` `cbrt-div` `flip3--` `flip3-+` `diff-log` `unpow3` `flip--` `flip-+` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 88

Calls

4 calls:

12.0ms	(cbrt (pow (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3))
12.0ms	(pow (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3)
8.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series224.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(cbrt (pow (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3))
116.0ms	(pow (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3)
48.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
18.0ms	(- (exp x) 1.0)

simplify46.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	374	825
1	1419	759
2	5001	749

prune289.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (exp (* 2.0 x)) 1.0) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
0.0b	(pow (sqrt (exp (* 2.0 x))) 3)
2.9b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
2.9b	(- (exp x) 1.0)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

24.0ms	(- (+ (exp (* 2.0 x)) 1.0) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
3.0ms	(pow (sqrt (exp (* 2.0 x))) 3)
8.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series197.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(- (+ (exp (* 2.0 x)) 1.0) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
46.0ms	(pow (sqrt (exp (* 2.0 x))) 3)
51.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify55.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	379	661
1	1487	605
2	5002	597

prune325.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes35.0ms

Accuracy

77.3% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 3.5b

bsearch66.0ms

Steps

Iters	Range		Point
9	-1.584377209801126e-13	-1.868744300701282e-18	-1.8282416705026107e-14

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	31
1	46	31

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.6s	6617×	body	10240	exit
726.0ms	12481×	body	80	nan
465.0ms	7395×	body	80	valid
83.0ms	730×	body	160	valid