Details

sample91.0ms

Algorithm

intervals

Results

42.0ms	71×	body	1280	valid
20.0ms	56×	body	640	valid
8.0ms	20×	body	2560	valid
5.0ms	23×	body	320	valid
4.0ms	64×	body	80	valid
3.0ms	22×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	5
1	10	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.6b

localize7.0ms

Local error

Found 3 expressions with local error:

0.7b	(+ x (sqrt (+ (* x x) 1.0)))
4.7b	(log (+ x (sqrt (+ (* x x) 1.0))))
12.8b	(sqrt (+ (* x x) 1.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `log-prod`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow` `hypot-def`

Counts

3 → 52

Calls

3 calls:

8.0ms	(+ x (sqrt (+ (* x x) 1.0)))
8.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms	(sqrt (+ (* x x) 1.0))

series285.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(+ x (sqrt (+ (* x x) 1.0)))
179.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
44.0ms	(sqrt (+ (* x x) 1.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	331	422
1	1127	385
2	5002	366

prune185.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
0.1b	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
220×	`associate-r`
184×	`add-sqr-sqrt`
140×	`unpow-prod-down` `cube-prod`
126×	`*-un-lft-identity`
120×	`add-cube-cbrt`
80×	`sqrt-prod`
40×	`sqr-pow`
30×	`cube-mult` `unpow3`
25×	`add-exp-log` `unswap-sqr`
10×	`prod-exp`
9×	`div-exp`
7×	`add-cbrt-cube`
6×	`pow1` `pow-to-exp` `pow-exp` `add-log-exp`
5×	`fma-neg` `prod-diff`
4×	`distribute-lft-out`
3×	`associate-r/` `associate-l*`
2×	`expm1-log1p-u` `diff-log` `log-pow` `frac-sub` `cbrt-unprod` `log1p-expm1-u`
1×	`cbrt-undiv` `sub-neg` `flip3--` `flip3-+` `pow-prod-down` `associate--l+` `sum-log` `*-commutative` `flip--` `flip-+` `div-inv`

Counts

2 → 300

Calls

2 calls:

132.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
69.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series298.0ms

Counts

2 → 6

Calls

2 calls:

156.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
142.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify125.0ms

Algorithm

egg-herbie

Counts

306 → 306

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	888	2291
1	4768	1819
2	5001	1795

prune516.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))
0.1b	(* (- 1/36) (pow (/ x (sqrt 1.0)) 6))
13.8b	(+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
36.0b	(/ (+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))) (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
26×	`associate-r`
25×	`unpow-prod-down`
14×	`add-exp-log`
10×	`associate-l` `sqrt-prod`
8×	`add-cbrt-cube`
6×	`add-log-exp`
5×	`unswap-sqr`
4×	`pow1` `expm1-log1p-u` `prod-exp` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-/r` `associate-/l`
2×	`associate-+r+` `flip3-+` `div-exp` `pow-exp` `flip-+` `div-inv` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `distribute-lft-neg-out` `distribute-rgt-in` `pow-to-exp` `neg-mul-1` `fma-def` `frac-2neg` `distribute-lft-in` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 114

Calls

4 calls:

0.0ms	(fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))
26.0ms	(* (- 1/36) (pow (/ x (sqrt 1.0)) 6))
14.0ms	(+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
41.0ms	(/ (+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))) (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

140.0ms	(fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))
171.0ms	(* (- 1/36) (pow (/ x (sqrt 1.0)) 6))
328.0ms	(+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
483.0ms	(/ (+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))) (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))

simplify82.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	576	2289
1	2501	2078
2	5001	2052

prune448.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

18.8b	(cbrt (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
18.8b	(cbrt (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
18.8b	(cbrt (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
36.0b	(/ (+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))) (* (* (cbrt (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))) (cbrt (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))) (cbrt (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log`
9×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `pow1/3` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`associate-/l/`
1×	`frac-2neg` `flip3-+` `clear-num` `associate-/r*` `flip-+` `div-inv`

Counts

4 → 66

Calls

4 calls:

0.0ms	(cbrt (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
0.0ms	(cbrt (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
0.0ms	(cbrt (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
55.0ms	(/ (+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))) (* (* (cbrt (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))) (cbrt (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))) (cbrt (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))))

series1.9s

Counts

4 → 12

Calls

4 calls:

478.0ms	(cbrt (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
449.0ms	(cbrt (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
484.0ms	(cbrt (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
490.0ms	(/ (+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))) (* (* (cbrt (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))) (cbrt (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))) (cbrt (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))))

simplify61.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	425	2741
1	1910	2321
2	5002	2098

prune347.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes45.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.6b

bsearch102.0ms

Steps

Iters	Range		Point
9	0.00035723662727133143	33.11368705657117	0.001008797149416407
10	-29.541817090935037	-6.322351620237733e-11	-1.0202654642914022

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	26
1	45	26

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.3s	2347×	body	1280	valid
558.0ms	1579×	body	640	valid
324.0ms	781×	body	2560	valid
187.0ms	793×	body	320	valid
151.0ms	2075×	body	80	valid
63.0ms	425×	body	160	valid