Details

sample96.0ms

Algorithm

intervals

Results

38.0ms	99×	body	1280	valid
19.0ms	78×	body	640	valid
15.0ms	240×	body	80	overflowed
10.0ms	47×	body	320	valid
2.0ms	19×	body	160	valid
1.0ms	13×	body	80	valid

simplify46.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 7 (45.0ms)

Iter	Nodes	Cost
0	15	9
1	24	9
2	32	9
3	44	9
4	63	9
5	179	9
6	1184	9
7	5001	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1 1 (exp (+ x x)))
0.5b	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube`
3×	`associate-/r` `associate-/l`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv` `expm1-udef`

Counts

2 → 40

Calls

2 calls:

0.0ms	(fma 1 1 (exp (+ x x)))
2.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

series88.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(fma 1 1 (exp (+ x x)))
67.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify75.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	150	395
1	512	351
2	2464	344
3	5002	343

prune117.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp (* 2 x)) 1)
0.0b	(/ 1 (+ (exp (* 2 x)) 1))
0.5b	(* (expm1 (+ x x)) (/ 1 (+ (exp (* 2 x)) 1)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
26×	`times-frac`
22×	`add-cube-cbrt`
18×	`associate-r`
16×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`distribute-lft-out`
6×	`pow1`
5×	`add-log-exp`
4×	`div-exp` `prod-exp` `associate-/r*` `associate-/r/`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `associate-l` `flip-+` `log1p-expm1-u` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

3 → 99

Calls

3 calls:

4.0ms	(+ (exp (* 2 x)) 1)
7.0ms	(/ 1 (+ (exp (* 2 x)) 1))
19.0ms	(* (expm1 (+ x x)) (/ 1 (+ (exp (* 2 x)) 1)))

series81.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(+ (exp (* 2 x)) 1)
18.0ms	(/ 1 (+ (exp (* 2 x)) 1))
54.0ms	(* (expm1 (+ x x)) (/ 1 (+ (exp (* 2 x)) 1)))

simplify43.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	320	771
1	1601	634
2	5001	594

prune198.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (expm1 (+ x x)) (+ (pow (exp (* 2 x)) 3) 1)) (+ (* (exp (* 2 x)) (exp (* 2 x))) (- (* 1 1) (* (exp (* 2 x)) 1))))
0.4b	(+ (* (exp (* 2 x)) (exp (* 2 x))) (- (* 1 1) (* (exp (* 2 x)) 1)))
0.5b	(/ (expm1 (+ x x)) (+ (pow (exp (* 2 x)) 3) 1))
5.7b	(- (* 1 1) (* (exp (* 2 x)) 1))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
25×	`times-frac`
22×	`add-cube-cbrt`
18×	`associate-l`
11×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`distribute-lft-out`
6×	`pow1`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `associate-/r*` `associate-/r/` `log1p-expm1-u`
3×	`associate-+r+` `associate-r` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `sub-neg` `diff-log` `associate-*r/` `div-exp` `prod-diff` `prod-exp` `sum-log` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `associate-+r-` `flip3--` `distribute-rgt-out--` `fma-def` `frac-2neg` `distribute-lft-in` `fma-neg` `div-sub` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `flip--` `expm1-udef`

Counts

4 → 117

Calls

4 calls:

96.0ms	(* (/ (expm1 (+ x x)) (+ (pow (exp (* 2 x)) 3) 1)) (+ (* (exp (* 2 x)) (exp (* 2 x))) (- (* 1 1) (* (exp (* 2 x)) 1))))
15.0ms	(+ (* (exp (* 2 x)) (exp (* 2 x))) (- (* 1 1) (* (exp (* 2 x)) 1)))
15.0ms	(/ (expm1 (+ x x)) (+ (pow (exp (* 2 x)) 3) 1))
5.0ms	(- (* 1 1) (* (exp (* 2 x)) 1))

series277.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(* (/ (expm1 (+ x x)) (+ (pow (exp (* 2 x)) 3) 1)) (+ (* (exp (* 2 x)) (exp (* 2 x))) (- (* 1 1) (* (exp (* 2 x)) 1))))
32.0ms	(+ (* (exp (* 2 x)) (exp (* 2 x))) (- (* 1 1) (* (exp (* 2 x)) 1)))
65.0ms	(/ (expm1 (+ x x)) (+ (pow (exp (* 2 x)) 3) 1))
17.0ms	(- (* 1 1) (* (exp (* 2 x)) 1))

simplify97.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	645	1822
1	3419	1592
2	5001	1578

prune415.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(exp (- 0 (log1p (exp (* 2 x)))))
0.5b	(log1p (exp (* 2 x)))
0.5b	(* (expm1 (+ x x)) (exp (- 0 (log1p (exp (* 2 x))))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `exp-sum`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt` `prod-diff`
14×	`associate-r`
7×	`add-log-exp`
5×	`pow1` `exp-prod` `add-cbrt-cube`
4×	`add-exp-log` `expm1-log1p-u`
3×	`exp-neg` `sub0-neg` `associate-l` `log1p-expm1-u` `rem-exp-log`
2×	`sub-neg` `log1p-udef` `exp-diff` `diff-log` `associate-*r/`
1×	`log1p-expm1` `pow-prod-down` `prod-exp` `un-div-inv` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 75

Calls

3 calls:

8.0ms	(exp (- 0 (log1p (exp (* 2 x)))))
0.0ms	(log1p (exp (* 2 x)))
31.0ms	(* (expm1 (+ x x)) (exp (- 0 (log1p (exp (* 2 x))))))

series418.0ms

Counts

3 → 9

Calls

3 calls:

120.0ms	(exp (- 0 (log1p (exp (* 2 x)))))
56.0ms	(log1p (exp (* 2 x)))
242.0ms	(* (expm1 (+ x x)) (exp (- 0 (log1p (exp (* 2 x))))))

simplify36.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	275	856
1	1011	634
2	5002	507

prune196.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

regimes21.0ms

Accuracy

0% (0.1b remaining)

Error of 0.7b against oracle of 0.6b and baseline of 0.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	18
1	31	18
2	31	18

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.3s	3320×	body	1280	valid
613.0ms	2464×	body	640	valid
478.0ms	7550×	body	80	overflowed
209.0ms	1220×	body	320	valid
71.0ms	574×	body	160	valid
33.0ms	422×	body	80	valid