Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	187×	body	80	valid
3.0ms	24×	body	1280	valid
3.0ms	15×	body	2560	valid
2.0ms	10×	body	5120	valid
1.0ms	10×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	2×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	8
1	24	8
2	30	8
3	35	8
4	35	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
1.0b	(- (sqrt (+ (* re re) (* im im))) re)
28.2b	(sqrt (+ (* re re) (* im im)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`add-log-exp`
6×	`*-un-lft-identity`
4×	`pow1` `add-cube-cbrt` `sqrt-prod`
3×	`add-exp-log` `add-cbrt-cube`
2×	`flip3-+` `sqrt-div` `flip-+` `difference-of-squares`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `sum-log` `flip--` `distribute-lft-out--`

Counts

3 → 41

Calls

3 calls:

8.0ms	(+ (* re re) (* im im))
41.0ms	(- (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series105.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+ (* re re) (* im im))
42.0ms	(- (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	172	305
1	661	282
2	1936	278
3	5002	276

prune139.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 16.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
5.7b	(exp (log (sqrt (+ (* re re) (* im im)))))
16.5b	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
28.2b	(sqrt (+ (* re re) (* im im)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`add-cube-cbrt` `log-prod` `exp-sum` `add-log-exp`
7×	`pow1` `sqrt-prod`
6×	`exp-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3-+` `log-pow` `flip-+` `difference-of-squares`
2×	`log-div` `sqrt-pow1` `pow1/2` `exp-diff`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `flip3--` `diff-log` `sum-log` `flip--` `rem-exp-log` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

8.0ms	(+ (* re re) (* im im))
10.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
61.0ms	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series139.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (* re re) (* im im))
35.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
43.0ms	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify65.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	223	519
1	737	467
2	2078	451
3	5001	442

prune202.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 16.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ re (sqrt (+ (* re re) (* im im))))
4.7b	(sqrt (* 2.0 (/ (pow im 2) (+ re (sqrt (+ (* re re) (* im im)))))))
21.9b	(/ (pow im 2) (+ re (sqrt (+ (* re re) (* im im)))))
28.2b	(sqrt (+ (* re re) (* im im)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
32×	`times-frac`
25×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
15×	`unpow-prod-down`
10×	`distribute-lft-out`
9×	`add-exp-log`
8×	`pow1` `associate-/l*`
6×	`add-cbrt-cube` `add-log-exp`
5×	`unpow2` `sqr-pow`
4×	`associate-/r*` `sqrt-prod`
3×	`sqrt-pow1` `flip3-+` `sqrt-div` `div-exp` `flip-+`
2×	`pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 99

Calls

4 calls:

14.0ms	(+ re (sqrt (+ (* re re) (* im im))))
21.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ re (sqrt (+ (* re re) (* im im)))))))
33.0ms	(/ (pow im 2) (+ re (sqrt (+ (* re re) (* im im)))))
10.0ms	(sqrt (+ (* re re) (* im im)))

series322.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(+ re (sqrt (+ (* re re) (* im im))))
184.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ re (sqrt (+ (* re re) (* im im)))))))
63.0ms	(/ (pow im 2) (+ re (sqrt (+ (* re re) (* im im)))))
33.0ms	(sqrt (+ (* re re) (* im im)))

simplify54.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	417	1079
1	1461	986
2	5001	978

prune288.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ im (/ (+ re (sqrt (+ (* re re) (* im im)))) im))
0.3b	(+ re (sqrt (+ (* re re) (* im im))))
4.7b	(sqrt (* 2.0 (/ im (/ (+ re (sqrt (+ (* re re) (* im im)))) im))))
28.2b	(sqrt (+ (* re re) (* im im)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

96×	`times-frac`
80×	`*-un-lft-identity`
55×	`add-sqr-sqrt`
54×	`add-cube-cbrt`
16×	`associate-/r*`
13×	`distribute-lft-out`
9×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`add-log-exp`
5×	`div-inv`
4×	`sqrt-prod`
3×	`cbrt-undiv` `sqrt-pow1` `sqrt-div` `div-exp` `associate-/l*`
2×	`flip3-+` `pow1/2` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `associate-*r/` `pow-prod-down` `clear-num` `sum-log` `associate-/r/`

Counts

4 → 121

Calls

4 calls:

36.0ms	(/ im (/ (+ re (sqrt (+ (* re re) (* im im)))) im))
15.0ms	(+ re (sqrt (+ (* re re) (* im im))))
22.0ms	(sqrt (* 2.0 (/ im (/ (+ re (sqrt (+ (* re re) (* im im)))) im))))
8.0ms	(sqrt (+ (* re re) (* im im)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ im (/ (+ re (sqrt (+ (* re re) (* im im)))) im))
45.0ms	(+ re (sqrt (+ (* re re) (* im im))))
184.0ms	(sqrt (* 2.0 (/ im (/ (+ re (sqrt (+ (* re re) (* im im)))) im))))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify75.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	575	1477
1	2626	1375
2	5001	1366

prune318.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.8b

regimes317.0ms

Accuracy

45.6% (18.4b remaining)

Error of 22.6b against oracle of 4.2b and baseline of 38.0b

bsearch188.0ms

Steps

Iters	Range		Point
8	1.1807101732312691e+142	5.3555028086657875e+144	5.301975457738901e+144
8	2.8505148529471227e-220	1.1324871769035144e-217	3.315327059634813e-219
8	-4.5513920484886933e-281	-4.293119643674365e-284	-2.3932815010602277e-282
6	-7.3832476150467864e-180	-8.505695752111334e-181	-8.861544571423392e-181
8	-3.72436965410306e+139	-1.0540944006331587e+136	-1.5057522058365376e+136

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	40
1	83	40
2	84	40
3	84	40

end0.0ms

sample711.0ms

Algorithm

intervals

Results

194.0ms	6046×	body	80	valid
123.0ms	661×	body	2560	valid
82.0ms	510×	body	1280	valid
77.0ms	300×	body	5120	valid
35.0ms	273×	body	640	valid
12.0ms	134×	body	320	valid
5.0ms	76×	body	160	valid