Details

sample110.0ms

Algorithm

intervals

Results

29.0ms	75×	body	10240	exit
26.0ms	62×	body	1280	valid
22.0ms	338×	body	80	valid
9.0ms	40×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	9×	body	160	valid

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (35.0ms)

Iter	Nodes	Cost
0	47	16
1	124	16
2	365	16
3	1376	16
4	5001	15

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
0.0b	(* (+ 1.0 eps) x)
0.0b	(* (- 1.0 eps) x)
3.1b	(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
13×	`add-cbrt-cube`
12×	`add-exp-log`
10×	`add-cube-cbrt`
9×	`associate-l`
8×	`pow1`
6×	`associate-r`
4×	`expm1-log1p-u` `times-frac` `associate-l/` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`prod-exp` `cbrt-unprod` `distribute-lft-out`
2×	`cbrt-undiv` `flip3-+` `div-exp` `pow-prod-down` `*-commutative` `flip-+` `associate-/l/` `unswap-sqr`
1×	`flip3--` `frac-2neg` `clear-num` `associate-/r*` `flip--` `fma-udef` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 84

Calls

4 calls:

49.0ms	(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
23.0ms	(* (+ 1.0 eps) x)
22.0ms	(* (- 1.0 eps) x)
0.0ms	(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

series305.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
29.0ms	(* (+ 1.0 eps) x)
26.0ms	(* (- 1.0 eps) x)
210.0ms	(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	462	738
1	1805	635
2	5002	628

prune336.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (pow x 2))
2.8b	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
4.5b	(/ (pow x 3) eps)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
36×	`times-frac`
31×	`add-cube-cbrt` `*-un-lft-identity`
16×	`unpow-prod-down`
13×	`add-exp-log`
12×	`cube-prod` `associate-/l*`
8×	`associate-r`
7×	`add-cbrt-cube`
6×	`sqr-pow`
4×	`cube-mult` `unpow3` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `div-exp` `associate-l` `prod-exp` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-exp` `unpow2`
1×	`cbrt-undiv` `frac-2neg` `clear-num` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv`

Counts

3 → 106

Calls

3 calls:

13.0ms	(* 0.5 (pow x 2))
0.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
13.0ms	(/ (pow x 3) eps)

series89.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(* 0.5 (pow x 2))
47.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
19.0ms	(/ (pow x 3) eps)

simplify58.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	305	506
1	1561	465
2	5001	451

prune262.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.7b	(/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))
2.8b	(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

185×	`times-frac`
83×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`add-exp-log`
14×	`cube-mult` `unpow-prod-down` `unpow3` `cube-prod` `sqr-pow`
13×	`associate-/r*`
12×	`div-exp`
10×	`div-inv`
9×	`add-cbrt-cube`
8×	`associate-/l*`
6×	`cbrt-prod`
4×	`pow1` `expm1-log1p-u` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv`
2×	`pow-to-exp` `pow1/3` `prod-exp`
1×	`frac-2neg` `clear-num` `associate-/r/` `fma-udef`

Counts

4 → 184

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
16.0ms	(/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))
0.0ms	(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))

series457.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(cbrt x)
172.0ms	(cbrt x)
47.0ms	(/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))
70.0ms	(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))

simplify150.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (133.0ms)

Iter	Nodes	Cost
0	721	1771
1	4325	1200
2	5001	1152

prune574.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
2.8b	(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (log (exp (cbrt x)))) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
10.8b	(log (exp (cbrt x)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
0.0ms	(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (log (exp (cbrt x)))) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
5.0ms	(log (exp (cbrt x)))

series605.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(cbrt x)
177.0ms	(cbrt x)
73.0ms	(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (log (exp (cbrt x)))) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
175.0ms	(log (exp (cbrt x)))

simplify66.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	139	339
1	329	286
2	1862	275
3	5001	275

prune277.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.6b

regimes128.0ms

Accuracy

95.9% (0.7b remaining)

Error of 4.3b against oracle of 3.6b and baseline of 19.4b

bsearch146.0ms

Steps

Iters	Range		Point
10	1.971837877766326e-28	2.5697900441600267e-15	3.790435428490655e-16

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	34
1	47	34

end0.0ms

sample2.9s

Algorithm

intervals

Results

796.0ms	1974×	body	10240	exit
741.0ms	1733×	body	1280	valid
531.0ms	9965×	body	80	valid
314.0ms	1287×	body	640	valid
102.0ms	634×	body	320	valid
31.0ms	303×	body	160	valid