Details

sample32.0ms

Algorithm

intervals

Results

17.0ms	97×	body	1280	valid
4.0ms	130×	body	80	valid
2.0ms	15×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	3×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	26	6
2	33	6
3	35	6
4	41	6
5	44	6
6	44	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
1.1b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
8.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.0ms	(/ 1.0 (hypot 1.0 x))
4.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series817.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
262.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
103.0ms	(/ 1.0 (hypot 1.0 x))
350.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify59.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	533	1129
1	2036	878
2	5001	876

prune281.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 13.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.6b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
2.0ms	(/ 1.0 (hypot 1.0 x))
2.0ms	(/ 1.0 (hypot 1.0 x))
4.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series462.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
102.0ms	(/ 1.0 (hypot 1.0 x))
102.0ms	(/ 1.0 (hypot 1.0 x))
152.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify37.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	319	561
1	1141	522
2	5001	520

prune347.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.6b	(log (/ 1.0 (hypot 1.0 x)))
0.6b	(fma (- 0.5) (+ 1.0 (exp (log (/ 1.0 (hypot 1.0 x))))) (* 1.0 1.0))
3.0b	(exp (log (/ 1.0 (hypot 1.0 x))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
26×	`log-prod`
13×	`exp-sum`
9×	`add-exp-log`
6×	`pow1` `add-cbrt-cube`
4×	`expm1-log1p-u` `exp-prod` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `div-inv` `associate-/l`
2×	`log-div` `div-exp` `rem-log-exp` `log-pow`
1×	`cbrt-undiv` `frac-2neg` `exp-diff` `clear-num` `fma-udef` `rem-exp-log`

Counts

4 → 93

Calls

4 calls:

2.0ms	(/ 1.0 (hypot 1.0 x))
2.0ms	(log (/ 1.0 (hypot 1.0 x)))
0.0ms	(fma (- 0.5) (+ 1.0 (exp (log (/ 1.0 (hypot 1.0 x))))) (* 1.0 1.0))
3.0ms	(exp (log (/ 1.0 (hypot 1.0 x))))

series612.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ 1.0 (hypot 1.0 x))
252.0ms	(log (/ 1.0 (hypot 1.0 x)))
149.0ms	(fma (- 0.5) (+ 1.0 (exp (log (/ 1.0 (hypot 1.0 x))))) (* 1.0 1.0))
110.0ms	(exp (log (/ 1.0 (hypot 1.0 x))))

simplify43.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	438	713
1	1561	658
2	5001	639

prune400.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(log (/ (cbrt 1.0) (cbrt (hypot 1.0 x))))
0.6b	(log (/ (cbrt 1.0) (cbrt (hypot 1.0 x))))
0.6b	(fma (- 0.5) (+ 1.0 (exp (+ (* 2 (log (/ (cbrt 1.0) (cbrt (hypot 1.0 x))))) (log (/ (cbrt 1.0) (cbrt (hypot 1.0 x))))))) (* 1.0 1.0))
3.0b	(exp (+ (* 2 (log (/ (cbrt 1.0) (cbrt (hypot 1.0 x))))) (log (/ (cbrt 1.0) (cbrt (hypot 1.0 x))))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

80×	`log-prod`
72×	`cbrt-prod` `times-frac`
57×	`*-un-lft-identity`
55×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`add-exp-log`
8×	`pow1`
6×	`exp-prod` `add-log-exp`
4×	`expm1-log1p-u` `distribute-rgt-out` `rem-log-exp` `log-pow` `add-cbrt-cube` `log1p-expm1-u`
3×	`log-div`
2×	`exp-to-pow` `div-exp` `div-inv` `rem-exp-log`
1×	`associate-+r-` `distribute-lft1-in` `exp-diff` `exp-sum` `sum-log` `fma-udef`

Counts

4 → 137

Calls

4 calls:

4.0ms	(log (/ (cbrt 1.0) (cbrt (hypot 1.0 x))))
4.0ms	(log (/ (cbrt 1.0) (cbrt (hypot 1.0 x))))
0.0ms	(fma (- 0.5) (+ 1.0 (exp (+ (* 2 (log (/ (cbrt 1.0) (cbrt (hypot 1.0 x))))) (log (/ (cbrt 1.0) (cbrt (hypot 1.0 x))))))) (* 1.0 1.0))
20.0ms	(exp (+ (* 2 (log (/ (cbrt 1.0) (cbrt (hypot 1.0 x))))) (log (/ (cbrt 1.0) (cbrt (hypot 1.0 x))))))

series1.7s

Counts

4 → 12

Calls

4 calls:

482.0ms	(log (/ (cbrt 1.0) (cbrt (hypot 1.0 x))))
485.0ms	(log (/ (cbrt 1.0) (cbrt (hypot 1.0 x))))
177.0ms	(fma (- 0.5) (+ 1.0 (exp (+ (* 2 (log (/ (cbrt 1.0) (cbrt (hypot 1.0 x))))) (log (/ (cbrt 1.0) (cbrt (hypot 1.0 x))))))) (* 1.0 1.0))
561.0ms	(exp (+ (* 2 (log (/ (cbrt 1.0) (cbrt (hypot 1.0 x))))) (log (/ (cbrt 1.0) (cbrt (hypot 1.0 x))))))

simplify63.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	516	1848
1	1630	1718
2	5002	1676

prune835.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

regimes245.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 15.3b

bsearch149.0ms

Steps

Iters	Range		Point
7	0.0001516457190089863	0.003342748024832997	0.0004640566086554118
9	-118.89002763209811	-0.00028315217264546786	-0.0014084429389572513

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	62
1	64	62

end0.0ms

sample862.0ms

Algorithm

intervals

Results

500.0ms	2859×	body	1280	valid
123.0ms	4020×	body	80	valid
87.0ms	647×	body	640	valid
32.0ms	322×	body	320	valid
9.0ms	152×	body	160	valid