Details

sample341.0ms

Algorithm

intervals

Results

44.0ms	228×	body	10240	exit
12.0ms	397×	body	80	nan
7.0ms	235×	body	80	valid
2.0ms	24×	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	41	7
3	75	7
4	182	7
5	576	7
6	2666	7
7	5001	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize21.0ms

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))
4.2b	(- (exp (* 2.0 x)) 1.0)
4.3b	(- (exp x) 1.0)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
51×	`times-frac`
41×	`add-cube-cbrt`
31×	`sqrt-prod`
24×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`add-log-exp`
6×	`add-exp-log` `fma-neg` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
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 → 155

Calls

4 calls:

13.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
16.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series203.0ms

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))
35.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp x) 1.0)

simplify60.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	480	1694
1	1523	1484
2	5001	1470

prune382.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.0b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
4.2b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.2b	(- (exp (* 2.0 x)) 1.0)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
12×	`times-frac`
9×	`prod-diff`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`distribute-lft-out`
4×	`pow1` `expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`fma-def` `fma-neg` `associate-/l*`
2×	`flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `flip--` `fma-udef` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 90

Calls

4 calls:

4.0ms	(+ (exp x) 1.0)
7.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series143.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (exp x) 1.0)
65.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
41.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
29.0ms	(- (exp (* 2.0 x)) 1.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	333	817
1	1098	690
2	5001	678

prune307.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (exp x))
0.1b	(* (cbrt (exp x)) (cbrt (exp x)))
4.2b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.2b	(- (exp (* 2.0 x)) 1.0)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`cbrt-prod`
11×	`pow1`
9×	`prod-diff`
7×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `unswap-sqr`
3×	`fma-neg`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `diff-log` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 93

Calls

4 calls:

1.0ms	(cbrt (exp x))
7.0ms	(* (cbrt (exp x)) (cbrt (exp x)))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series246.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(cbrt (exp x))
97.0ms	(* (cbrt (exp x)) (cbrt (exp x)))
40.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
29.0ms	(- (exp (* 2.0 x)) 1.0)

simplify165.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 3 (158.0ms)

Iter	Nodes	Cost
0	289	659
1	923	542
2	4806	504
3	5001	489

prune352.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
27.8b	(sqrt (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
2×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

2 → 25

Calls

2 calls:

0.0ms	(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
1.0ms	(sqrt (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

series102.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
80.0ms	(sqrt (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

simplify67.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	139	185
1	458	173
2	2447	165
3	5001	162

prune74.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes27.0ms

Accuracy

71.6% (0.8b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 2.7b

bsearch39.0ms

Steps

Iters	Range		Point
8	-2.0375349863986032e-05	-6.670553018524384e-09	-9.387622745415482e-06

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	16
1	26	16

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	6819×	body	10240	exit
374.0ms	12561×	body	80	nan
247.0ms	7396×	body	80	valid
59.0ms	727×	body	160	valid