Details

sample86.0ms

Algorithm

intervals

Results

35.0ms	65×	body	1280	valid
17.0ms	48×	body	640	valid
12.0ms	29×	body	2560	valid
7.0ms	30×	body	320	valid
5.0ms	71×	body	80	valid
2.0ms	13×	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: 52.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.6b	(+ x (sqrt (+ (* x x) 1.0)))
3.0b	(log (+ x (sqrt (+ (* x x) 1.0))))
15.4b	(sqrt (+ (* x x) 1.0))

rewrite23.0ms

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:

9.0ms	(+ x (sqrt (+ (* x x) 1.0)))
8.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
5.0ms	(sqrt (+ (* x x) 1.0))

series274.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(+ x (sqrt (+ (* x x) 1.0)))
176.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
42.0ms	(sqrt (+ (* x x) 1.0))

simplify35.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (29.0ms)

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

prune170.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize11.0ms

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)))

rewrite223.0ms

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)))

series271.0ms

Counts

2 → 6

Calls

2 calls:

146.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
125.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify126.0ms

Algorithm

egg-herbie

Counts

306 → 306

Iterations

Useful iterations: 2 (98.0ms)

Iter	Nodes	Cost
0	888	2345
1	4813	1909
2	5001	1888

prune433.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot x (sqrt 1.0))
0.6b	(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
3.0b	(log (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

0.0ms	(hypot x (sqrt 1.0))
2.0ms	(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
2.0ms	(log (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))

series496.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(hypot x (sqrt 1.0))
127.0ms	(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
274.0ms	(log (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))

simplify106.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	288	436
1	1009	384
2	4313	367
3	5001	362

prune145.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
0.6b	(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
3.0b	(log (sqrt (+ x (* (sqrt 1) (hypot x (sqrt 1.0))))))
3.0b	(log (sqrt (+ x (* (sqrt 1) (hypot x (sqrt 1.0))))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

2.0ms	(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
2.0ms	(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
2.0ms	(log (sqrt (+ x (* (sqrt 1) (hypot x (sqrt 1.0))))))
5.0ms	(log (sqrt (+ x (* (sqrt 1) (hypot x (sqrt 1.0))))))

series830.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
132.0ms	(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
291.0ms	(log (sqrt (+ x (* (sqrt 1) (hypot x (sqrt 1.0))))))
282.0ms	(log (sqrt (+ x (* (sqrt 1) (hypot x (sqrt 1.0))))))

simplify129.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (121.0ms)

Iter	Nodes	Cost
0	301	916
1	1005	822
2	4610	794
3	5001	788

prune287.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes29.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.1b

bsearch99.0ms

Steps

Iters	Range		Point
9	2.0114125408603258e-10	0.4954286465087044	0.00101459111765151
10	-1.7081313977704333	-1.7977825652338532e-10	-1.0118201374548368

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	35
1	47	35

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	2338×	body	1280	valid
534.0ms	1552×	body	640	valid
336.0ms	843×	body	2560	valid
170.0ms	771×	body	320	valid
145.0ms	2124×	body	80	valid
54.0ms	372×	body	160	valid